-lS8TH CoNoRESS,} HOUSE OF REPRESENTATIVES. {DocuMENT 

. ~ SeNJion. . No. 694. 

Water-Supply and Imgation Pap+W No. 95 Series M, General Hydrographic Investigations, tOo 

DEPARTMENT OF THE INTERIOR 

UNITED STATES GEOLOGICAL SURVEY 

CHARLES I>. WALCOTT, DIRE(,'TOR 

ACC}URAC)Y 

OF 

STREAM MEASUREMENTS 

(SECOND, ENLARGED EDITION) 

BY 

EDWARD CHARLES MURPHY 

WASHINGTON 

GOVERNMENT PRINTING OI''FIC~ 

1904 

CONTENTS. 

Page. 

Letter of transmittal ______________ . ___________ . ______ ~ ____ . ____ .. __ .. _ . . . . 9 

Introduction .. __ . _____ . ______ . ____________ . _. _. __ . ________ .. _ _ _ _ _ _ _ _ _ _ _ _ _ 11 

Factors controlling accuracy of stream measuremeJ't:l ___________ . _.......... 11 

~Methods of measuring velocity _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 13 

Direct methods .. ______________________ . __________ . _ _ _ _ _ _ _ .. _______ .. 14 

Surface floats ___________________ . __________ . _____________ . __ . _ . . . . 14 

Double floats. ______________________________________________ . _ _ _ _ _ 14 

Float rods. _____________________________________________________ ._ 16 

Float fra1ne _. ____ . _______________________________________ .. ___ . . . 17 

Indirect methods. ___ . _ _ _ _ _ _ _ _ _______________ . _ _ _ _ _ _____________ . . . . 17 

Float wheel ___ .. _____ . __________________________________ . _ _ _ _ _ _ _ _ 17 . 

Pressure plate. ____ . _________ . _________________________ ... _ ...... _ 18 

Box with hole in side. _____ . ______________________ .. ________ .. ___ . 18 

Hydrometric tube ___ . __ . __ . _ .... ___ ... ___ . _______________ . _ .. _. _ _ 18 · 

Hydrometric pendulum __ . __ .. _. _______________ . __ . ___ . ___ .. ___ .__ 18 

Thermometer ..... __ .. _ . _ .. __ . __ ... ______ . __ .. ___ . __ ......... _ . . . 18 

Pitot tube ..... __ .. ______ .. _._ ... _____ ._. ______ . ______ . _______ .___ 18 

Current meter _________ . _____ . ______ . __ ... ________ ._._. __ .. __ ..... 20 

Slope formnla __ . ___ . _____ .. _. ____ . ____ . _ ... ___ . _____ . ___ . _______ . 23 

Measurement of surface fluctuations ___ .. ______ . ___ ... _ .... _ ... _ _ _ _ _ _ _ _ _ _ _ _ _ 24 

Vertical velocity curves ___ ._. _____________________ . __ . ____ . ___ . ______ . ___ . 26 

Pulsation of moving vmter _____ . ________ . __ ..... _ . _____________ . ___ .•.. _ . _ . 28 

Methods of measuring and computing Atream flow_ .. __ . ____ .. _. __ . ___ ...... 32 

Weirs _ ..... _ ..... __ ... _ .. __ ...... _ .. _ . ___________ . ____ . ___________ . . 32 

Francis's experiments and formula .. __ .. ___________________ .. ______ 32 

Fteley and Stearns's experiments an11 fonnr:.b. _________ . _______ .. _ _ 33 

Bazin's formula._ ... ___ ._ .... _. _________ . ______ . __ . ________ ... ____ 34 

Current meters _____________ . ______ ... ___ . ____ ~ __ ... _ . _ . _ .... _ .... _ . . . 34 

Point and integration methods .. ____ .. _ .. _. __________ . _____ ........ 37 

Coefficient work ______ . ___ . __ . ____ .. _. ___ . ________________ . ______ . 38 

Rating of meters and construction of ratfng tables .. _ .. ___ .. _. ___ .. _. 40 

Formulre for computing discharge _______ . _____ . ___________ ...... ___ ... 44 

Coniparisons of results with different instruments an(l methorh;. __ .... ___ .... 47 

Surface floats and Pi tot tube. _____ .. __ . _____________________ . ______ . _ _ _ 47 

Pitot tube and rectangular orifices .. _____________ . _________ . __ ... _ .. _... 47 

Double floats ~d current meter _. __ . ____ . ____ .. __ . _ ..... ___________ . _. _ 48 

Ellis's experiments __ ..... _._ ... __ ...... __________ ._. __ ._ .... _ ... _ 48 

Marr's experiments._._ .... _. __ ._ .... _. __ . ______ . ______ .... _...... 49 

Henry's e.t:periments . ______ . _. _____ .... _. __ . _________ ..... _ .. __ .. 50 

Gordon's experiments •. __ .. _ . _ .. __ . ___________________ . ___ ... _ . . . 52 

Float rods and current meter ____ . ________ . ____ .. _______ .. _______ . . . . . . 52 

New York State canal survey experiments _. _____ . _ ... ___ ..... . . . . . 52 

Float rods and weir_ • ______ .... _______ . ________ . __ . ________ .. __ .. _ . . . . 54 

Francis's experiments. _______ .. _______ .. _. __ .. _ ... __ . _. _. ___ .. . . . . 54 

Cornell University experiments. __ . __ . ____ . __ . __ ... _ ... _ .. ·- ... __ .. _ 55 

3 
- 4 CONTENTS. 

Comparisons of results with different instruments aml methotls-Cont'd. l'age. 

Current meter and weir_ ...................... _ ....... _ . _ .. ____ . _ .... ·- 58 

Fteley and Stearns's experiments ........•......•.... _ .. _._........ 58 

Experiments at Cornell University hydraulic laboratory.................... 59 

Introduction ................... _ ..............•.. __ ..... _ ... _ . __ . _ . . . 59 

Description of Cornell hydraulic laboratory ... _ .... _. _... . . . . . . . . . . . . . . 60 

Scope of experiments ........... _ ..... ____ ... _ ..... __ .. _ ...... _ .. _ . . . . 62 

Method of experimentation ... _ . _. _ ........ ~ ................ _. . . . . . . . . 63 

Reduction of experiments._ ...... _ ..... _ ...... _ .......... _. _ .. _....... 64 

Discussion of results ............•... _ .. __ ... __ .. ________ . ___ .... ____ . _ 65 

Comparisons of discharge measurements .......... _ ... _ ........... _ 65 

Velocity curves ..•...••........................ _ ........... _ . . . . . 73 

Mean yelocity by integration in verticals .. ___ ...................... 80 

Rating meters in still and in moving water. . . . . . . . . . . • . . . . . . . . . . . . . 80 

Error in using average of bottom and surface velocities for mean 

velocity .... _ .............................•.... _ .. _ ....... _ . . . . 82 

Comparison of resultH by three methods of operating meter......... 83 

, Comparison of results obtained in 1900 with those obtained in 1901. __ 85 

Effect of method of holding meter in water ...•......... _ .•.... _ . . . 85 

Surface velocity experiments with float rods and with current meters. 90 

Low velocity current meter and weir comparisons . _ ..... _ . _. _ ... _. . 93 

Current-meter and Pitot-tube comparisons . . . . . . . . . . . . . . . . . . . . . . . . . 96 

Application of results to ordinary river gaging_ .. _ . . . . . . . . . . . . . . . . . 96 

Accuracy of results ................................... __ . _ . . . . . . . . 97 

Conclusions_ .................... _ ......... _ . . . . . . . . . . . . . . . . . . . . . . 98 

Tests of low-watf'lr stream measurements ...•.•... _ ..... _~ ....•....... _._.__ 100 

Studies of accuracy of measurement of stream flow ....••......... _ ....... __ . 105 

'Vork on Chittenango Creek at Chittenango, N. Y .............. _....... 106 

Work on Skaneateles Lake outlet, New York . _. . . .. .. . .. .. .. .. . .. .. .. . 108 

Work on Truckee River at Farad, Cal .................. _ ... _ .. . . .. .. .. 111 

Work on Chenango River at Binghamton, N. Y . . • • . . . . . . . . . . . . . . . . . . . . 112 

Work on Susquehanna River at Binghamton, N. Y _ .... _ ........ _...... 122 

Work on Oswego River at Battle Island, N. Y .. _ ............ _ .... __ ... 129 

Conclusions .........••••.. _ ...... _ ... __ .... _ ... _..................... 137 

Vertical velocity measurements ......................................... _. 139 

On Southern rivers ...... _ .................................. _ • • • .. .. . . 139 

On streams in the Catskill Mountains ........................... _...... 150 

On ice-covered streams • . . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . • . • • . . • . . . . . . . . 158 
I L J1 U S T R A T I 0 N S . 

Page 

PLATE I. Price electric current meters. ___________ . ____________ ._. __ - ____ .- 20 

II. Hydraulic laboratory canal of Cornell University, showing corps 

engaged in making discharge experiments _____ . __ . __ ---- _ ---.- 56 

III. Flume, penstock, and wheel house of Cornell hydraulic laboratory canal _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 60 

IV. Cornell hydraulic laboratory canal, showing disturbed water surface 

during experiments in series B _________________________ - __ • _ _ _ 62 

V. Flume, weir, meters, etc---------------------------------------- 102 

VI. A, Truckee River flume; B, Car a1icl cable at Oswego River gaging 

station, Battle l:;;iand, New York _________________ "' __ • ____ . ___ . 112 

Fm. 1. Double float used by Ellis in Connecticut River survey in 1874....... 15 

2. Pi tot tube _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 19 

3. Moore current meter _____ . __________________ . ____________ .... _ . . . . 21 

4. Haskell current meter _____ . _ . ____ . _____ . ______ . ____ . ____ .. _ . __ . _ . . 22 

5. Fteley current meter _____________ . ____ . _________________________ . . 23 

6. Self-registering water gage used by United States Lake Survey .. ----- 25 

7. Record made by self-registering water gage used by United States 

Lake Survey _____ .. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 25 

8. Hook gage for measuring surhcc fluctuations _____ .. _ .......... - . --- 26 

9. Sharp-crested weir____________________ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 33 

10. Method of using current meter on large river ________ . _ ..... _._ .... -- 35 

11. Device for holding meter in place. ___________________ ._. __ .________ 36 

12. Harlacher's apparatus for n10ving a meter with uniform velocity -.. - 38 

)3. Details of Harlacher's apparatus £or moving a meter with uniform 

velocity_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 39 

14. Diagram illustration Harlacher's method of computing flood discharge ____________________________________________ .• ____ . _____ . 47 

15. Plan and elevation of Corm·ll University experiment canaL. ___ ... -- 61 

16. Diagram showing difference between meter discharge by orrlinary 

method and weir discharg.·, from measurements in Cornell University experiment" canal _ · ________________________________________ . 69 

17. Diagram showing difference between meter discharge by six-tenthsdepth and integmtion methods and weir discharge, from measurements in Cornell U t1iversity experiment canal._ .......... __ -- .. -- 70 

18. Diagram showing difference between meter discharge with different 

meters and weir discharge in experiments of series E in Cornell University experiment canal ___________________________________ . __ . 70 

Hl. Curves of equal velocity in experiment No. 11, series A . _______ ----- 73 

20. Curves of equal velocity in experim.ent No. 12, series B, with large 

Price meter No. 88 ________ ••• ________ • _______ • __ • __ •• _ . _ . _ ... _ _ 73 

5 
6 ILLUSTRATIONS. 

Page. 

FIG. 21. Curves of equal velocity in exl)eriment No. 14, series C ..... _ .. __ ._. 74 

22. Curves of equal velocity in experiment No. 20, series D ... __ .. __ . __ _ 74 

23. Vertical velocity curves obtained with large Price meter No. 88 and 

with small Price meter No. 351 in experiments in series A __ •. ___ _ 

24. Vertical velocity curves obtained with Fteley current meter in experiments in series A. _____________________________ . _. ___ . _. ____ ... _ 

25. Vertical velocity curves obtained with sn1all Price meter No. 351, large 

Price meter No. 88, and Fteley meter in experiments in series B .. _ 

26. V ertieal velocity curves obtained with small Price meters Nos. 36:1 

and 351 in experiments in series C __ . ________________________ .. __ 

27. Vertical velocity curves obtained with small Price meters NoH. 36:3 

an1l 351 in experiments in series C _____________ .. _________ ...... . 

2R. Vertical velocity curves obtained with Haskell meter No.3 and small 

Price meter No. 363 in experiments in series D __ . _______________ _ 

29. Curves showing relation between revolutions of meter and ratio 

between velocity of water and revolutions of meter from three 

ratings of small Price meters No. 351 at Chevy Cha13e, lH•l., May 

9, 1901.---- ------------------------------------ ------------ ----

30. Y ertieal velocity curves from simultaneous experiments of series E 

75 

75 

76 

76 

77 

77 

89 

with small Price meter No. 363 and with Haskell meter No. 3 _ _ _ _ _ DO 

31. Diagram showing results of ratings in still and moving- water, Fteley n1eter ___________________________________________ . _________ . _ _ _ D5 

32. Diagram showing results of ratings in still and moving water, small 

Priee n1eter _________ . _______________________ . _____ . _____ . _ _ _ _ _ _ 96 

33. Plan and sections of fium.e _____________________________ . _ _ _ _ _ _ _ _ _ _ 101 

34. Cross section of Chittenango Creek .. _______ . ___ . _. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 107 

35. Vertical velocity curves of Chittenango Creek. ___ . ______ .. _____ . __ . 107 

36. Plan of Willowglen weir ____ . _________________ . _____ . ____________ . 109 

37. Vertic-al velocity curves, Willowglen, N. Y ______ .. __ .. ___ . __ ... _ _ _ _ 110 

38. Curves in upper seetion, Farad flume, California _ . ___ ; _. ___ . __ . _ _ _ _ 111 

39. Curves in lower section, Farad flume, California._ . _________ . ___ .. _. 112 

40. Contour of bottom of Chenango River at Court Street Bridge, Binghainpton, N. Y ________ . ____ . _____________________________ . _ _ _ _ 113 

41. Cross section of Chenango River at upper side of Court Street 

Brirlge, Binghampton, N. Y ------------------------------------ 113 

4') Station rating curve, Chenango River, Court Street Bridge, Bing- hampton, N. Y ___________________________________________ . _ _ _ _ 115 

43. Groups of vertieal velocity curves, Chenango River, Binghampton, 

N. Y ---------------------------------------------------------- 117 

44. Groups of vertical velocity curves, Chenango River, Binghampton, 

N. Y -------------------------·--------------·------------------- 118 

45. Diagram showing results in vertical 140 feet frmn initial point, 

Court Street Bri•lge, Bing hampton, N. Y _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 120 

46. Diagram showing change in surface slope fo'r change in river stage, 

Chenango River, Binghampton, N. Y _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 121 

47. Contours of Susquehanna River bed at Exchange Street Bridge, Binghampton, N. Y _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 122 

48. Cross section of Susquehanna River, upper side, Exchange Street 

Bridge, Binghampton, N. Y __ . _______________ . ____ . _ _ _ _ _ _ _ _ _ _ _ _ 128 

49. Station rating curve, Susquehanna River, Exchange Street Bridge, 

Binghampton, N. y ____________ ·------------------------------- 124 

50. Vertical velocity curves, Susquehanna River, Exchange Street Bridge. 125 
FIG. 51. 

52. 

53. 

54. 

55. 

56. 

57. 

58. 

59. 

ILLUSTRATIONS. 

Vertical velocity curves, ~~lusquehanna River, Exchange Street Bridge. 

Diagram showing change in velocity and in ratios ~' l;~~, for changes 

in river stage .... ___ . _ .... ____ .. ___ ... _ ...........•.......•.•... 

Slope of Susquehanna Riyer frmn Exchange Street Bridge to Washington Street Bridge, Binghampton, N. Y _ .. ___ ....•. _ .... __ . _ .. 

Cross section of Oswego River at cable station. ___ .... ___ . _ ..... _ ... 

Station rating curve, Oswego River, Battle Island, N. Y ..... _. ____ _ 

V ertieal velocity curves for Oswego River at Battle Island, N. Y .. _. 

Vertical velocity curves for Oswego River at Battle Island, N. Y .... 

Vertical velocity curves ·for Oswego River at Battle Island, N. Y •.•. 

Slope of surfaee of Oswego River at Battle Island, N. Y. ------------

'1 

Page. 

126 

126 

128 

129 

130 

131 

133 

134' 

135 

LETTER OF TRANSMITTAL. 

DEPARTMENT OF THE INTERIOR, 

UNITED STATES GEOLOGICAL S"GRVEY, 

HYDROGRAPHIC BRANCH, 

lVasldn.gton, JJ. 0., lJecem.ber 5, 1903. 

SIR: I have the honor to transmit herewith a manuscript entitled 

"Accuraey of Stream J\tlea~urement,', hy Edward C. Murphy. 

This paper is a revision and enlargement of paper No. 64. It 

embodies the results of an extension of the investigations, in the 

hydraulic laboratory of Cornell University, of the flow of small and 

moderate-sized streams. 

"'.,..bile the methods o-f river measurement at present in use arc 

believed to be suffieiently aceurate for the purposes o-f ascertaining 

water resources, yet it is important to know their probable accuracy 

and particul~rly the accuracy of the instruments which are commonly 

employed. Through such know ledge and experienee gained -from time 

to time it will be possible to improvB upon the Inethods, in the intere:-.t 

of greater exaetness ol· wider diffmlion of the work. I therefore 

request that this manuseript be published in the serie.s of Water-Supply 

and Irrigation Papers. 

very respectfully' 

Hon. CHARLES D. 1VALCOTT, 

F. H. NEWELL, 

OJ~,,l:ef ljJng/neer. 

lJi'l•ect(rl' [hu'ted 8tate8 Geolog·ical Swrvey. 

9 

ACCURACY OF STREAM MEASUR.EMENTS. 

By EDwARD C. MuRPHY. 

INTRODUCTION. 

Since 1902, when the first edition of tho paper on the accuracy of 

stream measurements wa:-; published, many additional data relating to 

thi:; subject have been collActecl and ;-;tudied, both by the author and 

by variom; engineers of the United States Geolog·ical Survey. 

In order to give the public the benefit of these later data and studies, 

and also to supply thecontinued denm11d for the first edition, the supply of which had become exhausted, it was thought desirable to prepare and issue a second edition. In preparing this enlarged edition 

the material. presented in the first edition has been revised in accordance with the new data. 

FACTORS CONTROLLING ACCURACY OF STREAM MEASUREMEN'l'S. 

The accuracy of a stream measurement depends largely upon the 

accuracy with which the cross-sectional area and the velocity are 

measured. There i:-; no special difficulty in lneasut·ing the tir:-;t factor, 

but the second factor-the velocity-i:-; very diffict~lt to measure, chiefly 

for the reason that it i:-; constantly changing. It not only varies from 

the surface to the bottom and from one bank of the stream to the other, 

so that it i:-; necesl:lary to measure it at many points, but it is constantly 

changing at every point, even when the cross-Hectional area and the 

discharge (and eonsequently the mean velocity) remain constant. Several experimenters have observed the phenomenon of "pulsation of 

moving water," and a few have tried to measure it, but as yet little 

is known of the magnitude and frequeney of the pull:lations or of the 

laws governing them. .T. B. Francis says: a '"It is observed tbat there 

is a COJltinual change in all part:-; of these channels, although there · 

may be no sensible change in the volume of water flowing and consea Trans. Am. Soe. Civ. Eng., vol. 7, p.lll. 

11 
12 ACCURACY OF STREAM MEASUREl\lENTS. [No. 95. 

quently in the mean velocity." Captain Cunningham says: a ~'One of 

the most important conclusions of modern experiments is that the 

motion of water, even when tranquil to the eye, is extremely unsteady, 

so that there is no definite velocity at any point, but the veklcity varies 

everywhere, largely from instant to instant. * * * ,_,.jt is analogous to the unsteady motion of wind, which i~ exemplified by the 

swaying of wind vanes and by the fluttering of pinions." D. F. Henry 

says:b "All water in motbn has an intermittent velocity, increasing 

and decreasing according to some undiscovered law," and Henry found 

this true of streams of all sizes, from small mill races to the great St. 

Lawrence River. 

A knowledge of these phenomena is evidently of vital importance in 

making and computing :-;tream measurements. If only a few observations of velocity are made, these may all, or nearly all, he made at a 

time of maximum impulse, and thus the measured mean velocity be 

too large; or it is possible that 1nost of the observations may be made 

at a time of minimum impulse, and thus the mean velocity be too 

small. They also have an important bearing on the kind of instrument 

best suited to measure the velocity, as some-the float rod, for example-give the velocity of a single impuh;e, while others, as the current 

tneter, show the average velocity due to all the impulses during the 

observation. 

Tho motion of water in an open channel is not, however, simply a 

succession of impulses. On the contrary, it is exceedingly complex, 

very different from the uniform flow in parallel straight lines that is 

assumed in deriving the common hydraulic formulre. When closely 

observed the water of the most undisturbed streams is seen to "boil" 

and swirl and to be very unsteady, some particles moving up, others 

down, others across, but all as a rule having a general motion downstream. 

The accuracy of a discharge measurement also depends much upon 

the physica:I features of the stream at the dis_chat·ge section or point 

of measurement. When possible, this section should be on a straight 

reach and far enough from a bend t6 be out of its influence, the bed 

should be permanent and not stony, and the slope and wetted perimeter such that at high and low stages of the stream, the velocity in all 

parts of the section will he easily measureahle. The banks should be 

sufficiently high not to be overflowed at flood stage, and the section 

should be free from the influence of milldams and bridge piers. In 

addition, economy requires that the section selected he ea:-;ily accessi-

,ble from a railway station and that there be a person living near who 

will read the elevation of the water surface at stated times. Seldom 

if ever are all of these conditions even approximately satisfied. ·Scour 

a Recent Hydraulic Experiments: Proc. Inst. Civ. Eng., vol. 71, p. 7. 

bJour. Franklin lust., vol. 62, p. 323. 
MURPHY.) METHODS OF MEARURING VELOCITY. 13 

of bed in some cases and silting in other eases give much trouble; too 

great a velocity at high stages and too low a velocity at low stages to 

measure with accuracy are common difficulties; and milldams often 

give trouble, on account of storage and irregular discharge through 

their wheels; so that the hydrographer must make the most of the 

best location he can find, always having in mind the desirable and 

the undesirable qualities. 

Rapid fluctuations of the water surface or river height during 

measurement and the condition of the velocity-measuring instrument 

are other factors which affect the accuracy of a stream measurement. 

A great many discharge measurements of natural and artificial 

channels have been made with various kinds of instruments and in 

various ways. The earlier ones were made with crude instruments, 

and in some cases the surface velocity only was observed, the mean 

velocity being computed from a formula which we now know is not 

correct. Very littl~ appears to have been done in the way of determining the degree of accuracy of the measurements. Even when the 

experimenter has ws~d two or more instruments to measure velocity, 

he does not appear to have made simultaneous measurements with 

different instruments, or employed different methods with the same 

instruments, in order to test the accuracy of the results. 

_These matters are all discussed in detail in the following pages. 

METHODS OF MEASURING VELOCITY. 

The met ocls that have been used for measuring velocity may be 

divided int two general classes-the direct and indirect. The direct 

Il}.ethods in lude all ways of ascertaining the velocity of water fi·om 

bodies floa ing in it~ such as surface floats, float rods, double floats, 

etc. The indirect methods include measurements with the current 

meter, pre sure plates, the thermometer, etc., by which the velocity 

of the wat r is inferred from its impact, its pressure, or its temperature. Me surements by the clireet methods are simple, requiring only 

the measu ement of the time that it takes a body in the water to move 

over a cer i t distance, while in the indireet methods the constant of 

the instant must first be found from experiment. The latter methods 

are, however, theoretically better than the former. 

By the direct methods the mean velocity of a comparatively few 

particles of water is found for the time required for the float to move 

between the sections of observation-that is, the float is acted upon 

by the particles about ~t during the time it is passing over the measured distance. It is carried along by a single impulse of the water, 

and is not affected by the succeeding impulses, which may be greater 

or less than the impulse which moves it. Instruments of the second 

class, on the other hand-as, for instance, the n1eter-measure instan-
14 ACCURACY OF STREAM MEASUREMENTS. [NO, 95. 

tancously the yelocity of all the particles that strike it during the 

observation. If there were no pulsations of water, and if the particles 

following one another at any given point n1oved with uniforn1 velocity, 

then the direct methods might, in the absence of wind, give good 

resul.ts; but since all moving water, even the most undisturbed, has 

these pulsation:-;, velocity measurements by the indirect Inethods are 

decidedly more accurate than those by the direct methods. One Ineasurement with a current meter is worth several measurements with 

floats. 

There is another reason why indirect measurements are preferable 

to direet measurements. Since in the latter the mean velocity is found 

over a certain distance, usually from 50 to 200 feet, it is necessary to 

know the mean area over that cli~tanee, and this requires the measurement of many cross sections hetween the upper and the lower section, 

while by the indirect methods the measurement of only one area is 

required. 

DIRECT METHODS. 

SUI-t:I!'ACE FLOATS. 

Surface floats are small, light bodies, such as wood or wax, which 

:float on the surface of the water and can readily be seen from the 

shore. Measurement by this means is rapid, hut the velocities 

obtained may be greatly in error, due to the action of wind on the 

float. At best it only indicates the velocity for a short time of a 

comparatively few particles of water, and the mean velocity must be 

found from the relation between surface velocity and mean velocity, 

which is not well establi:-:;hecl. The time consumed by the :floats in 

passing over a measured distance-usually from 50 to 200 feet-is 

observed, and the dbtance divided by the obseryed time gives the 

surface velocity at that point for that time. 

This method was used by Dubunt in 177H in gaging the Canal du 

.Turd, in France, and in 1782 in gaging the Haine River, Belgium; by 

Trechsel, in 1825, to gage the Outer Aar, near Thun; by Wampfier, 

in 1867, to gage the Sinune Canal, Switzerland; by Harlacher, in 1881, 

to gage the Elbe, in Bohemia (at high water only); by Ellet, in 1858. 

in gaging the Ohio; and by others. 

DOUBLE FLOATS. 

The double float consists of a light surface :float and a subsurface 

flo11t somewhat heavier than water connected to it t>y a cord or a small 

rope. The office of the upper float is to support the lower :float and 

indicate its position. The connecting cord ean be lengthened at will 

and the lower float be placed at any desired depth. Fig. 1 shows the 

double float used by T. G. Ellis in the Connecticut River survey in 
MURPHY.) DOUBLE :FLOATS. 15 

1874. This subsurface float was a hollow annulus of tin 8! inches 

high~ 8! inches outside diameter~ and 7! inches inside diameter. Two 

bras~:~ wires were soldered aCI·oss the bottom at right angles to each 

other, to which was attached 28 ounces of lead as a sinker. Two 

other wires were soldered at right angles to each other at the center, 

to which the connecting corcl was attached. The Rur:face :float was an 

ellipsoid of tin 6 inches in diameter and1! inches thick, with a cork in 

the top holding a small flag and an eye in the bottom for the connecting cord. The connecting cord had a diameter of 0.036 inch. 

The method of measuring stream flow by double floats as used by 

Humphreys and Abbot in gaging the Mississippi River in 1851 and 

1858 is substantin.lly as :follows: a A suitable place was selected on the 

river, a base line 200 feet long was n1easured off on one bank parallel 

to the axis of the current, and a seetion at each end of this base was 

marked out at right angles to it. 

The time consumed by each float in 

passing between these sections aml 

the position of each float when it 

passed them were noted by :four 

men, two at each end of the base, 

each party having a stop watch and 

a theodolite. At a signal :from the 

engineer the fleats were placed in 

the river :from a bon.t about 100 :fe'et 

above the upper section and were 

picked up by a man in a boat some 

tlista11ce below the lower seetio11. =---___:-- ___=---

At the instant a float passed the 

upper section a signal was given, 

the watches were started, and the Fw. 1.-Double float used by Ellis in Connecticut River survey in 1874. angular position of the float was 

read with both theodolites. The instant the float passed the lower 

section a signal was again given~ the watches were stopped, and the 

angular position of the float 'vas again read with both theodolites. 

These readings gave the distance of the float :from the base line when 

it passed the sections and two independent measurements of the time 

consumed by it in passing between the sections. Soundings were taken 

at the end sections and at one or more intermediate sections, from 

which the area of the mean section was computed. 

In some cases where this method has been used the base was 300 

feet long and the time of run of the floats has heen recorded on a 

chronograph. 

This method has its advantages and "its disadvantages. In very 

deep rivers, such as the Mississippi, or in stream:-~ carrying- weeds 

nReport on the Mis.'->issippi River, by Humphreys and Abbot, p. 2'24, 
16 ACCURACY OF STREAM MEASUREMENTS. (NO. 95. 

and grass, it is almost the only available method. Humphreys and 

Abbot, in their report on the Mi::;sissippi River, say: a "Saxton's current meter was tried but found to be unsuited .to measurements in a 

river of such great depth and violence of current. Only double floats 

were found to give reliable results." 

In regard to the disadvantages, D. F. Henry, who had charge of the 

field work of the gaging of the outlets of the Great Lakes and who 

has used this and other methods for deep rivet·s, says:b "'All the 

-objections to the surface float apply with greater force to the double 

float, and additional ones peculiar to itself." It is impossible to 

determine the exact position or depth of the lower float. Its position 

is determined from that of the surface float, but it varies with the 

direction and velocity of the wind and the length of the cord connecting the floats. The depth of the float is determined from the length 

of the connecting cord, but on account of the upward "'boiling" 

motion of the water, and also the pressure of the water on a long .connecting cord, the depth may be 1nueh less than the length of the eord. 

The upper float may drag the lower one or be dragged by it. At best 

it can only give the velocity of a few particles for a short spaee of 

time. 

This method of gaging was used in Mississippi River and tributaries from 1857 to 1881. Since that time the current meter has been 

largely used. In 1869 it was used in conjunction with the current 

meter for gaging the outlets of the Great Lakes. It was also used by 

T. G. Ellis in 1874 in his survey of the Connecticut River, in conjunction with the current meter, and by Gordon in 1873 to gage the 

Irawadi River. For comparisons of aecuracy of this method with 

others, see pages 48 to 52. 

FLOAT RODS. 

Professor Cabeo c was the first to use the float rod for measuring 

velocity. This ·was in 1646. The rod is of wood or tin, from 1 to 2 

inches in diameter, weighted at the lower end so as to float vertically. 

Its lower end should nearly touch the bottom and its upper end project a few inches above the surface of the water, so as to be visible. 

The method of using float rods as followed by the writer in 1HOO in 

the New York State canal survey is as follows: Two surveyors' 100-

foot chains were stretched across the canal from 10 to 30 feet apart 

and at right angles to the axis of the canal. Fifteen feet above the 

upper chain a rope was stretched across the canal, and to this n. boat 

was attached by pulleys, s·o that a man in the boat could easily n10ve 

himself back and forth by pulling on the rope. Another rope was 

a Op. cit., p. 2'25. . 

bJour. Franklin Inst., vol. 62, p. 167. 

cSee Report of New York Barge Canal, 1901, p. 869. 
MURPHY.) FLOAT RODS. 17 

stretched across the canal from 6 to 8 feet below the lower e4ain and 

a boat operated from it in a similar way. The fioatt:~ were put in by 

the man in the upper boat, two at a time and about five feet apart, and 

were observed by him until they passed the upper chain, when he 

called to the recorder the pot!ition of each. : At:~ they passed under the 

lower chain the man in the lower boat called out their position, and 

when they reached his boat he took them out of the water and brought 

them to the shore. An observer with two stop watches noted the 

time of passage of eaeh pair of float~:; between the chains. A short 

run was used on account ·of the low velocity of the water. 

·The advantages. and disadvantages of the method may be summed 

up briefly as follO'Wt!: 

Ad-m~·:ntaqe8.--For artificial channels of moderate and uniform depth 

" and with floating grass and weeds this is probably the best method to 

use. The advantage~:; of float rods at:~ given by Captain Cunningham, 

who has used them to a large extent in his gagings of the Ganges 

Canal, are as follows: b (1) They interfere less with the natural motion 

of the water~ (2) they measure velocity direct; (:3) they can be used in 

a stream of any size; (4) they arc not affected by silt and weeds; (5) 

they measure forward velocity; (H) they can be m~de by a common 

workman; and (7) they are cheap. 

Dt'&ulvtudage8.-The rods are affected to some extent by wind; they 

do not giYe mean velocity, hut velocity of impuises; they can not be 

used in deep streams or in streams of rough or it-regular bed, and 

they are expensive to operate. 

Float rods have been used by Cunningham, on the Ganges Canal, 

in 1~80; by Francis, in '1852, on a canal at Lowell, Mas~.; by Buffon, 

on the Tiber River, in 1821; by Krayenhoff, on the R.hine, in 1812; 

and by the Mississippi River Commission, on the Upper Mississippi, 

in 1881. 

FLOAT FRAME. 

Hirn used, for obtaining veloeity, a light frame of wood which 

nearly filled the cross section of the channel, but there are practical 

difficultie:-~ in the way of the use of this instrument. 

INDIRECT METHODS. 

The following instruments and methods have beet used at one time 

or another for measuring velocity indirectly. Several of them are 

now of historical interest only. 

FLOAT WHEEL. 

The float wheel was used by Borda and Dubuat for measuring surface velocities. That used by the latter was 2 feet in diameter, and 

recorded the revolutions on dials. 

b Proc. Inst. Civil Eng., vol. 71, p. 1. 

IRR 95-04-2 
18 ACCURACY OF STREAM MEASUREMENTS. [NO. 95. 

PREHSURE PLATE. 

In 1!79 Gaunthy invented the pressure plate, which consists of a. 

disk of metal opposed to the pressure of water, the velocity being 

computed frmn the weight nece:;sary to keep it vertical. The taehometer used by Briinings to gage the Rhine and the one used by 

Racourt in his gagings of the Neva were nmde on this principle. 

Captain Boileau abo used a pressure plate in his tachometer. 

BOX WITH HOLE IN SIDE. 

A box with a hole in the side was used by G1:andi in 1730 to measure 

velocity. It was lowered gradually from the su1~face to the bottom 

and raised again at the same rate, the velocity being inferred from 

the amount of water in the box. 

HYDROMETRIC TUBE. 

This instrument was used by Captain Boileau in 1850. It eonsistS 

of a glass tube suspended in a frame, having a full-sized opening at 

one end and a small opening at the other end. The tn be is filled with 

water and a bubble of air, and is placed in the water with the small 

end upstream. The large end is then opened and the time required 

for the bubble to traverse the tube is noted. From this time and the 

areas of the ends of the tube the velocity i~:~ computed. 

HYDROMETRIC PENDULUM. 

This instrun1ent was used by Castelli in 1~28. It consists of a ball 

suspended from the center of a graduated arc. The velocity is com~ 

puted from the weight of the ball and the angle of the string when 

the water i_mpinges on it. 

THERMOMETER. 

Leslie used a thermmueter for 1ueasuring velocity. The principle 

of this method is that the temperature of water in motion is greater 

than the temperature when at rest. 

PITOT TUBE. 

This instrument was invented by Pitot in1730. Fig. 2 shows it as 

improved and used by Darcy and Bazin. a It consists essentially of 

two tubes, one drawn to a fine point and pointing upstream, the 

other straight and with an opening at the lower end the size of the tube. 

The air in both tubes is partly exhausted, so that the water columns 

a Recherches hydrauliqueR, entreprises par M. H. Darcy oontinuees par M. H. Bazin. Premiere 

partie de Recherches experimentales sur l'ecoulement de l'eau dans les canaux decouverts: Extrait 

des Memoires presentes par divers savants a l'academie des sciences de Institut Imperial de France, 

Paris, 1865, vol. 19, pl. xvii, fig. 5. · 
MURPHY.) PITOT TUBE. 

will rise to a cmnTenient height. 

The veloc.ity is found from 

the difference in the readings 

of the water columns. Like 

floats, this is · an ill'lpulsemeasuring imJtrument, but in 

using it both maximum and 

minimum impulses are observed and a mean is found. 

After the instrument is in place 

and the stopcocks Rand R' are 

opened one o£ the observers applies his mouth to the tube 0, 

removes the air until the sur~ 

face of the water in the tubes 

stands at a convenient height 

to read, and then closes the 

upper coek (R). He observes 

the cohunns until they reach 

a maximum hejght, when he 

doses the cock R' and reads 

the surface of both columns; 

then he opens the cock R and 

observes the surface of both 

until the columns reach a minimum position, when he closes 

cock R' and reads both surfaces again. He now has a 

maximum and a minimum reading of each eolumn, from which 

be makes the following deduction: If a/ is the maximum 

reading of column A, and l/ 

is the maximum reading of column B, and a/' is the minimum 

reading of column A, and b" 

is the minimum reading of 

column B, th(\n a'-b'=d', the· 

difference for the maximum 

impulse, and a" -b" = d", the 

difference for the minimum imd' X d'' 

pulse, and •J.· is the mean ..:.; 

difference of the column readings for the two impulses. ====:c:l=~u19 

FIG. _2.-Pitot tube. 
20 ACCURACY OF STREAM MEA8UREMENTS. [NO. 95. 

Two or three sets of these readings arc taken at each point. Then if 

_....,~IS "">'d. h f l l (~ l t e mean o t 1e values of these column c ifferenees ~ l = .:.1 

d' +d" + ), the velocity at that point is given hy the formula 

V=c-J 2g:Z~, c being the coefficient found l)y rating and !I the accel- .:.~ -

eration of gravity. The velocity can very quickly he found by one 

accustomed to using the instrument. The aecnraey of V depends on 

that of c and of .../ 2' d, the greater the number of d's or sets of observations, the more nearly aeeurate will he the value of T~ 

CURRI<~NT METER. 

The current meter had itti beginning in the float wheel. used by 

Borda and Duhuat to obtain surface: veloeities. In 1"7!t0 Waltman 

modified this whe~l so that it could be used below the surface. Hi;-; 

meter had helicoidal blades and an endless screw on its axis, which 

by gearing into a train of wheelti ea.used a. reeord of the number of 

revolutions of the wheel to be made on dials. It was moved up 

and down on a rod, the lower end of whieh was driven firmly into 

the river bed. The recording apparatus was thrown in or out of 

action by a pull on a string. It was necessary to lift the meter to the 

surfaee to read the revolutions, whieh was a great drawback to its use, 

as was also the faet that dirt in the water retarded the train of wheels. 

-Lepont soug·ht to remove these difficulties by bringing the recording 

apparatus to the surfaee, away from the dirty water and where it 

could he read without lifting the meter. He did this by introducing a 

vertical shaft or rod with beveled gearing, but this increased the 

friction so that it could only be used in shallow water. Baumgarten, 

Saxton, and others following modified its form somewhat, but did not 

materially improve it. Brewster made one in which the axis of the 

meter was a long screw and the revolutions were given by the distance the wheel traveled along this screw. The friction was thus 

lessened, hut the meter had to he stopped before the wheel traveled the 

whole length of the screw. It was a long step in advance that was 

taken by D. F. Henry when he applied an electric recording device to 

the meter, for by it the diffienlties that Lepont and others sought to 

avoid are very successfully overcome, the friction of the train of 

recording wheels being entirely done away with. If a recording device 

is used it f.-s worked by a spring and not by the meter, and, furthermore, it is not necessary to lift the Ineter to the surface to read the 

number of revolutions, which are recorded electrically, or may be 

counted from the indications of a buzzer. The electric meter as used 

by Henry is shown in fig. 10, page 35; that used by Moore in fig. 3. 
U. S. GEOLOGICAL SURVEY WATER-SUPPLY PAPER NO. 95 Pl. I 

PRICE ELECT RIC CURRENT MET ERS. 
llftlRPHY.) PRESENT-DAY :METERS. 21 

J\'Ieters in use at the present day may be divided ir1to two classes: 

(1) Those in which the revolving part turns about a horizontal axis, 

and (2) those in which it revolves ahout a vertical axis. The former 

class is illustrated b_y the Haskell and Fteley n1eters, shown in :figs. 4 

and 5, respectively, and the latter class by the Price meter, shown in 

Pl. I. Meters of the latte:r class have some advantages over those of 

------ ---- --- --- ---

FIG .. 3.-l\Ioore current meter. 

the former class: First, friction is usually less, since it nearly all 

comes- on one point, and this point can be protected from the action 

of grit in the water and fron1 jars; and, second, for a given high 

velocity the wheel will not revolve as rapidly as the wheel of a meter 

of the :first class under the same conditions, and at the same time the 

wheel will start in a less velocity than will the wheel of a meter of 
ACCURACY OF STREAM MEASUREMENTS. [No. 95. 

the former class, so that both low and hig-h velocities can be measured 

IHOI~e accurately with n1eters of the seeond class than with those of 

the first class. For example, by comparing the 1·ating table of HasFIG. 4.-Haskell l'urrent meter. 

kell meter No. :3 on page 81 with that of ~mall Price meter No. 363 

on page 42, we find that the former requires a velocity of about 0.20 

foot per second to start it, and that it makes 6.5 re\'olutions per secFIG. 5.-Fteley current meter. 

ond in water having a velocity of 

1 feet per second, ·while the latter 

requires a veloeity of about 0.06 

foot per seconc\ to start it and 

makes only 3.0~ revolutions in 

water having a velocity of 7 feet 

per second. A rate of 3 revolutions per second can easily be reeorded or counted, but a rate of 

. 6. 5 revolutions per second can not 

be counted or easily recorded. 

The disadvantages of the current 

meter are, briefly, as follows: (1) 

It can not he used where there is 

much floating grass or weeds, as 

on canals where the weeds are cut 

and allowed to float in the water, 

float rods being much better in 

such cases; (2) it I'equires rating 

before use and frequently thereafter; and (3) it must· be used with 

care. These last two conditions, 

however, are true for alL instruments used for measuring velocity 

indirectly. 

The meter that qas no electrical 

device for indicating to the observer the revolutions in a given time, 

and that n1ust he lifted out of the water to read the revolutions, is 

a thing of the past. Too much time is lost in n1aking the readings. 

The acoustic meter is not a success; the clicks are not sufficiently loud 

to be heard when the water is deep and the place noisy. 
MURPHY.] SLOPE FOR)HlLA.. 23 

The advantages of the meter are as :follows: (1) It gives integrated 

or mean velocity (any kind of tt float gi \

7 es the velocity of a comparatively few particles at some stage of a pulsation of the water, and not 

mean velocity); and (2) it can be used on streams of all sizes. 

For large streams the choice of instrun1ents is between the current 

meter and the double float, and the meter is preferable except where 

a large amount of weeds and grass is carried along in the water. For 

artificial channels the choice is between the meter and the float rod, 

and the meter has the preference except where there is a considerable 

amount of floating weeds, and possibly for very slow velocities also, 

but the latter is still in doubt. For velocities of 0.35 foot per second 

the meter will give the mean velocity as accurately and more rapidly 

than the rods, and at less cost, for at least four persons are necessary 

with the rod method, whereas one per:-;on, or at most two persons, 

can make the gaging with the meter, and the expense of moving the 

equipment from place to place is much grea,ter for the rods than for 

the meter. 

SLOPE FORMULA. 

The velocity of a stream can he computed from measurements of 

the slope of the surface, the dimensions of the cross section, and a 

know ledge of the roughness of the hottoin and sides. The formula 

which is now almost universally used for.this purpose was devised by 

Kutter in 1869 a and is as follows: 

[ 

41.6+ 1.811 + .00281 J Tr n 8 --

. = 1 +(±1.6+.00281) . __!!__ .V R 8 

s ../Rs _ 

In this fornmla Y=velocity, in feet per second; 8~~urface slope=i,.h 

being the fall of the surface in the distance l; R=hydraulic 

radius= F, F being the cross-sectional area and 1'-' the wetted perilp.- ·w 

eter; and n a ratio whose value varies froin 0.009 for a well-planed 

wooden channel to 0.035 for a channel overgrown with weeds or covered with stones. 

This formula is said to apply to streams of all sizes, from creeks and 

sew~rs to large rivers like the Mississippi, its constants being determined from Bazin's gagings of small clmnnel~, from Humphreys und 

Abbot's gagings of Mississippi River, from Cunningham's gagings of 

the Ganges Canal, and from gagings by many others. 

The disadvantage of the method is that it is very difficult to measure 

accurately the surface slope (s) of large rivers. T. G. Ellis says" 

that on Connecticut River the slope of parts 100 to 400 feet long was 

aGanguillet, E., and Kutter, W. R., Flow of Water in Rivers and Other Channels. 

b Trans. Am. 1:5oc. Civ. Eng., vol. 11, p. 23. 
24 ACCURACY OF STREAM MEASUREMENTS. [NO. 95. 

very carefully measured and the discharge computed~ using the best 

modern slope formulre. The discharge found from these formulre 

differed by 50 to 250 per cent from that found by gaging. He thinks 

the slope is so uncertain an element that slope· formulre are of little 

value. Captain Cunningham, after an examination of five hundred 

slope mea.surmnents of the Ganges Canal, says: ct "It [the slope of 

surface measurement] is so delicate a matter that the results are of 

doubtful use. " He found that the slope was very different at different 

parts of a reach from 1 to 2 miles long, and that the slope at opposite 

sides differed 50 per cent. Ellet says, b in regard to the slope of the 

Mississippi River: "'It not unfrequently happens that while the mass 

of the water which its channel bears is sweeping to the 8rmth, at a speed 

of four or five miles per hour, the water near the shore is running to 

the north. at a speed of one or two miles per hour. It is no unusual 

thing to find a swift <"Urrent and a eorresponding fall on one shore 

toward the south, and on the opposite shore a dsible current and an 

appreeiable slope toward the north.,, 

Only in very rare cases is it advisable to use this method. 

MEASUREMENT OF SURFACE FLUCTUATIONS. 

Any change in the elevation of the surface of a stream affects the 

discharge in two ways: The cross-sectional area is changed and as a 

rule the velocity also is changed. c It is neeessary, therefore, in 

aeeurate work to measure the surface fluctuations with great eare. 

Wave action, due to wind or other causes, should be eliminated. 

There are two classes of instruments in use at the present time for 

indicating surface elevations: (1) Self-registering gages, which give 

a eontinuous record of the changes in surface elevation; and (2) a 

fixed scaie from which the elevation of the surface is read at any 

time, or a moving scale with a fixed index fl.·om which the elevation 

of the surface is reacl. 

The United States Lake Survey self-registering water gage, shown 

in Fig. H, is a good illustration of instruments of the first class. The 

center pin is connected to a float on the surface of the lake, ~nd its 

motion is proportional to the change in elevation of the float. This 

motion is traced by the pen on a sheet of paper on the drum, which is 

1noved at a uniform rate by clockwork. The two outer pens reeord 

the time. Fig. 7 is a reproduction of the record made by this instrument on May 17, 1899. ·The elevation of the surface at any instant is 

given by the corresponding ordinate of this curve. This figure illusa Proc. Inst. Civ. Eng., Vol. 71, p. 11. , 

b Humphreys and Abbot, Report on the Mississippi River, p. 218. 

c On some streams there are places where the mean velocity remains nearly constant for several 

feet variation in Rtageof river. This is true of the Verdigris River at Liberty, Kans. See Nineteenth 

Ann. Rept. U. S. Geol. Survey, pt. 4, 1899, p. 374. 
MURPHY.] SELF-REGISTERING WATER GAGES. 25 

ti·ates the need of an accurate reeorcl of the change L stage, for it 

shows a change of surface elevation of 2. 5 feet in one and five-tenths 

hours. 

The hook gage, shown in fig. S, is a good illustration of a gage of 

the second elass. The frame is-fastened firmly to a post in the water, 

FIG. it-Self-registering water gage used by United States Lake SurVl'Yand the· elevation of the zero reading is determined. By turning the 

milled nut the hook is rabed until its point comes to the surface of 

the water. ThfS can be done very accurately in still wate1'; hy meam; 

of the little spot of light on the point of the hook. The seal(~ b then 

read, and from it the surface elevation is found. 

? 

Tracedo/lime ncils 

1/erticaf scale 

--===~"""""---"""""' ~ori'zontal ~ale 

Trc:.,ced lz.y tlme encils 

NOON li! 13 14 IS 

FIG. 7.-Record made by self-registering water gage used by United States Lake Survey. 

16 

The water gage used by the United States Board of Engineers on 

Deep ""WTaterways in 18H7-98, on Niagara River at Buffalo, N. Y., was 

of the box-with-float type. The box was of wood, 7 inches high, 7 
26 ACCURACY OF STREAM MEASUREMENTS. (NO. 95. 

inches wide, and 7 feet long, with a dosed bottom and a removable 

cover. The box was fastened firmly in the water, with half its length 

below the surface. Water was admitted through one or more of three 

:l--inch holes, allowing the float to chang·e its elevation as the river 

stage changed and at the same time eliminating the effect 

of wave.-;. The float was a ~-quart bottle with a 7-foot 

staff, marked to feet, tenths, and hundredths, wedged 

into it. ThiH staff extended up through the cover, and 

wus marked so as to. give the rise of the water surface 

above a certain plane us read at the cover of the box. 

VERTICAT_. VELOCI'l'Y CURVES. 

The relation between velocity and depth in a vertical 

section of a stream parallel to the thread of the current, 

or the vertical veloeity curve i:-; very desirable. From 

such a curve the ratio of velocity at any depth to mean 

velocity can easily be found and the discharge be- computed from observations at one depth only in verticals. 

Much .effort has been expended in investigating this 

relation and the change in it for change in river· stage. 

As might be expected, the results of experiments in this 

clirection do not agree. Each in vestigat<ft· adopts a new 

form of curve to fit his obHervations. In 1791 Waltman 

made some observations on the Rhine, fr~m which he 

concluded that the vertical velocity curve is a reversed 

parabola with its vertex below the heel of the river. In 

1820 De Fontaine found the greatest velocity of the 

Rhine to be at the .-;urface. He states that two inclined 

right lines intersecting about mid depth satisfy his 

vertical-curve observations. In 1824-1826 Racourt 

made observations on Neva River, from which he concluded that this curve is an ellipse whose minor axis 

is a little below the sut·face. Funk adopted a logarithmic curve for his observations on the Weser in 

1820. In 1844 Boileau found this curve for a small 

canal to be a parabola with its axis near the- surface. 

Darcy and Bazin found it to be a reversed parabola 

for their experiment canal, the perimeter changing with Fw. 8.-Hook gage for measuring the character of the bed. For Mississippi River, 

surface fluctua- Humphreys and Abbot found it to be a parabola whose 

tions. axis is three-tenths depth below the surface. Henry 

found it to be an ellipse for St. Clair River, while Baumgarten 

says that no simple curve will fit the observations in a vertical. 

From the results of these investigations and others that might be 
MURPHY.] VERTICAL VELOCITY CURVES. 

mentioned it appears that the shape of the vertical velocity curve 

depends much on local conditions, such as roughness of bed, slope, ratio 

of depth. to width, wind, obstructions, etc. Two facts must be borne 

in mind, however: (1) All the vertical-velocity-curve observations 

obtained with a single 1neter will not when plotted fall on any one 

line, but the results will be scattered more or less, and it will be 

possible to pass a number of curves among them, one satisfying the 

observations about as well as another; and (2) there is some part of 

each of the curves mentioned which if placed by the side of some part 

of another curve will coincide with it dosely; so that it-is quite possibl~ for any or an of these curves to fit more or less closely a set of 

imperfect vertieal-veloeity-cnrve observations. 

Theec are two methods of obtaining vertical velocity cneves with 

current 1neters: (1) The single-meter method, and (2) the multiplemeter metl}od. In the former a 1neter is held at as many points in a 

vertical as desired-at each tenth of the depth, for example-for a 

time sufficiently long to eliminate the effec.t of pulsations. This 

requires one or more hours to a vet tical, during which time a perlnanent change may occur in the mean velocity. In the latter met~od, 

however, this difficulty i:-; ove.rcome, for enough meters are use.d siiilultaneow.,ly to give the whole- curve in one operation. · 

In the vertical-velocity-curve work on Bt. Clair River, under I the 

direction of E. E. Haskell, United States assistant engineer, el~ven 

meters were used at a time. These were fastened between two cal~les, 

which were attached to a 200-pound sinker at the lower end and to a 

drum at the upper end, and operated from a catamaran. The lqwer 

meter was 1.15 feet abbve the bottom; the other ten were placed at tach 

tenth of the depth. Each meter was connected with an electric tregister, and by means of a switch all of the circuits could be opened in 

one ope.ration. The observer, with a stop watch in one hand and; the 

switch handle in the other, started the wakh and at a given in~tant 

closed all of the circuits through the meters and registers. Ati the 

end of the observation he stopped the watch and opened the cir¢uits 

at the same instant. One observation of six hundred seconds 1 was 

made with the meters al'ranged as described, and frmn one toi ten 

other~ of one hun:lred seconds each with the meters arranged in 9ther 

ways m each verttcal. : 

There should be some criterion for the rejection of doubtful ot' servations and the grouping of vertic.al velocity curves. The folio ing 

tn,ble gives the position of the vertex of sixty-nine vertical vel city 

curves obtained on Mississippi River by Humphreys and Abbot~ and 

illustrates this need. , 

I 
28 ACCURACY OF S'I'REAM MEASUREMENTS. [No. 95. 

TaUe showing position of 1'ertn: of ?'ertical 1'elocily cm·ves obt£lined on Jfississippi RiNT. 

First series. Second series. Total. 

Depth. Number Number Number ' Number Number Number ~ ~ ~ ~ ~ ~ 

verticals. floats. verticals. floats. verticals. floats. 

-------------1-------------------

Surface . . . . . . . . . . . .. . . . . . .. .. . . . . . . .. .. . . 12 63 8 17 

One-tenth................................ 11 46 1 2 Two-tenths . . . . . . .. . .. . . .. . . . . . .. . . . . . . . . 5 33 .................. .. Three-tenths............................. 3 20 1 3 Four-tenths.................................................. 4 9 Five-tenths.............................. 2 22 1 3 Six-tenths............................... 5 30 1 3 Seven-tenths............................. . . . . . . . . . . . . . . . . . . . . 6 18 Eight-tenths .. .. . .. .. . . .. .. . .. .. .. .. . . .. . .. . . . . . .. . .. . . .. . .. . 6 15 Nine-tenths.................................................. 2 5 Bottom . . . . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 8 ................... _ 

Sum .............................. . 222 30 

20 

12 

5 

5 

4 

3 

6 

6 

6 

2 

1 

69 

80 

48 

33 

23 

9 

25 

33 

18 

15 

5 

8 

297 

The vertex of 3--! per cent of the curves in the foregoing table is at 

or below mid depth of the river. Using all of them the vertex is 

three-tenths depth below the surface. This combination of curves so 

dissimilar is, to say the least, very questionable. Those in which the 

vertex is at or below seven-tenths depth should be rejec.ted, or at least 

not combined with the others, for they are due either to errors or to 

abnormal conditions, and should not be used in deriving a general law. 

Vertic.al velocity euiTes obtained in different parts of the discharge 

section for different depths are frequently combined by combining 

the velocities at each tenth of the depth. This assumes that the 

curves are similar in all parts of the discharge section, which is not 

true except in rare ca8e;o;. 

There is very little available data on the change in the vertical 

velocity curve with change of river stage. In the data on this point 

that have come to the \vriter\; oh8ervation the change in stc'tge is 

small and the inference to be drawn not conclusive. The effect of 

roughness of bed decreaseH, while that of slope and hydraulic radius 

increases with increase of stage. The effect of these on the shape of 

the curve can only be determined by careful measurements in which 

there is a wide range of stage. 

PULSATION OF MOVING W A.TER. 

Attention has already been called to the fact that one of the reasons 

for the difficulty in measuring accurately the velocity of water is that the 

velocity at any given point in a stream is constantly changing. This 

is true of both natural and artificial channels of all sizes. Captain 

Cunningham, who observed this pulsation of moving water in his 

experiments on the Ganges Canal, of India, states that he considers 

fifty repetitions with float rods necessary in order to get a g·ood average value of the velocity in one vertieal of a eanal. a ~T. B. Francis 

haH made numerous measurements of the velocity with float rods in 

a rectangular wooden flume at Lowell, Mass., every precaution being 

aProc. Inst. Civ. Eng., vol. 71, p. 8. 
MURPHY.] PULSATION OF MOVING WATER. 29 

taken to have the usual c.auses of irregularity of motion suppressed. 

The time of run was obtained by the u~c of an eleetric telegraph and 

a chronogTaph, and the depth was· very carefully measured with a · 

hook gage, and yet he found that the velocity shown hy these floats 

varied from 8.57 per cent above the mean to 11.4 per cent helow it. 

He says: "Similar and probably grPater variations occur in different 

parts of the depth from the same eanse. ,, It Adam Baum has made 

some observations on the variation of velocity in the Rhine near the 

Bridge of Constance.b He fixed a current n1eter in the river and 

noted the time of each 100 revolutions of the meter wheel for a period 

of two hours. The results show a continual change in the velocity 

for a constant depth of water. He concludes that for an accurate 

measurement of velocity it is necessary to extend the observations 

over a period of one hour at each point. 

Professor Unwin has made some observations with a current meter 

on the variation in velocity in the river Thames. c He noted the tin1e 

of each 100 revolutions, and upon plotting the time and the revolutions found that they gave a very irregular curve. The 1nean of each 

500 revolutions, however, when plotted with the corresponding time 

gave a rather regular curve. The following are some of the results 

of Professor Unwin,s observations: 

Vm·iation in relocity at three points of a t•atical uf Tlwmcs River a.~ found by Unwin. 

At 3 me- At 6 me- At 0.5 meter depth; ters depth; ters depth; 

velocity found from- velocity velocity Variation c~-=-!") " I'm . fouml found 

from 100 from 100 ----c--------c----1 

100 revolu- 500 revolu- revolu- revolu- At 0.!) me- At 3 me- At 6 metions. tionB. tionB. tions. l-te_r_d_e_p_tl_L_ 1

_te_rs_c_le_p_th_. 1_t_er_s_d_e_pt_.h_. 1 

liiet. pa sec. JJiet. pet .~ec. ltfct. per sec . .bfff. per ~ec. Per cent. Per cent. Per cent. 1.909 1.1:177 1.861 1.111 -1.8 +6.6 -3.6 

1. 942 1. 846 2. 030 1. 069 -3. 6 -1. 9 + 0. 3 1. 987 1. 846 1. 9~ 0. 977 -6.0 +2. 6 + l:l. 9 1. 942 1. 846 2. 030 1. 1)-10 -3. 6 - L 9 -lO. 1 

1. 861 1. 832 2. 030 1. OH +0. 7 -1.!) + 2. tl 

1. 861 1. 832 2. 060 0. 937 +0. 7 -3. 4 + 12. G 

1. 887 1. S23 1. 909 1. 021 -0. 7 +4. 2 + 4. 8 

1. 861 1. 787 1. 009 0. 998 +0. 7 +4. 2 + 7. 0 1. 861 1. 809 1. 8li1 0. 977 +0. 7 +6. 7 + 8.!) 1. 8tl1 I. 787 2. 030 1. 09-l +0. 7 -1. 9 - 2. 1 

1. 9-12 L 861 2.125 0. 900 -3.6 -6.7 +16.1 1. 760 1. 823 2. 030 1. 09-1 +6.1 -1.9 - 2.1 

l. 831 ------------ 2. 086 1. 021 +2. 4 --4. 7 + 4. 7 1.719 ·----------- 1.994 1.1:->0 +8.3 0.0 -10.1 1. 9-12 - . ---- . -- --- 2. 08t:i 1. 079 -3. 6 -4. 7 - 0. 7 

1.831 -----· ------ 1.909 1.472 +2.4 +4.2 -37.4 

1. 875 1.993 1. 072 - - - - - . - - - . - - - - - - - - - - - . - - - - - - - - - - -- - -

I 

a l'=velocity; Vm =mean velocity. 

It is seen that during the period required for the meter to make 

1,600 revolutions the greatest variations from the mean velocity at 

0.5 meter depth are +8.3 per cent and -6 per cent and at 6 meters 

depth+ 16.1 per cent ancl -37.4 per .cei1t. The greatest difference in 

aTrans. Am. Soc. Civ. Eng., vol. 7, p. 117. 

bProc. lnBt. Civ. Eng., vol. 71, pp. 456-459. 

cOp. cit., pp. 348, 349. 
30 ACCURACY OF STREAM MEASUREMENTS. [NO. 95. 

velocity, as shown by two consecutive ioo-revolution periods, i~ 12 

per cent at 0.5 meter depth and 36.7 pe_r cent at 6 meters depth. A 

velocity measurement of 100 revolutions 0.5 Ineter below the surface 

may be in error 8 per cent and one 6 meters below may be in error 

37 per cent. 

D. F. Hem·y(t has observed this fluctuation in velocity at a given 

point in large and in small streams. He says: "The lesser fluctuations have a duration of 30 to 60 seconds and the larger one:-; from 5 

to 10 minutes. They do not seem to be synchronous with the surface 

fluctuations, and are smaller at the surface than at the bottom." 

Harlacherb found the velocity near the surface of the Rhine to vary 

20 per cent in a few seconds, and near the bottom he found it to 

-vary 50 per cent in the same period. 

Ma1-r's simultaneous observations of velocity in the l\fississippi 

River at Burlington, Iowa,C with five current meters are described on 

pages ±H, 50. The following table gives the velocity, as shown by two 

of his current meters, one near the surface and the other near the 

bottom, for consecutive periods of one minute each. The depth in 

the first section is 11 feet, in the second section 27.6 feet, the meter 

being 4 feet above the bottom: 

nm:aaon in. t'elocity per minute ·in Jfississippi River at Burl-ington, Iou,a. 

Simultaneous observations in section No.1. Simultaheous observations in section No. 2. 

Velocity Varia- Velocity Varia- Velocity Varia- Velocity Varia1 foot be- tion 9.1 feet be- tion 3.6feet be- tion. 23.6 feet tion 

low sur- (_!'t_n-=-!) low sur- crm-r) low sur- (l:'!'J.;::-I). below sur- ( rm -- r) face ( n. r . face ( l'm). rm . face { J"). face ( rm)· l' . m m 

- Ft. per sec. Per cent. Ft. pet· sec. Per cent. Ft. per St"e. Per cent. Ft. per sec. Per cent. 2.242 +2.0 1. 724 0.0 2.286 +4.8 1. 966 + 2.4 2.267 +0.9 1. 675 + 2.9 2. 3.53 +1.3 1. 817 + 9.8 2.252 +1.1 1. 761 - 2 ') 2.437 -2.3 1.985 + 1.5 2.236 +2.2 1. 744 - 1.2 2.300 +3.5 2.008 + 0.3 2.267 +0.9 1. 797 - 4.3 2.404 -0.9 2.00.5 - 2.5 

I 2.299 -0.5 1. 766 -- 2.4 2.378 +0.2 2.119 - 5.2 2.289 0.0 1. 772 - 2.8 2.414 -1.3 1. 926 + 4.4 2.274 +0.6 1.819 - 5.5 2.392 -0.4 2.008 + 0.3 2. 211 +3.3 l. 712 + 0. 7 2.313 +3.0 1.983 + 1.5 2. 224 +2.8 l.644 + 4. 7 2.296 +3.8 2.081 - 3.3 2.280 +0.3 1.698 + 1.5 2.383 0.0 2.104 - 4-.5 2.239 +2.1 1. 915 -11.1 2.397 -0.6 2.276 -13.3 2.280 +0.3. 1.670 + 3.1 2.420 -1.6 2.092 - 3.9 2.289 0.0 1. 775 - 3.1 2.361 +0.9 2.008 + 0.3 2.321 -1.5 1.582 + 8.3 2.278 +4.4 2.047 - 1.6 2.420 -6.0 1.664 + 3.5 2.445 -2.6 1.848 + 8.3 2.445 -6.9 1. 741 - 1.0 2.459 -3.2 2.024 - 1:0 2.308 -0.9 1. 717 + 0.5 2.428 -1.9 2.070 - 2.8 2.333 -2.0 1.800 - 4.4 2.456 -3.1 1. 796 +10.8 2.264 +1.0 1.69;) + 1.7 2.460 -3.2 2.055 - 2.4 2.W27 -1.3 1.812 - 5.1 ................... 2.311 -1.0 1.689 + 2.0 ...................... ::::::::::::1:::::::::::::::::::::::: 2.305 -0.8 I. 792 - 4.0 ..................... ...................... ........................................... 2.311 -1.0 1.627 + 5. 7 ....................... 1 ..................... ..................... ...................... 2.277 +0.4 1.554 + 9.9 ...................... -·---------- ----------- ------------ 2.274 +0.6 1.678 + 2. 7 ......................... ....................... ....................... ·----------- 2.292 -0.2 1. 731 - 0.4 ........................ ....................... ------------ ------------ 2.271 +0.7 1. 704 + 1.1 ....................... ........................ ....................... ------------ 2.321 -1.5 1. 698 + 1.5 ........................ --·--------- .................... ------------ 2.261 +1.1 1. 723 0.0 ....................... ...................... ......................... ...................... 2.217 +3.6 1. 757 -- 1.9 ........................ ......................... ...................... ........................ 2.280 +0.3 1. 743 - 1.1 ....................... .................... 

2.287 -.. --~~ ~~ ~- .I: : : : : : : : : :: : I· .. ------.-. 1. 72·1 .................... 2.383 . ................... 

aJour. Franklin Inst., vol. 62, p. 323. 

b Trans. Am. Soc. Civ. Eng., vol. 12, p. BU. 

c McKenzie, A., Report on Current Meter Observations, Burlington, Iowa, 1884. 
MURPHY.] FLUCTUATIONS IN VELOCITY. 31 

It is seen that in the first section the greatest departures of velocity 

from the mean are +3.6 per cent and -6.9 pm· cent at 1 foot below 

the surface, and +9.9 per cent and -11.1 per cent at 9.1 feet below 

the surface, or 2 feet above the bottom. The greatest difference in 

velocity obtained from two consecutive 1-minute periods is 6 per cent 

at 1 foot below the surface and 12.5 per cent at 9.1 feet below the 

surface, or 2 feet above the bottom. In the second section the greatest 

departures of velocities from the mean are +4.8 per cent and -3.2 

per cent at 3.6 feet below the surface, and +10.8 per cent and -13.3 

per cent at 23.6 feet below the surface, or 4 feet above the bottom. 

The greatest difference in velocity obtained from two consecutive 

1-minute periods is 7-per cent at 3.6 feet below the surface and 13.6 

per cent at 4 feet above the bottom. In the first section a velocity 

measurement near the surface inay be in error 7 per cent and a measurement 2 feet above the bottmn may be in error 11 per cent. In 

the second section !L velocity n1easurement 3. 6 feet below the surface 

may be in errol.· 4.8 per. cent and a measurmnent 4 feet above the 

bottom in error 13.3 per cent. 

In 1899, while measurii1g the discharge of the St. Clair River, Mr. 

L. C. Sabin, assistant engineer, nutde smne experiments to determine 

the pulsations or fluctuations in the velocity of the river at the discharge station. Four Ineters were used, placed 50 feet apart and at 

the same depth. In the first ~eries of observations the rqeters were in 

a line across the river and at right angles to the current; in the second 

series they '\Vere in a line with the axis of the current. Simultaneous 

readings of the four meters were taken every fifteen seconds for several periods. of ten minutes each. The results were plotted, using time 

as abscissre, and velocity as ordinates, and a curve drawn for each 

meter, showing the fluctuations in velocity in each fifteen seconds of 

time at four points 50 feet apart. These curves have two sets of wavessmall ones of fifteen to si.xty seconds amplitude and larger ones of three 

to six or more minutes an1plitucle. The range of velocity as found from 

the large waves is in some cases 35 i)er cent of the mean velocity shown 

by the meter for ten minutes. The curves for two adjacent meters are 

at times nearly parallel, but they soon diverge and cross each other 

occasionally. The curves for the meters in a line with the axis of the 

river resemble one another more closely and are nwre nearly parallel 

than those of the meters in a line across the river. These experiments 

indicate that the pulsations are very lin1ited in exterit in a direction at 

right angles to the current, but that they can be traced for some distance in the direction of the thread of the current. The whole depth 

of the river is affected by them, and their effect decreases from the 

bottom toward the surface. 

The practical lesson to be drawn from the experiment-, by Sabin 

and others is ~hat velocity observations of short duration are of little 
32 ACCURACY OF STREAM MEASUREMENTS. [NO. 95. 

value unless they are numerous and well distributed over the disoharge 

area. In order to eliminate the effect of the pull-lations, each observation should extend over a period of from six to ten minutes. Long 

single observations and rapid fluctuations of water-surface elevation 

req.tJ.ire that discharge be found from single observations in comparatively few verticals, and that the ratio of veloeity at this depth to 

n1ean velocity he known from vertical veloeity curves. This emphasizes the need of a thorough investigation of the relation between 

velocity and depth in a vertical-longitudinal plane and the change in 

this relation with change of river stage. 

METHODS OF MEASURING AND COJ\IPUTING STREAJ\I E~LO,V. 

WEIRS. 

The discharge of a stream can be obtained by eam;ing it to flow 

over a weir or dam, the coefficient of whieh is known, by the substitution of observed data in a weir formula. Three· sharp-crested or 

standard weir formulrn are in use, viz, Fran'cis's, Fteley and Stearns's, 

and Bazin's. They differ much in form, and each is derived from 

experiments on small weirs with low heads. A brief dil'!cusHiou of 

each formula is here given beeaul'!e of its bearing on the aeenraey of 

discharge measurements. Bazin has determined the values of the 

coefficient of discharge over weirs of many other shapes of crest, and 

the Cornell University experiments qf the Board of Engineers on 

Deep Waterways have extended the values of the coeffieients of a 

few of these to the higher heads. Time and spaee, however, will not 

permit more than the 1nention of them here. (t 

The weir is the most accurate method of measuring discharge yet 

used for small streams if the coefficient of the weir· be accurately 

known. The head on the weir and the velocity of approaeh are the 

only variables, and these ean easily and aectirately be measured. The 

disadvantages are (1) the eost of construetiug a weir, or the difficulty 

of finding one in use whose shape elosely resemhles one whose coeffieient, is known, and (2) the limited range of values of the eoeffieient of 

a weir of any shape and the limited number of shapes that have been. 

investigated. 

FRANCis's EXPERIMENTS AND FORMULA. 

In 1852 J. B. Francis made numerous very eareful measurements of 

the volume of water passing over small weirs and the eorresponcling 

heads at Lowell, Mass.b His measuring ta!1k was a eanal lock. whieh 

had a eapaeity of 12,138 eubic feet for a depth of 9.5 feet; the greatest 

length of erest was 10 feAt; the head on the weir varied frmn 5 to 19 

inehes, and was measured with two hook gages 6 f<Jet upstream from 

a A discussion of these experiments, which were conducted by George W, :)la,fter, will be found in 

Trans. Am. Soc. Civ. Eng., vol. 44, pp. 22Q-398. 

b Francis, J. B., Lowell Hydraulic Experiments, p. 133, 
MURPHY.) MEASUREMENTS OF STREAM FLOW. 

the crest; th.e width of the channel was about 14 feet. His formula, 

derived f~·om these experiments, is as follows: 

Q=i x 0.622.-h2(b-T1o nh2)v2 gh2=3.33 (b- 1 \r nh,2)h2!. 

Q=discharge in cubic feet per second; h,=head on weir, or difference 

in elevation of weir crest and water surface; n is a constant whose 

value is 0 when both 

ends of the weir are 

flush with the sides of 

the channel, 1 when one 

side onlyiis flush, and 2 

when ne~ther side is 

flush; g:::::::acceleration 

of gravity. (Seefig. 9.) 

The head on. the weir 

should be not less than 

0.5 foot nor more than 

FIG. 9.-Sharp-crested weir. 

2 feet, the depth of water in the canal should be at least three times 

the head on the weir, and the air should have free entranee under the 

sheet. The velocity of approach of the water to the weir must be 

measured and the head correeted for it. The formula for this purpose js Jt,2=[(h,+h1)!-h/J, h being the measured head, h1 the head 

due to th~ velocity of approach= ~~ 2 and l~ = bQh. · (See :fig. 9.) ~g o ·o 

Hamilton Smith, jr.; says of this formula:a "It stands in the :first 

rank in reliability." 

Francis nmde eighty-eight experin1ents with two weirs of 10 and 8 

feet length, in addition to those to derive his formula, and found that 

the greatest percentage difference between his measured diseharge 

and the discharge computed by his formula was 0.9 per cent for the 

mear~ of two experiments and 0. 68 per cent for the mean of eight 

experiments; for the other e)even means the difference is less than 0.4: 

per cent. 

]'TELEY AND STEARNS'S EXPERIMENTS AND FORMULA. 

In 187V and 1879 Fteley and Stearns b n1easured the discharg-e over 

weirs of: 5 and 19 feet crest length and the corresponding head on 

weir,"frdm whieh they derived the following formula for a standard 

weir with end contractions suppressed: · 

I [ VT2] 3 

Q=3.31b h+1.5 2~ 2 -0.007p. ' 

Q=diseharge in cubic feet per second, b=length of crest, h=head 

on weir, l~ =velocity of approach in feet per second. (See fig. 9.) 

a Sm~h, Hamilton, Hydraulics, p. 93. 

IRR 1..,5-04-3 

i 

b Trans, Am, Soc, Civ. Eng. vol12, p. 1, 
34 ACCURACY OF S'l'RlJAM MEASUREMENTS. [NO. 95. 

Their n1easuring tank was a section of the Sudbury conduit having 

a capacity of 300,000 cublc feet for an increase in depth of 3 feet. 

The head on the weir was measured with a hook gage 6 feet upstream v2 from the crest. The term 1. 5-1 corrects for velocity of approach. 2g 

The head on the weir must be not less than 0. 06 foot, and the air must 

have free access under the sheet. This forn1ula is not used as generally as is that of Francis or Bazin. It was used by Fteley and Stearns 

to cmnpute the discharge of the weir used in their current-meter and 

weir comparisons; (See p. 58, 59.) 

BAZIN'S FORMULA. 

In 1886 and1887 Bazin (t made numerous measurements of the volume passing over weirs having lengths of frou1 0.5 meter to 2 meters 

and the corresponding heads. From these he derived the following 

formula for a standard weir with end contractions suppressed: 

Q=iJl[ 1+0.55 (p!h.)2

] bhv2gh 

d ') 6075+ 0.0148 

an JL='" · It (in feet)" 

This formula is true for any system of units (feet or meters). 

Q=discharge, b=length of crest, h.=head on weir, p=distance of 

crest above bottom. (See fig. 9.) This formula needs no correction 

for velocity of approach. The measuring tank was a section of a 

rectangular channel 200 meters long, 2 meters wide, and 1.2 meters 

deep. The head on the weir varied from 0.05 Ineter to 0.6 meter. 

The air had free aceess under the sheet. Each of these formulre will 

give the discharge to within about 1 per cent if the conditions existing when the observations on whieh the formula is based are exactly 

duplicated. Discharges computed from any two of these formulre 

may differ 3 per cent. · 

CURRENT METERS. 

If the stream be small, meter measurements are made frmn a bridge, 

if one can be found in a suitable location. Bridge piers, however, 

disturb the natural flow of a stream, as well as distort the vertical 

and transverse velocity curves and render them of only local application. Discharge measurements made where there are piers in the 

channel are, as a rule, less accurate than measurements made where 

there are no piers to obstruct the flow. 

In case there is not a bridge at the desired place, the observer wades, 

if the water he shallow, taking observations of depth and velocity at 

a Annales des ponts et chaussees, 1888, p. 416. 
MURPHY.] CURRENT METERS. 35 

as many :points in the cross section as desired. If the water be deep 

and switt, a cable is stretched across the stream at a convenient 

height above the water, an4 a car or box is suspended from it. From 

this car-,1 which is n1oved back and forth across the stream by the 

observel[ in it, the depth and velocity of the water are measured. If 

the curr~nt be not swift, a surveyor's chain or a cable can be stretched 

across tlie stream temporar~ly and the depth and velocity be measured 

from a rbwboat at points marked on the chain or cable. 

In a l~rge river like the Mississippi, where a steamboat can conveniently anchor, a method that has been used satisfactorily is shown in 

fig. 10. a The boat is anchored in the proper place, a'itd a lead weight of 

FIG. 10.-Method of using current meter on large river. 

50 pounds connected to the anchor is lowered over the stern. A copper 

wire is connected to this weight and to the spring pole in the boat, 

and the meter is moved up and down on this wire by a rope. The 

revolutions of the meter are recorded electrically-in the boat, the copper wire being connected to one pole of the battery and an insulated 

wire connected to the meter and the other pole. 

On large rivers where boats can not anchor the measurements are 

made from a boat towed by a stearnboat.b The meter is kept in position by two lines of range poles at right angles to each other. The 

pilot on the steamboat steers it so as to keep it in line with one range, 

while th~ engineer, with his hand on the steam valve and his eye on 

a Jour. Franklin Inst., vol. 62, p. 171. bJour. West. Soc. Eng., vol. 3, No.3. 
36 ACCURACY 01!, S'I'REAM MEASUREMENTS. [NO. 95. 

the other range, controls the speed of the boat so that it will remain 

in a fixed position. 

In a swift current the meter and its sinker will be carried downstream a distance depending on the weight of the sinker and the depth 

and velocity of the water. There are two methods of treating this 

difficulty. One is to apply a special device like that shown in fig. 11 

-~~~---

--=- -::::....=--..::: --- -

FIG. 11.-Device for holding meter'in place. 

to keep the meter in place; a the other is to compute from the weight 

of the sinker and the depth and approximate velocity of the water the 

additional length of cable to use in order that the meter may sink to 

the required depth. b The first is the better for streams of ordinary 

size. In the device shown in fig. 11 the stay line is attached to the 

a Twentieth Ann. Rept. U.S. Geol. Survey, pt. 4, 1900, p. 20. 

bJour. West. Soc. Eng., vol. 4, No.6. 
MURPHY.] POINT AND INTEGRATION METHODS. 37 

meter and is passed over a pulley at the end of the stay pole, its end 

being held by an assistant. By 111eans of this stay line and the vertical 

cord the meter can be kept nearly in position. Instead of a stay pole 

a wire cable is sometimes used to keep the stay line in place. 

POINT AND INTEGRATION :METHODS. 

There are two methods of using a meter in a cross section, as follows: (1) The point method, in which the meter is held at certain 

points in the cross section for a stated period of time, usually fifty 

seconds, and the number of revolutions of its wheel during that 

time are carefully observed, either by counting the clicks of a 

buzzer or reading a register; and (2) the integration method, in 

which, instead of holding the Ineter at certain points, it is moved 

with a uniform speed through the section, the time and number of 

revolutions being observed as before. The point method is the more 

accurate if sufficient observations are taken in the section. The 

velocity found by the integration method is the resultant of the 

velocity of the water and that of the meter as it is carried by the 

observer, and must always be greater than the true velocity. The 

error increases with the speed of the meter, and also increases as 

the velocity of the water decrease~:;. When the point method is used 

the meter may be held at several points in certain verticals, in which 

case we will call it the ordinary method; or it may be ,held at the 

surface, at mid depth, and at the bottom in certain verticals, and the 

discharge be found from these (see Moore's method, p. 46); or it may 

be held at the surface and the bottom only in several verticals, and the 

mean· velocity be found from these; or it may be held at three-tenths, 

at six-tenths, or at mid depth in certain verticals, and the mean velocity 

be found by applying a factor. The three-tenths-depth point (t is used 

because it is said to be the point of maximum velocity in a vertical, 

and a small error in the position of this point will not affect the result 

much. The mid-depth pointb is employed because the factor which is 

used to obtain the mean velocity is more nearly constant for it than 

.for any other point on a vertical curve. The six-tenths-depth pointe 

is used because it is believed to be the depth of the thread of mean 

velocity. 

In the integration method the meter may be moved down seyeral 

times in certain verticals only, as used by Harlacher, a or across the 

dtream at a given depth, as used by Price on the Mississippi River at 

Carrollton, La., e or diagonally across from one side to the other at the 

same time that it is moved from the surface to the bottom several 

a Jour. West. Soc. Eng., vol. 3, No.3. 

b McKenzie, A., Report on Current Meter Observations, Burlington, Iowa, 1884. 

c Proc. Inst. Civ. Eng., vol. 71, p. 60. 

d Ibid., vol. 67, p. 358. 

e Jour. West. Soc. Eng., vol. :!, No.3. 
38 ACCURACY OF STREAM MEASUREMENTS [NO. 95. 

times, as used by the writer and others. Harlacher,s apparatus for 

moving a meter with a uniform velocity is shown in figs. 12 and 13. 

The meter B is mov_ecl up or clown on the iron tube AA by the rope 

D attached to the drum F. E is a bracket holding the pulley e. G 

is an arm supporting the drum F, andj~ (fig. 13) is a dial on which is 

registered the depth. The fanJ: (fig. 13) and the gearing .fs regulate 

the rate of motion of the Ineter; h, is a crank lever for raising the 

meter, and ~fs a ratchet wheel for arresting the motion. I (fig. 12) is 

an electric battery, and H (fig. 12) is the 

reg-istering apparatus. 

When accurate results are desired the 

meter should be held with a rod, if the 

depth be not too great, in which case it is 

not free to turn sidewise, but keeps its axis 

parallel to the axis of the stream and can 

be placed close to the bottom. Ordinarily 

it is held with an insulated wire, and is free 

,~~-~~~~- to take the direction of the water at the ~ ___ _ point where it is held. 

COEFFICIENT WORK. 

Coefficient work in river gaging coQ.sists 

of obtaining the ratio of the velocity at any 

- - -- l)oint in the de.pth of the sti,eam (callecl the 

index point)-as, for example, the threetenths-depth point-to the mean velocity 

in the whole depth. When this ratio or 

coefficient is known for a vertical, the mean 

velocity in that vertical can be found by 

making an observation at the index point 

and applying the coefficient. 

Let 01, C~, 03 , etc., be the coefficients for 

FIG. 12.-Harlacher's apparatus for the component parts, ~, p;, F;, etc., of the 

moving a meter with unifor"m TT 

velocity. discharge area F; T~, V:;, r 3, etc., the observed velocities at the index points of these 

areas; and V the mean velocity for the whole discharge area. The 

discharge Q=FV= ~ l~ + «p; ~+ DsFa ¥:;+ ---------------(1). 

A value of each of these coefficients can be found for each foot 

variation of river stage. The discharge of the stream is then computed by equation (1) from observed values of V:, ~' v;, etc., at the 

index peints, using the set of values· of the coefficients which correspond with the observed river stage. · 

Coefficient work can be done with one current tneter, but it can be 

done more rapidly with two or more meters. When two meters are 
MURPHY.] COEFFICIENT WORK. 3.9 

used, one is placed at the index point and the other is held for several 

minutes at as many points in the vertical as desired, and simultaneous 

readings of the two meters are obtained at each point. The two meters 

are .occasionally held at the same depth and relative readings of the 

meters are obtained. A chart can be prepared from the ratings of 

the meters in still water which will give the velocity ratio from the 

sinulltaneous readings of the two Ineters. For example: The index 

FIG. 13.-Details of Harlacher's apparatus for n10ving a meter with uniform velocity. 

meter at three-tenths depth indicates 2.34: revolutions per second. 

The other meter, at eight-tenths depth, indicates 2.05 revolutions per 

second. The chart. shows the velocity ratio for these meter speeds to 

be 0.89. From the velocity ratio at each tenth of the depth the ratio 

of the -Inean velocity in the vertical to the index ve~ocity, or D, is 

found. 
40 .ACCURACY OF ST.RE.A:M M:E.ASUREMENTS. [No. 95. 

On account of the rapid changes of surface elevation of large 

streams~ this coefficient method of _gaging is better and more accurate 

for such streams than the slower one in which velocity observations 

are n1ade at several points in each vertical. 

RATING OF MET~RS AND CONSTRUCTION OF RATING TABLES. 

The accuracy of a discharge measurement depends largely on the 

accuracy of rating the meter used. Errors of observation are as 

likely to be too large as too small, and are compensating. Errors in a 

rating table always have the same sign and are cumulative, hence the:r 

should be eliminated or reduced to a 1ninimum. 

There are two kinds of rating of a current meter-absolute and 

relative. From the former the absolute velocity at a single point is 

found; from the latter the ratio or coefficient of velocity at any two 

points is found. The former is usually employed in still water; the 

latter in running water. 

Four methods have been used for rating meters: (1) By the use of 

surface floats; (2) by moving the meter through still water with a 

known velocity; (3) by observing velocity at many points in a cross 

section and comparing this with the known mean velocity; and ( ±) by 

attaching the instrument to a long arn1 and revolving it about a vertical axis in a body of still water. The second method is the one now 

universally used. The meter is suspended from a car or a boat and is 

moved with a uniform velocity through still water at a depth of ~ or 

more feet below the surface. The length of a run varies from 100 to 

300 feet, with a starting run' sufficient to allow the 1neter wheel to 

reach the proper speed before entering the run. It is moved across 

and back over the run to eliminate the effect of velocity in either 

direction. The rating equipment should be such as to give time of 

run to the tenth of a second and speed of meter to the tenth of a revolution (a chronograph recording time~ revolutions, and the instants of 

beginning and ending the run should meet this requirement). 

The range of velocities employed in rating should be those for which 

the meter is to be used. If it is to be employed mainly to measure 

low velocities the speeds in rating should be low. The rating table 

should not be extended beyond the limits of velocity used in the 

rating. 

The relation between distance passed over by the meter and the 

corresponding revolutions of the meter wheel is often assumed to be 

a straight line. It is always a curved line, and must be so on account 

of friction of bearings and inertia of moving wheel. A velocity of 

·from 0.1 to 0.5 foot per second is necessary to start the wheel. .As the 

velocity increases the effect of friction and inertia becomes proportionately less and the curve approaches a straight line. The relation 

between velocity and r~volutions of wheel, per second, is of the second 
MURPHY.] THE RATING OF ME'rERS. 41 

degree a:nd concave to the axis of velocity. For velocities of 2 or 

more feet per second this curve differs little from a straight line. 

The results of the rating are usually plotted on squared paper, 

using revolutions per second as ordinates and velocity as abscissre, 

and all observations that fall much from a well-defined line are 

rejected. If this line be nearly straight between the limits of the 

observed revolutions its equation is assumed to be of the form 

y=a.+b;x·, y being velocity, w revolutions per second, and a and b constants. If the results indicate a curved line its equation is afsumed 

to be of the form y=a+b;l!+cx 2

• There are two methods of preparing the rating table from the observations. The first method is 

rapid. The most probable curve is drawn among the plotted observations, and the velocities to tenths of a revolution are read from the 

curve. In the second method the equation of the most probable 

relation is derived by the method of "least squares" and then the 

table is prepared from the equation. The writer has found it better 

to plot values of w and the ratio of y to w (see fig. 29, p. 89) instead of 

x and y. The reason is that the ratio y to ;-v changes rapidly as w 

increases and can be read more accurately from this curve than 

from a nearly straight line. It can be shown mathematically that 

these curves are approximately branches of hyperbolas. 

The second method, which is to derive the equation of the most 

probable relation between velocity and revolutions by the method of 

"least squares," first rejecting the observations that fall much outside of a well-defined curv~, is the most accurate, but it requires the 

most time. If the meter is to 1neasure low velocities to within 1 per 

cent, the second method must be used. It gives n observation equations of the form y-a-bx=·v if the relation be linear, or ·y-a.-brllcw 2 =·v if it be parabolic. 'V iR a small quantity called a residual, or a 

residual error. Its value would be zero if the observations were perfect. According to the principle of least squares, the best values of 

the constants- are those that make the sum of the squares of the residuals a minimum. 

Squaring each of these n equations and adding, we have 

~·li=t't +v:/+·v + . . . = [y' -a-bx' -(~a:l +[y'' -a-b;v" -cw112J2· 

+Lv'" -a-bx.'" +cw"'2]2+ 

Taking the first derivative of this equation with respect to a, b, and c 

and placing these equal to 0, we have 

d(~dv ) =-2 [y'-a-bw'-c,Il 2 ]-2 [y"-a-bw"-ca/' 2] 

,a =0 

~v2 

d db = -2;-v' [y'-a-b.-v' -cx'2

] -2w" [y" -a-bw" -ca:l112] =0 

:Z2 

d d~ =-2w'2 [y'- a-b.111

- c.z"2

]-2a,'2 [y'' -a -b;e'' -c,v''2

] =0 

From these normal equations the values of a., b, and c can be found. 
42 ACCURACY OF STREAM MEASUREMENTS. (NO. 95. 

For the lineal: function these eqtiations become two in number and 

have the forn1 

a~m+b~iv2 = ~wy 

na+b~m =~y 

and a and bare found from these equations. 

This relation between revolutions per second and velocity, whatever 

it may he, is not constant. Below are given the ratings of a Price 

meter, obtained by J. C. Bailey, United States a~sistant engineer: a 

Res·ults of joztr ratings of n Price meter used in 189;3 on Nia.gant Ri1•er. 

Date. of obser- Velocity. _ Remarks. Number _ ~etael"__('~e~ fticiebnts._, 

vations. 

--------------l------l--------l----------- 1--------------------

Ft. per sec. 20 2. 5 to 7. 3 34 2.1 to 6. 7 49 1. 7 to 7. 7 

April28 ............... . April29 .............. . May4 ................. . May17 ................ . 43 2. 0 to 8.0 

4.239 +0 4. 2.')6 +0. 061 4. 046 +0. 207 4. 130 +0. 067 

4.168 +0. 0848 

Still·water; base 150 feet long. Do. 

Do. Still water-;· base 300 feet long. 

Yalues computed jt·mn f11'0 ratings of current meter on April 29 and llfay 4, 1892. 

[April29, T"1=4.256R+0.061; May 4, l"2=4.046R+0.207.] 

R r1 r l2- l'i l2- T'i_ 

---------------

2 

----------

~ 

0.05 0.274 0.409 0.135 0.314 0.10 0.487 0.612 o:125 0.204 0.15 0.699 0.814 0.115 0.141 0.20 0.912 1.016 0.104 0.102 0.25 1.125 1. 219 0.094 0.077 0.30 1.338 1. 421 0.083 0.058 0.35 1.551 1.623 0.072 0.044 0.40 1. 763 1.825 0.062 0.034 0.45 1. 967 2. 0'28 0.052 0.026 0.50 2.189 2.230 0.041 0.018 

The foregoing table shows that if on May 4 velocity measut:ements 

had been made from 0.05 to 0.50 revolution per second and the- rating 

table of April 29 had been used the results would be in error from 1.8 

per cent to 31.± per cent. It is true that neither set of values of a and 

b was determined for low velocities. This·, howe~er, emphasizes the 

fact that values of a and b found for high velocities may be greatly 

in error for the low velocities if the linear relation is assumed. These 

four ratings of a meter in less than one month show considerable 

·variation in the values of a and b, and indicate that when a meter is 

in constant use its rating should be exarrilned once a week if accurate 

work is required. · 

A rating table that gives velocity to only two places of decimals is 

not sufficiently accurate for low velocities. To illustrate this we will 

take the case of the rating table of small Price meter No. 363, rated 

at Chevy Chase, Md., June 26, 1900. The velocity corresponding with 

0. 05 revolution per second is given as 0.17 foot per second. This may 

mean any value from 0.166 foot per second to 0.17 4 foot per second. 

This is 2.12 per cent of 0.17. Hence if the computed revolutions 

a Engineering News, vol. 29, 1893. 
MURPHY.] RATING TABLES. 43 

were either 0.166 or 0.17 4 the error introduced by using this rating 

table would be 2.12 per cent. The following table shows the error for 

other velocities given in this rating table. If the velocity be 0.25 foot 

per second it may be in error nearly 2 per cent if found-from this table. 

Table showing greaiest percentage e1·ror in 1·at·ing table of small Price meter No. 363, · ·which gives 'l'elocity to only two places of decimals. 

Revolu- Error Revoln-~ Error 

tions per Velocity. 0.004 tions per Velocity. 0.004 

second. -y- second. ---v 

Ft. per sec. Per cent. Ft. per sec. Pn· cent. 0 0.06 6. 7 0.25 0.63 0.6 0.05 0.17 2.4 0.30 0. 75 0.5 0.10 0.29 1.4 0.35 0.86 0.5 0.15 0.40 1.0 0.40 0.98 0.4 0.20 0.52 0.8 0.45 1.09 0.4 

Darcy and Bazin employed the first three n1ethods to rate the Pitot 

tube which 'they used in their hyclrauli'c investigations on canals.a 

Fig. 2, page 19, shows this instrument as they used it. A discussion 

of the results of the ratings is given here on account of the light they 

throw on accuracy tests. 

Re.mlts of Pitot tube ratings by Da·rcy and B3z·in. 

First method. b Second method. e Third method. d 

No. of Num- ex- Value ber of Veloc- Value 

peri- of coef- experi- ity of of coefficient. boat. ficient. ment. ments. 

--------------

11-Ietet·s. 2 0.987 8 0.609 1. 040 3 1. 0'24 8 0.692 1.053 4 0.981 R 0. 785 1. 032 5 1.013 8 0.938 1.033 6 1.006 8 f), 980 1.040 7 0.988 8 1.120 1.015 8 1.012 8 1. 231 1.028 9 1.008 4 1.333 1. 032 10 1.008 4 1. 385 1.048 11 1. 009 4 1. 470 1. 0'29 12 1.007 4 1.500 1. 040 13 1.015 4 1.611 1.033 14 1.039 4 1.661 1. 027 15 0.994 4 1. 775 1.042 16 1.007 4 1. 819 1.031 17 1.023 4 1. 863 1. 0'27 ............. .. ........... 1.930 1.039 .............. ................ .. ~ -........... 1. 976 1.025 ................. ................. ................ 2.034 1.037 ................. .............. .............. .. ............... .............. ................. .............. ............... .............. .............. ............... ................. ............... ................ ............... ................. ............... ............... ................. ................ ................ .. .............. ............... .................. ............... .................. ............... ............... ............... ................ .................. ................ .............. .................. .............. .................. ................. . ............ .................. ................ ................ ................ ............... ................. ............... ................ ............. .. ........... ............. ................ ................. .............. ............... ................. ........... ................ ............... ............... .............. --- --- 1.006 1.034 

a Darcy and Bazin, Recherches hydrauliques, 1865, pp. 63-70. 

bBy surface floats. 

cin still water. 

din moving water. 

Num- Designation Channel. 

ber of of experi- Value Mean 

experi- ment. of coef- velocficient. ity. ments. Series. No. Shape. Width. 

--------------------

Metet·s. Mete-rs. 2 51 1 1.021 0.508 (e) 0.8 1 51 2 1.010 0. 768 (e) 0.8 

3 51 3 1.018 1.028 ~e) 0.8 1 52 1 1.029 0.376 e) 0.48 

3 52 2 1.000 0.542 

I 

(e) 0.48 1 52 3 1. 006 {).694 ~e) 0.48 1 58 4 1.005 1.429 e) 1.994 1 59 4- 0.969 2.318 

~ =~ 1.994 

1 60 2 0.968 2.571 1. 994 

1 61 4 0.966 1. 267 (f) 1.994 

1 62 4 0.965 1. 979 (f) 1.994 2 63 3 0.988 2.199 (f) 1. 994 

1 64 1 0.996 0.856 (f) 1.994 1 64 2 0.988 0.948 (f) 1.994 

3 65 4 0.978 ,1.511 (f) 1. 994 

3 66 1 1. 015 1.464 (f~ 1.994 

1 66 2 0.984 1. 675 (f 1. 994 

4 68 4 0.976 1.497 ~g) 1.984 1 71 6 0.968 1.810 h) 1.40 .............. 72 5 1. 017 1. 679 (h) 1.40 ................ 73 4 0.967 1.612 (h) 1.40 ................ 74. 4 1.014 1. 229 (h) 1.40 

............. 84 2 1.014 1.033 ~ l) 1. 990 ............... 84 3 0.984 1. 246 i) 1.990 

.. ............. 85 1 0.998 1.011 ( i~ 1.990 

............... 85 2 0.997 1.218 (i, 1. 990 ............... 8.5 3 0.990 1.473 (i) 1.990 

.............. 88 1 0.995 0.894 rJ 1.990 

. ........... 88 2 0.986 0.921. i) 1.990 

........... 88 3 0.980 0.955 i) 1. 990 

.............. 88 4 0.993 1.010 (i) 1.990 

---

0.993 

e Rectangular covered wooden ehannel. 

f Rectangular open wooden channel covered with cloth. 

g Trapezoidal open wooden channel oovered with cloth. 

h Semicircular. 

i Rectangular. 
44 ACCURACY OF STREAM MEASUREMENTS. [NO. 95. 

In the first method the floats were run over a distance of 40 meters 

and the tube was held with its point 0.02 meter below the su·rface of 

the water. (}is found frmn '('= aJ"2q:E2d' '/) being known from the 

floats. In the second 1nethod the tube was fastened in front of a 

boat and was drawn through still water at different observed. velocities. In the third1nethod the instrument was he.ld at many points in 

a cross section of an experiment canal 2 meters wide the mean velocity in which was known, and the mean velocity as shown by the 

tube was computed. 

It is seen that the three values of C found by these three methods 

differ somewhat, although each is the· mean of many observations. 

The value found by the second method (the one now commonly used) 

is the largest of the three, at~d is rejected on account of the action of 

the boat on the instrument. The pull on the boat as it was drawn 

through the water tipped the point of the tube down slightly, making 

its indications less than they should be and making C too large. By 

the first method the mean of experiments Nos. 2 to 8 is 1.0016 and 

the mean of experiments Nos. 9 to 17 is 1. 0122. The difference 

between these is nearly 1 per cent of the former. The greatest variations frmn the mean of all the observations by the first method are 

+ 1. 8 per cent and -2.5 per cent. The value of 0 found by the third 

method is 0.99R, obtained from thirty-one measuren1ents of discharge 

of the experiment canal. The tube was held ·at man:r points in the 

cross section. The variations from this mean are +3.6 per cent and 

-2.8 per cent. Darcy uses the mean of the values found by the first 

and third methods, which makes 0 = 1. The extreme variations from 

this mean are +3.9 per cent and -3.5 per cent. The velocity of the 

water during these ratings varied from 0.5 to 2.5 meters per sec)nd, 

or from 1.64 feet to 8.20 feet per second. 

FORMULJE FOR COMPUTING DISCHARGE . . The discharge i~ a function of the cross section and velocity. Each 

of these factors must be measured at a sufficiently large number of 

points in the cross section to give the required degree of accuracy. 

For streams from 5 to 10 fc::et wide the depth should be measured· 

at each foot of width; for streams from 10 to 30 feet wide, at each 2 

to 5 feet of width; for widths from 30 to 100 feet, depths should be 

measured at each 5 to 10 feet, and for widths greater than 100 feet, at 

each 10 to 25 feet, depending on the width and unevenness of the bed. 

The general formula for the discharge per second is 

(1) 

~, F;, Jt~, etc., are the component parts of the cross section, and 

~' ~' V~, etc., the mean veiocity in each of these parts. If the 
MURPHY.] DISCHARGE FORMUiuE. 45 

width of these component parts is b and the 1nean depth in each is 

d1 , d2 , d3 , this formula can be written 

Q=b ( T~d + T~d + T~ds+ ..... ). (2) 

If d1 = d2 = d3 • • • • • , that is, if the channel i:-; rectangular in cross 

section, then formula (2) becomes 

Q=b(l ( T~+ ~+ T~+ ..... ). (3) 

The mean velocity of a component area may be computed from 

observations at its ends or at its center. Occasionally two consecutive 

component areas are considered tog ether arid the mean velocity for 

the double strip computed from observations at the ends and center of 

it. The mean velocity in a vertical is found '(1) from a single observation at same depth by applying a coefficient, as a mid-depth velocity 

observation multiplied by 0. 95, or a six-tenths-depth observation multiplied by unity, and (2) from a vertical velocity curve. The latter, as 

already explained, is found from numerous observations at points in 

the depth, and the mean veloeity in this vertical is then the area 

inclosed between the vertical curve and a vertical line representing no 

velocity divided by the depth. Harlacher,s method of integrating a in 

a vertical gives each component velocity very 1~eadily and quickly; any 

component velocity is Rj!, R being the observed revolutions, T the 

observed time in seconds, and 0 the number, which changes from 

revolutions to. velocity. 

In n1easuring the discharge of a large river the component velocities are always found from an observation at some given depth and 

the use of a coefficient. As the depth or stage of a river is almost 

constantly changing, it is-necessary to make the velocity observation 

in a short time-one or two hours at most. The value of the coefficient to use to reduce observed velocity at any depth to mean velocity 

in that vertical should be found from measurmnent if possible. 

The discharge measurements of the Niagara River made in 1897 

and 1898 by the United States Board of Engineers on Deep Water-· 

ways b fron1 the international bridge 3 miles below the head of the 

river were computed from velocity observations at three-tenths 

depth, using coefficients whose values were found from vertical velocity 

curves. The meter stations were about 80 feet apart and were at the 

middle of each half span of the short spans and at the middle of each 

one-third span of the long spans. The value of the coefficient for 

reducing observed velocity to mean velocity ranged from 0.61 to 1.17, 

being influenced by the piers of the bridge. 

The whole cross-section area can readily be computed from the 

formula: 

b . . F=3[d1+± (d +d~+d + .. +dn-1)+2 (d3+d5+ ... +dn)+dn+1] •• (4) 

a Proc. lnst. Civ. Eng., vol. 67, p. 358. bJm;tr. West. Soc. Eng., vol. 4,No. 6. 
46 ACCURACY 01!' STREAM MEASUREMENTS. [NO. 95. 

d0 d2 , d3 , etc., being depths and b the distance between the points 

where the depths are Ineasured; n is the number of component.areas 

and should always be an even number. This formula is based on the 

assumption that the bed is a parabolic arc between each double component area. 

When n=2, this formula gives the area of two consecutive component areas and becomes: 

F'=~(d +4 +d )=~(d +4 d2+d3) ------------ --------------- (5) 

e being equal to 2b. 

A some-what simpler formula for the area of two consecutive component areas is: 

F' = ( dt td2 + d2 t da) b = 1( ell+ 2d2 + da) - - ---- - - - --- -- -- -- - ~ - ( 6) 

T.V. Moore in his discharge measurements of the Thames a assumed 

the vertical velocity curve to be a parabola, and computed its area 

from the formula A=i[ T:+4 TTm+ T~], d being the Jepth, T: the surface velocity, v-m the velocity at mid depth, and T~ the bottom velocity. 

The discharge per second flowing between the end sections he computed from the formula V=~[~A +4~A +2~A ], h being the 

distance between the consecutive sections, ~A1 the sum of the two end 

sections, ~A2 the smn of t~e odd sections, and ~A3 the areas of the 

even sections. The discharge is found by adding to this the small 

volume flowing between each end section and the shore. 

T. G. Ellis, in computing the discharge of the Connecticut River in 

187 4, multiplied the velocity at mid depth in each component area by 

0. 95 to find the mean velocity in that area. b In computing the discharge of the Mississippi River in 1882 the velocity at Inid depth in 

each component area was multiplied by 0. 91 for the observations taken 

·when the river. was covered with ice, and by 0. 96 when free from ice, 

to reduce the mean velocity in a vertical. c From 1885 to 1887 the 

velocity at six-tenths depth was observed in the component areas, and 

this was taken as the mean velocity in each area. 

Harlacher's method of computing flood discharge where the surface 

velocity only could be measured is illustrated in fig. 14. d The surface 

velocity was measured at a sufficient number of points (1, 2, 3, etc.) 

in the cross section .. A. OB to determine the surface velocity curve 

ADB. The line A CB shows the depth at each point and is plotted 

from soundings taken immediately before or after the flood. 

The openings between EF and G .ll are bridge piers, the measure 

a Proc. Inst. Civ. Eng., vol. 45, p. 2'20. 

b Trans. Am. Soc. Civ. Eng., vol. 4, p. 303. 

<"Jour. West. Soc. Eng., vol. 3, No.3. 

dProc. Inst. Civ. Eng., vol. 91, p. 399. 
MURPHY.) COMPARISON OF RESULTS. 47 

ments being made from a bridge. The product of the surface velocity 

1-'s and the corresponding depth t is found for a sufficient number of 

points, depending on the irregularity of the bottom, and the curve 

FIG. H.-Diagram illustrating Harlacher's method of computing flood discharge. 

AEFG I£B drawn. The discharge per second is the area between the 

line AB and the curve·AEFGIJB, less the piers, multiplied by 0.85. 

COl\IP ARISONS Q]j-, RESULTS WITH Dl]j.,jj.,ERENT INSTRUMENTS AND METHODS. 

SURF ACE FLOATS AND PI TOT TUBE. 

On page 43 we have given the results of three ratings of a Pitot 

tube b.v Darcy and Bazin. ct In the first method the surface velocity 

was found fron1 surface floats and a Pitot tube, as already described. 

Ninety-two experiments were made. The results are combined, accord-

-ing to velocity, into seven groups of eight experiments each and nine 

groups of fo1u experiments each. The value of the coefficient as found 

from the fir~t seven groups differs from that found from the mean of 

the last groups by about 1 per cent. The extreme variations of these 

individual means from the mean of all the experiments are - 1.8 per 

cent and + 2. 5 per cent. The individual values of the coefficient are 

not given. Their extreme variation from the mean of all must be at 

least twice that of the individual means from the general mean. 

PITOT TUBE AND RECTANGULAR ORIFICES. 

On page 43 are given the results of a third rating of a Pitot tube 

by Darcy and Bazin (third method). This is also a comparison of the 

discharge of a canal 2 meters wide, as found from rectangular orifices 

and as found from numerous velocity measurements in a cross section 

of the canal with the same Pitot· tube. The di::;charge of the rectangular orifices admitting water to the canal was d.etermined by 

a Darcy and Bazin, Recherehes hydrauliques, 1865, pp. 63-70. 
48 ACCURACY 0~' STREAM MEASUREMENTS. [No.95. 

experiment for diffetent heads on them. The number of velocity 

measurements in each experiment or discharge measurement varied 

with the depth of the water in the canal, being from twenty-seven in 

the smallest channel, which was 0.30 meter by 0.48 meter, to ninety· 

one in the canal 2 meters wide. The points of measurement were 

nearest together where the velocity changed most rapidly. The 1:esults 

of thirty-one discharge measurements are given, the mean velocity 

varying from 0.38 meter to 2.57 meters per second. The extreme variations from the mean of all the values of the coefficient are + 3.6 per 

cent and - 2. 8 per cent. 

DOUBLE FLOATS AND CURRENT METERS. 

ELLIS,S EXPERIMENTS. 

In 1874 T. G. Ellis made numerous velocity measurements on the Connecticut 'River at Thompsonville, Conn., with current meters and with 

double floats like that shown in fig. 1, p. 15.a Vertical velocity curves 

were obtained in planes parallel with the axis of the river and 100 feet 

apart, with the meters and with the floats. Each of these curves was 

plotted on cross-section paper and divided into tenths of the depth. 

All of the curves in which the mean velocity was less than 1.86 feet 

were combined by combining all the observations at each tenth of 

depth; all in which the mean velocity was more than 1.86 feet were 

combined in the same way. From the resultant vertical velocity 

curves the results in the following table are taken: 

Comparison of velocity by double floats and current meters from measurements by T. G. 

Ellis on Connecticut Rive1· in 1874. 

Mean velocity, in feet per second, at various depths. 

Observations. Mean. VariaSur- 0.1 0.2 0.3 0.4 0.5 0.6 0. 7 0.8 0.9 Bot- tion. 

face. tom. ------------------------

Meter (av. veloci- P.ct. 

tylessthan) 1.86. 1.15 1.19 1. 2'-Z 1. 22 1.19 1.14 1.11 1.03 0.94 0. 79 0.46 1.063 } Float (av. veloci- 25. ty less than) 1.86. 1.50 1. 52 1.52 1. 53 1.49 1. 46 1. 35 1.29 1. 20 0.97 0.58 1.337 Meter (av. velocity more than) 1.86 ............. 2.96 3.08 3.12 3.06 2.99 2. 91 !!.78 2.62 2.42 2.16 1. 47 2. 735 ) Float (av. veloci- 5. ty more than) 

1.86 .. -···· ...... 3.26 3.24 3.17 3.17 3.11 3.01 2.94 2.80 2.60 2.35 1. 78 2.891 

8 

7 

All meter obser- vations ••.....•. 2.05 2.12 2.15 2.13 2.08 2.01 1. 93 1. 81 1. 67 1.47 0.96 1.887 } All float observa- 12. tions ............ ~.38 2.38 :.!.35 2.35 2.30 2.23 2.15 2.04 1. 90 1.60 1.18 2.114 o· 

It is seen from the foreg-omg table that the velocity as found with 

the meter is from 6 to 26 per cent less than that found with the floats, 

and that the dtfference between the-meter and float velocities increases 

as the velocity decreases. 

aRept. Chief Eng. U.S. A., 1878, Appendix B. 
MURPHY.] DOUBLE FLOATS AND CURRENT METERS. 49 

Ellis giyes also the following values of the ratio of mean velocity in 

a vertical ( l~,J to mid-depth velocity in that vertical (TTl .D) and the' 

ratio of distance below the surface of mean velocity (rn) to total 

depth (D). 

Mew~ ratios from vertical ·velocity curves obtained by Ellis on Connect·icut River ·in 1874. 

Observations. 

Meter at low velocities .....•................................................... Floats at low velocities ....................................................... . Mean of low velocities ........................................................ . Meter at high velocities ....................................................... . 

~~~:~s oi\!i~hh ;e~~occi~~~~:::::::::::::::::::::::::::::: _:::::::::::::::::::::::: Mean of meter measurements ................................................ . Mean of float measurements .................................................. . Mean of all measurements .................................................... . 

0.933 

0.918 

0.930 

0.939 

0.961 

0.944 

0.937 

0.947 

0.940 

0.£56 

0.622 

0.652 

0.628 

0.637 

0.629 

0.638 

0.632 

0.636 

From _the foregoing table it is seen that l~D varies from about 0. 92 

1n 

to 0.96 and]) from 0.62 to 0.66-about the same range of values. 

MARR'S EXPERIMENTS. 

In October, 1879, G. A. Marr made simultaneous velocity measurements of the Mississippi River at Burlington, Iowa, with double floats 

. like those shown in fig. 1 and with five current meters.(~ The river 

where measured was 'about 2,000 feet wide, and the path of the floats 

was near the center, where the depth was about 16.± feet. Ten floats 

were run in succession in a period of about twenty-five minutes over 

a distance of 200 feet, and the time of entering and leaving each 

quarter of the run was recorded on a ehronograph of eight pens. The 

five current meters were fastened to a cable held vertically 16 feet 

below the end of the run. One meter was at mid depth (the depth of 

the lower float), and the other four were arranged two above and two 

below it, so as to divide the depth jnto equal parts.. One pen of the 

ehronograph reeorded the time of passage of each float, two recorded 

the time as shown by a chronometer, and the other five recorded the 

revolutions of the five meters. From a table giving the velocity of 

each float over eaeh quarter of the run and the velocity shown by each 

of these meters during the time of passage over these distances the 

following table has been prepared. 

a McKenzie, A., Report on Current Meter Observations, Burlington, Iowa, 1884. 

IRR 95-04-4 
50 ACCUR-ACY OJ!' S1.'RE.AM MEASUREMENTS. [No. 95. 

Compa·rison of 'l'elocity by double floats and cm·rent meters .fro·rn measurements by G. A. 

Jfarr on Jfzssissippi River at Burlington, Iowa, October, 1879. 

I 

Mean velocity found from 200-foot run. Number Difference 

of fiaat. Float Meter O'm-l·j). 

( lj). ( Vm)· 

Ft. per sec. 1...... 2.543 Ft. per sec. Ft. per· sec. 2. 604 +0. 061 2...... 2. 741 2. 546 -0.195 3...... 2.634 2. 520 -0. 114 4...... 2.446 2. 435 -0. 011 5...... 2.850 2. 468 -0. 382 6...... 2.672 2. 700 +0. 028 7...... 2.514 2. 545 +O. 031 8...... 2.832 2. 457 -0. 375 9...... 2.476 2. 625 +0.149 10...... 2.829 

2.654 -- ::: /----~"·~: 

Mean velocity found from 50-foot run. Difference 

Float Meter (I'm)- Jj). 

( lj). (Vm). 

Ft. per· sec. Ft. per· sel'. Ft. per sec. 2.660 ::!.597 -0.063 2.976 2.657 -0.319 2.674 2.630 --0.044 2.456 2.481 +0.025 2.847 2.590 -0.257 2. 778 2.649 -0.129 2.674 2.484 -0.190 2.857 2. 749 -0.108 2.569 2. 821 +0.252 3.012 2.823 -0.189 

2. 750 2. 648 aa•••••••••• 

In the foregoing observations the velocity of a float was not the 

same over each 50-foot length of the run .. Each velocity given in the 

second column is a mean for the whole run of 200 feet, and the meter 

velocity in the third column is for the time of the full run. The 

velocity in the fifth column is for the fourth section of the run, and 

the corresponding num her in that column is the meter velocity for the 

next consecutive and equal interval of time. The chief thing to be 

noticed is that the float velocity, whether computed from the whole 

run of 200 feet or from the shorter run of 50 feet, is greater than the 

meter velocity by about 3.5 per eent. We may note also that we have · 

here forty Inid-depth velocities in nearly the same vertieal taken ,in 

about twenty-five minutes. · For the ten found from the floats on the 

long run the variations of velocity from the mean are from -7.4 per 

cent to +7.8 per cent, and for the short run of 50 feet the variations 

are from -9.5 per cent to +10.7 per cent. For the meter long run 

the variations are from -7.5 per eent to + 12.1 per eent, and for the 

short run from -6.5 per cent to +6.3 per. cent. 

Individual measurements of velocity by either of these methods 

differ much from the mean, but the means by the two methods differ 

little from each other. The excess of mid-depth velocity by double 

floats over that by meter may be due to the upper float dragging the 

lower one. 

HENRY'S EXPERIMENTS. 

D. F. Ilenry also gives a comparison of velocity measured with 

double floats like the one shown in fig. 1 (p. 15) and with current 

meter, made on St. Clair River in 1869. a The results of the comparison are given in the following table: 

aJour. Franklin Inst., vol. 62, p. 322. 
1\lURPHY.] DOUBLE FLOATS .AND CURRENT METERS. 51 

Comparison of 11eloc:ity by double floats and current 'meter from measurements by D. F. 

Henry on St. Cla·ir Rit,er in 186.9. 

Depth of Velocity of current. 

Number Direction and observa- of obser- velocity of tion be- vations. wind. low sur- Floats. Meter. Difference. 

face. 

]files per hou1·. Feet. Ft. per sec. Ft. per sec. Ft. per sec. 50 ..•... 3.26 up ....... 1 3.619 3.655 -0.036 62 ..... 1.92up ....... 5 3. 759 3. 783 --0.024 56 ...... 1.27up ....... 10 3. 703 3.674 +0.029 50 ...... 0.48up ....... 15 3.590 3.516 +0.074 &1 ....•• 0.29 down ••.• 20 3.598 3.405 +0.193 31.. .... 0. 53 up ....... 25 3.637 3.441 +0.196 37 ....•. 0.80up •...... 30 3.546 3.279 +0.267 29 ...... 2.18 down .... 35 3.556 3.166 +0.390 12 ...... 4.85 down .... 40 3.636 3.142 +0.494 7 ...... 0. 74 up ••..... 45 3.542 2.985 +0.557 

It is seen that the float velocity is less than the meter velocity to a 

depth of about 5 feet. Below that depth the float velocity is greater 

than the meter velocity, the difference increasing with the depth. The 

discharge as found with the floats is 10 per cent greater than that 

found with the meter. While the action o' the upper float on the 

lower float may not account for all the difference between the float 

and n1eter velocities, it will account for some of it. The velocity as 

shown by the vertical velocity curve increases from the surface to a 

depth of from 5 to 10 feet and then decreases to the bottom. The surface float will therefore move more slowly than the lower float for 

depths of from 0 to 5 or 10 feet, and hence the lower float will be 

retarded by the upper :float to that depth. For depths greater than 

10 feet the upper float will 1nove faster than the lower float and will 

drag it, and the velocity shown will be too large. 

Henry gives also a comparison of velocity as found with double 

float'S and current meter in a small canal- at Ogdensburg, N. Y. a _ The 

floats were run over a distance of 200 feet at 3 feet below the surface, 

the time being recorded on a chronograph. The current meter was 

held at the same depth at the middle of the run. The results are as 

follows: 

Comparison of 'Velocity by double floats and cur1·ent meter from measurements made by 

D. F. Henry ·in small can~tl at Ogdensburg, N. Y., 3 feet below surface. 

Number Velocity. 

of obser- vation!'l. Floats. Meter. Difference·. 

Ft. per sec. Ft. pe·r sec. Ft. per sec. 24 ...... 1.992 1. 980 -0.012 6 ••• : •. 1.876 1. 916 +0.040 6 ...... 1.476 1.434 -0.042 

These results indicate that although the mean of a few float observations may differ much from the corresponding meter velocity, the 

means for thirty or forty observations differ little. The meter gives 

a little less velocity than the floats. 

a Jour. Franklin Ins• '\Ol. 62, p. 259. 
52 .ACCURACY OF STREAM MEASUREMENTS. [NO, 95 . 

Henry also gives a comparison of velocity found with floats and a 

propeller meter in St. Clair River. The lower float was 1 foot below 

the surface, and the meter was held at the same depth. The mean 

velocity given by 50 floats was 3.619 feet per second; that by meter 

was 3. 655 feet per second, or 0. 036 foot per second greater than by 

floats. There was a light wind blowing upstream, which may have 

retarded the floats somewhat.· 

GORDON'S EXPERIMENTS. 

In 1873 Gordon made comparisons of the discharge of the Irawadi 

River at Saiktha, Burma, as measured with double floats and with 

current n1eter. From these he concluded that the double-float dis~ 

charge was about 10 per cent too large. ·He therefore reduced all 

discharges found with double floats by that amount. 

FLOAT RODS AND CURRENT METERS. 

NEW YORK STATE CANAL SURVEY EXPERIMENTS. 

During the progress of the New York State canal survey of 1900 

comparative discharge measurements were made on four occasions for 

the purpose of comparing the discharge of the canal as found by. one 

rod-measuring party with that found by another party using ~;imilar 

rods and Inethods, and of comparing the discharge found with rods 

with that found simultaneously with a current meter. The results of 

the comparisons are summarized in the following table: 

Comparison of ·results of experiments of New rm·k State canal surrey dur-ing the summer 

of 1900. 

Place. Date. l

..,, ,. +Q',. Q'r Q"r 

l',. Q'r I Q",. • Qm Q~p;; 3~-~ ~~:·-; ------]-------------------------------

Ft. per 

1900. sec. Lockport...... .. . Sept. 14 ...... .. Rochester........ Sept. 20 ....... . Do .. .. . .. .. .. Sept. 21 0. 893 Do ............... do.' ......... . Do ............... do ......... .. Boonville........ Sept. 25 1.073 Do ............... do ......... .. Do ............... do .......... . Glens Falls . . . . . . Oct. 8 0. 821 Do ............... do... 0. 756 

Ft.per Ft.per Ou.jt. Cu.jt. Ou.jt. sec. sec. per sec. per sec. per sec. Per ct. Per ct. Per ct. 1.440 1.531 ........ 805.70 799.85 .. .. . ... .... .. .. +O. 73 0. 704 0. 736 -....... 235.12 251.57 .. .. .. .. .. .. .... -7.00 0.884 -....... 297.82 302.04 ........ -1.41 .............. .. 0. 889 0. 929 .. .. .. .. 301. 3fr 310.83 .. .. .. .. .. .. .. .. -3.14 0.899 0.939 ........ 307.08 317.54 ........ ........ -3.46 0. 813 -.. -.... 227. '12 '2'27. 51 .. .. .. .. -0.13 .............. .. 0.850 1.079 ........ 238.81 228.66 ........ ........ +4.25 0. 836 1. 111 .. .. .. .. 233. 54 234. 70 ............... - -0. 49 0. 690 .... -.. - 1fl4. 73 172.77 161.50 -4.88 +1. 94 +6. 52 0. 640 .. .. .. .. 149.66 158.57 155.23 -5. ~2 -3.72 +2. 11 

l".=mean velocity found by party No.1, with rods. 

F',=mean velocity found by-party No.2, with rods. 

r;n=mean velocity found with meter, using six-tenths-depth method. 

Q'.=discharge found by party No.1, with rods. 

Q".=discharge found by party No.2, with rods. 

Qm=discharge found with meter, using six-tenths-depth method. 

The Lockport experiments . were made on the Erie Canal about 1 

mile above the locks at Lockport; in a rock cut with rough, nearly 

vertical sides. The meter measurements were made 700 feet above 
MURPHY.) FLOAT RODS AND CURRENT METERS. 53 

the place where the discharge was measured with rods. The observations extended over a period of thirty-four minutes, during which 

time 60 rods were passed over a run of 21 feet, with an immerRion of 80 

to 90 per cent of the depth, and 13 meter observations of fifty ~econds 

each were made at six-tenths depth below the surface. There was no 

measurable fluctuation of surface level during the test. 

The Rochester experiments were made on the Rochester Aqueduct, 

which has smooth and nearly vertical sides. The width was 4:3 feet 

and the depth 7.5 feet. The flow was undisturbed for a half mile 

above the section of measurmnent, but there was a sharp curve less 

than 100 feet below the point where the lower rod-measuring party 

was stationed. In the first compari~on of rods with meter, September 

20, the period of observation was forty-two minutes; 6± rods were 

passed over a 20-foot run with 92 per cent depth of immersion; 19 

meter observations of fifty seconds each were made by the six-tenthsdepth method; the surface level fluctuated 0.05 foot during the observations, and. rain interfered somewhat with the work. In the first 

rod comparison, September 21, the ohservations extended over a 

period of sixty-five minutes; 79 rods were passed by party No .. 1, with 

a depth of immersion of from 90 to 97 per cent, and 100 .rods by par.ty 

No. 2, with a depth of irpmersion of 92 per cent. In the first rodand-meter comparison of September 21 the period of observation was 

forty-two minutes; 92 rods were passed by party No. 2, with 90 per 

cent depth of immersion, and 36 meter observations of fifty seconds 

each were taken by the six-tenths-depth method. In the second rodand-meter comparison the period of observation was forty minutes; 80 

rods were passed, with 92 per cent depth of immersion, and 36 meter 

observations of fifty seconds each were made at six-tenths depth. 

The Boonville comparisons were made on the Black River Canal at 

Boonville, where the top width of the canal is 43 feet, with gradual 

sloping sides, and a maximum depth at center of 7. 7 feet. There was 

an unobstructed flow for at least one-fourth mile above and one-half 

mile below the place selected. The parties were stationed about 200 

feet apart. There was practically no water entering or leaving the 

canal between these points. In the rod comparison, which lasted one 

hundred and forty-four minutes, with some interruptions, 185 rods 

.were passed over a 20-foot run by party No. 1, and 1±3 rods by party 

No. 2. In the first meter comparison, which lasted fifty-eight minutes, 55 rods were passed and 36 meter observations were made at sixtenths depth. In the second meter comparison, which lasted fiftythree minutes, 77 rods were passed and 42 meter observations of fifty 

seconds each were made by the six-tenths-depth n1ethod. 

The Glens Falls comparisons were made on the Glens Falls feeder, 

near Glens Falls. At the pla~e selected for the tests the feeder is 32 

feet wide and 6 feet deep, with nearly vertical sides. There is a bend 
54 ACCURACY OF 'STREAM MEASUREMENTS. [NO. 95, 

in the feeder about 100 feet above the upper place of measurement, 

and another about 1,000 feet below the lower place of measurement. 

The meter measurmnents were 1nade from a bridge about 100 feet 

from each of the points where the rod 1neasurements were made. The 

first comparison lasted seventy-six minutes, during which time party 

No.1 passed 56 rods, party No.2 passed 90 rods, and 28 meter observations of fifty seconds each were made. In the second comparison, 

which lasted fifty-eight n1inutes, party No. 1 passed 63 rods, party 

No.2 passed 108 rods, and 28 meter observations of fifty seconds each 

were made. 

The method of making these comparisons is the same as that used 

in the canal-discharge measurements, which is described on pages 

16, 17. 

The Rochester and Glens Falls comparisons are not so satisfactory 

as those at Lockport and Boonville. In the former the measurements 

were made too nea,r a curve. The huge variation in the time of run 

of the individual rods indicates this fact, and surface-level fluctua. 

tions and passing boats interfered somewhat with the work. There is 

a possibility of leakage from the feeder between the points of Jneasurement at Glens Falls. No leakage was visible on the surface, but 

there is a large amount of leakage not far distant from the place of 

measurement. The measurements there indicate a gradual loss from 

the upper to the lower point of measurement. 

The results of the rod comparisons agree more closely than those of 

meter with rods. It must not be concluded fron1 the Rochester comparisons that because the rod discharges agree closely and the meter 

discharge differs from the rod discharge 7 per cent this error is all 

due to the meter. The two sets of velocity 1neasurements obtained 

with the meter during this comparison agree closely, whereas the time 

of run of the individual rods differs considerably. At least half of this 

difference is due to errors in the rod discharge measurements. 

FLOAT RODS AND WEIR. 

FRANCIS'S EXPERIMENTS. 

In 1856 J. B. Francis compared the discharge of a canal at Lowell, 

Mass., as found with float rods with that shown -by a standard weir. a 

This wooden ·canal or. flume was 27.75 feet wide where the first 63 

experiments were 1nade and 14 feet wide where the remaining 52 

experiments were made. The length of run was 70 feet, with a starting run of 28 feet. The time of run was obtained to a tenth of a second 

and the depth to 0.0001 foot. Every precaution was taken to obtain 

accurate results. The floats were tin tubes, 2 inches in diameter, 

a Francis, J. B., Lowell Hydraulic Experiments, p. 170. 
MURPHY,] FLO.AT RODS AND WEIR. 55 

loaded at the lower end so as to float upright. They were put in the 

water at each foot of width of the canal, and the time of run was 

recorded on a chronograph. The observed velocities were plotted on 

cross-section paper and a mean curve was drawn among the points 

showing change in velocity from one side of the canal to the other. 

The mean velocity in the cross section was found from this curve by 

dividing the velocity area by the width. The variation of the observed 

velocities of individual rods from the velocity curve was from 8. 57 

per cent above to 11.± per cent below this curve in experiment No. 1. 

The rods used were not all of the proper depth of immersion, and 

Fran~is derived the following formula for computing the .correct discharge: Q'"= Q"[1-0.116(v D-0.1)], in which Q" is the measured 

discharge and D the depth of water in the flume less the depth of the 

immersed part of the rod, divided by the depth of water in the 

flume. After applying this formula he found that the variation of 

the rod discharge from the weir discharge for the 115 experiments is 

as follows: For 9 it is less than 0.1 per cent; for 79 it is less than 1 

per cent, for 23 it is from 1 per cent to 1.9 per cent, for 2 it is from 

2 per cent to 2.9 per cent, and for 1 it is 3.69 per cent. The mean 

veloeity in these experiments varied from 0.5 foot to 5 feet per second. 

CORNELL UNIVERSITY EXPERIMENTS. 

At the close of the field work of the New York State eanal survey 

of 1900 a series of experiments was made at the hydraulic laboratory 

of Cornell University for the purpose of comparing discharge as found 

with rods and current meter on the canals with that shown by the 

Cornell standard weir. These experiments were planned by the consulting engineer of the New York State canal survey, Mi·. E. Kuichling, and were carried out under the direction of Prof. G. S. Williams, 

in charge of the hydraulic laboratory, by the writer and by Mr. W. P. 

Boright, C. E., assisted by members of the class in hydraulics. 

The surface level of the seetions of the canals fluctuates rapidly on 

aceount of loekage of boats and irregular feed of water to lower sections. It was therefore necessary to make diseharge measurements 

rapidly and to make short runs and starting runs. The depth of water 

in the different sections varied from 5 to-10 feet at the eenter, so that 

the immersed portion of the rods used varied from 75 per cent to 95 

per cent of the depth of the water. The mean velocity varied from 

nearly 2 feet per second west of Lockport to 0 on the summit levels. 

In the laboratory experiments the eonditions were duplieated as closely 

as possible and the work was performed in the same way as on the 

canals, so that the results of the comparisons give a fair idea of the 

accuracy of the discharge me~surements of the State eanals and feeders. 

-Pl. II shows the laboratory canal and the observers employed in 
56 ACCURACY OF STREAM MEASUREMENTS. [No. 95. 

making the tests. A description of the laboratory and of the method 

of obtaining standard weir discharge will be found on pages 60 to 65. 

The gates at the head of the canal were opened until the head on the 

weir was such as to give the desired discharge; then the slits in the 

bulkhead and the height of the gates at the lower end of the canal 

were adjusted :-;o as to give the desired depth of water in the channel. 

As soon as the flow became :-;teady three parties began measuring the 

discharge of the canal, one with rods and two with current meters. 

Two series of rods were used, one of 75 per cent depth of immersion, 

the other of 90 per cent depth of immersion, the former lettered, the 

latter numbered, so that they could easily be recognized as they 

passed unde·r each wire. The lengths of the run and of the starting 

run were the same as in the canal work, being from 25 to 7 feet for 

the former and from 10 to 8 feet for the latter, depending on the 

velocity. The number of rods used in an experiment varied from 

50 to 150. Meter party No. 1 measured the discharge by the sixtenths-depth and the integration methods, and then a.ssisted the rodmeasuring party, four stop watches being used and the number 

of t:ods run in a ghren time nearly doubled. During eaeh experiment the head on the weir, the depth of water in the canal, and the 

slope of the surface were read every thirty seeonds and were checked 

occasionally by readings of the hook gage. The time of run of each 

rod wa.s platted on squared paper, using distance from side of canal 

as abscissffi and time of run, in seconds, as ordinates, and a mean 

time curve was drawn among them. The length of run divided by 

the mean ordinate of this curve gave the mean velocity, which multiplied by the cross-sectional area gave the discharge. The results 

of this rod-and-weir discharge comparison are given in the following 

table: 
U. S. GEOLOGICAL SURVEY WATER-SUPPLY PAPER NO. 95 PL. li 

HYDRAULIC LABORATORY OF CORNELL UNIVERSITY, SHOWING CORPS ENGAGED IN MAKING DISCHARGE EXPERIMENTS 
MtJRPHY.] ROD AND WEIR MEASURFJMENTS. 57 

Compari,son of float-rod and -weir velocity and d·ischarge measurements at Cornell hydraulic 

laboratory. 

.0 Rod gagings in laboratory canal. Mean error 

~~ Error of dis- of dis-

""' .s Immersion, 751 Immersion, 90 charge re- charge re- ooO ·~ <:.> <:.> <lJ<lJ per cent. per cent. ferred to ferred to ""g) iJ::"'· I'< standard weir. standard <lJ I'< .& """ s~ o:l weir. Date. 0~ 8Q;I i:::oa a;.~ """'bO 

'0~ Ve- Dis- Ve- Dis- b()QJ I'< locity locity 75per 90per 75 perloo per »o:l charge charge ~~ ;;::.c:l. per per cent cent cent cent 

.c:l"' <:.>O"i:j 

~ sec- per sec- per im- im- im- im- 01'< ~;8§ on d. second. on d. second. mer- mer- mer- mer- -~ ~ <lJ 

A > A sion. sion. sion. sion. ----------------------

19()[1, Ou.jt. Feet_ Feet. Feet. Ou.jt. Feet. Cu.jt. Pe-r ct. Per ct. P. ct. P.ct. October24 ..... -~214. 588 1.428 9.356 1.422 213.674 ............. ......... ~ ...... +0.43 

}·-~ Do . ________ . 140. 514 0.945 9.253 0.962 142.966 0.949 141.034 -1.74 -0.37 0. 75 Do ____ .--- --1 71. 670 0.484 9.222 0.490 72.621 0.476 70.546 -1.3:3 +1.57 Do _______ . __ 38. 308 0.269 8. 789 0.276 38.990 0. 272 38.425 -1.78 -0.31 October 26 ... ___ 178.553 1.473 7.543 1. 510 183.185 1. 525 184.832 -2.59 -3.52 

fa.96 Do __________ 125.29il 1.033 7.549 1.080 131.000 1.058 128.332 -4.55 -2.42 2.09 October27 .... __ 61.272 0.510 7.471 0.530 63.658 0.520 62.457 -3.89 -1.93 Do .......... 30.089 0.254 7.376 0.266 31.543 0. 255 30.239 -4.83 -0.50 Do ...•...... 196.387 1. 983 6.163 2.067 204.695 2.044 202.407 -4.23 -3.06 

~-" Do __________ 132. 408" 1.308 6. 299 1.363 137.956 1.341 135.730 -4.19 -2.51 2.95 Do .......... 91.056 0.910 6.228 f), 953 95.372 0.944 94.471 -4.7i -3.64 Do .......... 50.309 0.535 5.847 0.555 52.176 0.549 - 51.612 -3.71 -2.59 

October 31 _ ..... 198.258 1. 475 8.365• 1.537 206.554 1.507 202.523 -4.18 -2.15 

~.re Do .......... 125.299 0.930 8.393 0.958 129.174 ........... ............ -3.09 2. 78 October29 ...... 65.287 0.486 8. 3.55 0.512 68.766 0.501 67.288 -5.33 -3.07 November!---- 31.140 0.235 8.255 0.249 33.043 0.242 32.114 -6.11 -3.13 ---- 3.54 2.14 

It is seen that the discharge obtained with the rods is larger for all 

depthA, velocities, and percentage depths of immersion than the corresponding weir discharge, except in two cases. The greatest variation from the weir discharge is 6.11 per cent for the 75 per cent depth 

of immersion and 3. 64:- per cent for the 90 per cent depth of immersion. This variation from the weir discha-rge, or error, increases as the 

depth, velocity, and depth of immersion decrease. The mean error 

for all depths and velocities is 3.54 per cent for the 75 per cent depth 

of immersion and 2.1 ± per cent for the 90 per cent depth of immersion. 

The greatest variations from these means are + 1.14 pet• cent and 

-2.22 per cent for the 75 per cent depth of immersion and +0.81 per 

cent and -1.39 per cent for' the 90 per cent depth of immersion, a 

range of 3.4 per cent in the former and 2.2 per cent in the latter. 

From the last two columns is seen the extent to which the error 

increases as the depth decreases. 

It is to be expected that the rod discharge will be greater than that 

of the weir, especially for the 75 per cent depth of immersion, for as 

the rods do not extend to the bottom they are not affected by the bottom layers of slowly moving water, and hence move faster than the 

mean velocity. By applying Francis's correction formula {p. 55) to 

these results others will be obtained agreeing more closely with those 

shown by the weir. It will be shown further on {p. 93) that the weir 

discharges used in these experiments and computed from Bazin's 

formula are probably too small by from 0.5 per ce~t to 2.5 per cent, 
58 .ACCURACY OF STREAM MEASUREMENTS. (NO. 95 • 

the former for a head on weir of 1 foot, the· latter for a bead of 2. 5 

feet. When these two sets of corrections are applied it will be found 

that the rod discharge is correct to within about 2 per cent. This 

degree of accuracy is only attained, howeyer, by 1nany observations, 

equivalent to six or twelve gagings, with the rods started 2 feet apart 

from side to side of canal. a 

CURRENT METER AND WEIR . 

. FTELEY AND STEARNS'S EXPERIMENTS. 

Fteley and Stearns have made some comparisons of the discharge of 

. the Sudbury conduit as obtained by weir measurement and by current 

meter. b The weir was of the sharp-crested type, 19 feet long, and was 

located at the head of the conduit. The flow to it was controlled by 

rectangulal' gates, which were changed slightly from time to time so 

as to keep the head on the weir constant. The current-meter measurements were made from a manhole in the conduit 6,000 feet below the 

weir. The meter used was a Fteley like that shown in fig. 5, p. 22. 

Two methods of operating the meter were employed, viz, the point and 

the integration. When the point method was used the n1eter was 

held for thirty seconds at several points in the cross-sectional area. 

depending on the depth. For the greatest depth of 4:.5 feet the number of points of observation was 167. The rate of moying the meter 

while integrating was from 0.1 foot to 1 foot per second. The results 

for the 8-vane meter are as follows: 

Comparison of dischm·ge ·measured with 8-vane .Fteley meter and Ol'er 1ceir. 

Number Depth of Ratio of Variation of com- No. of parisons Rate of in- center of speed of Mean ve- of meter ex peri- meter meter to locity of discharge ment. included tegration. from speed of water. from weir inexperi- surface. water. discharge. ment. 

Feet Ft. per sec. Pacent. 1 1 0 1.5 0 1.83 +1.2 2 2 0 2.0 0 2.13 0.0 3 1 0 3.0 0 2.56 +0.1 4 1 0 4.0 0 2.83 +0.1 5 1 0 4.5 0 2.93 -0.4 & 1 0 3.0 0 1.71 -0.2 7 3 0.1 1.5 0.055 1.83 +0.8 8 3 0.1 2.0 0.047 2.13 +0.1 9 8 0.1 2.5 0.042 2.37 -0.6 10 3 0.1 3.0 0.039 2.56 -0.2 11 6 0.1 3.5 0.037 2. 71 -0.1 12 4 0.1 4.0 0.035 2.83 -0.5 13 4 0.1 4.5 0.034 2.93 -0.8 14 4 0.1 2.5 0.042 2.37 +0.2 15 1& 0.5 2.5 0.211 2.37 -3.6 16 15 0.5 3.5 0.185 2. 71 -1.8 17 20 1.0 3.5 0.369 2. 71 -6.5 18 3 0.1 3.0 0.058 1.71 -1.0 19 4 0.5 3.0 0.292 1.71 -4.5 20 7 1.0 3.0 0.585 1. 71 -9.4 

a See also pp. 90-93. 

bTrans. Am. Soc. Civ. Eng., vol. 12, p. 301. 
MURPHY.) CURRENT-METER AND WEIR RXPERIMENTS. 59 

The resultg of experiments Nos. 2 to 6 show a remarkably close 

agreement between measurements by this n1eter and those over the 

weir. The length of an observation, thirty seconds, was too short to 

give a good average indication of the velocity. The diseharge varied 

somewhat during the experiment. The depth of water in the conduit 

being small, any error in the depth must have introduced considerable 

error in the result. " 7 e would not expect, therefore, so close an agreement, which appears all the more remarkable when it is seen :from the 

following table that the discharge shown by two weirs may differ by 

3 per eeut: 

Vctlues of m in.formula Q=mlh ../ :Jgh, a:s .fownd by Bazin and by Fteley and Stearns.a 

Values of 111. 

Head on Fteleyand m1-m2 

m1-m2 

weir (h). StearnR Bazin 'In I 

(Ill<,!). (mi)· 

Jfeters. JJieters. Meters. JJieters. Pe1· cent. 0.1424 0.4149 0.4290 0.0141 3. 29 0.1969 0.4166 0.4263 0.0097 2. 28 0.2497 0.4191 0.4259 0. 0068 1.60 0. 3008 0.4218 0.4266 0. 0048 1.12 0.3.')30 0. 4247 0.4276 0.0029 0.6S 0. 3957 0.4272 0.4285 0.0013 0.33 0.4434 0.4296 0.4295 0.0001 0.02 0.4888 0.4323 0.4310 -0.0013 -0.33 

aAnnales des ponts et chaussees, memoireR et documents, 1888, p. 416. 

It is seen that for heads on the weir of :from 0. 5 foot to 1 foot the 

. variation in ·m is from 3 to 1 per cent. 

EXPERIMENTS AT CORNELL UNIVERSITY HYDRAULIC 

LABORATORY. 

INTRODUCTION. 

The results of numerous weir, current-meter, and other experiments 

by the writer at the Cornell hydraulic. laboratory are discussed in 

detail on the :following pages; also the application of the results to 

ordinary river gaging and the general conclusions reached from these 

recent studies and investigations. 

The investigation was begun by the writer in May, lHOO, while a 

fellow in civil engineering at Cornell University. It was interrupted 

from July 1 to December 4 of that year, on account of the New York 

State canal survey, in which the writer participated, and again from 

December H to April1, on account of freezing weather, and was completed in May, 1901. Its object was -to eompare the discharge of the 

Cornell University experiment canal as obtained with a sharp-crested 

weir with that obtained from current meters operated by different 

methods, and thus determine the accuraey of velocity and discharge 
60 ACCURACY OF STREAM :MEASUREMENTS. [No. 95. 

obtained by current-meter methods. The scarcity of meters available 

for the work, the lack of ready facilities for frequent testing and rating of the meters used, and the scarcity of water during the first 

months of the investigation render the results somewhat less valuable 

than they otherwise would be. 

The writer takes this occasion to acknowledge his indebtedness to 

Mr. F. H. Newell, chief hydrographer of the United States Geological 

Survey, for his hearty cooperation; to Prof. E. A. Fuertes, director 

and dean of the College of Civil Engineering, Cornell University, for 

the use of the hydraulic laboratory and a chronograph, computing 

machine, current meter, and electric register, and for kindly interest 

in the work; to Prof. GardenerS. Williams, in charge of the hydraulic 

laboratory, for many valuable suggestions and for the use of a chart 

for converting head on the Cornell University standard weir into 

cubic meters; also to Mr. C. E. Torrance, scholar in civil engineering, 

to members of the senior class in civil engineering, and to Mr. C. D. 

Cass, assistant mechanician of the college, for their cheerful assistance. 

DESCRIPTION OF CORNELL HYDRAULIC LABORATORY. 

The Cornell hydraulic laboratory consists essentially, as shown 111 

Pis. II, III, and IV and fig. 15, of a canal16 feet wide. 10 feet deep, 

and 415 feet long, with concrete bottom and sides and with a bed 

slope of 1 foot in 500. There are six rectangular gates at the upper 

end for controlling water entering the canal and four gates near the 

lower end, two on each side, for controlling the depth of water in the 

canal. Fifty-nine feet below the entrance gates is a bulkhead about 

10.5 feet high built of 12-inch by 12-inch timbers. On the top of this, 

or 11.1 feet above the bottom of the canal, is fastened a steel angle ~ 

iron 3.5 inches by 5 inches by 16 feet long, with edges five-sixteenths 

inch thick, which forms the standard sharp-crested weir. The lower 

end of the canal is closed with 12-inch by 12-inch timbers, which can 

be moved up or down if desired. so as to allow the. water to pass out 

of the canal at the end instead of under the side gates. In the upper 

chamber are two sets of baffies for checking the velocity of the water 

after it passes under the entrance gates. One of these is 7.4 feet 

from the gates and is made of ±-inch by 12-inch timbers placed hori:. 

zontally, with the wide face toward the current and- spaced from 8 to 

12 inches apart. On the. upper side of these timbers are l-inch by 

6-inch strips, fastened diagonally and spaced 12 inches from center to 

center. The second baffie is about 6.5 feet below the first one and is 

similar in construction, except that the 1-inch by 6-inch strips are 

placed vertically and are spaced 10 inches from center to center. 

Twenty-eight fee.t below the weir is a baffle made of l-inch by 6-inch 

strips placed 3 inches from center to center, with the narrow side 
U. S. GEOLOGICAL SURVEY WATER - SUPPLY PAPER NO. 95 PL. Ill 

FLUME, PENSTOCK, AND WHEEL HOUSE OF CORNELL HYDRAULIC 

LABORATORY CANAL, 
MI_:RPHY.] CORNELL HYDRAULIC LABORATORY. 61 

toward the current. To still further quiet the waters after passing 

the weir, when the depth is small and the velocity large, a second 

baffie was constructed of l-inch by 6-inch pieces placed vertically, 

spaced 2 inches from center to center~ and fastened on the upper side 

of the baffie just described. 

Air is admitted under the falling sheet of water through 12-inch by 

10-inch passages in tl~e concrete, one on each side of the weir. The 

head of the weir and the depth of water in the canal are measured by 

piezometers and a hook gage. As rough checks on these readings 

gage boards and a dial gage were occasionally read. The piezometer 

for giving the head on the standard weir is formed of three l-inch pipes 

(1), P, P, fig. 15) perforated for 3 feet of their length with ±-inch 

holes iJ inches apart around the pipes. These are placed 27 feet 

upstream from the weir, with their axes parallel with the ~xis of the 

FIG. 15.-Plan and elevation.of Cornell University experiment canal. 

canal, 4 feet from the bottom, and each connected to a pipe which 

extends down the south side of the canal to a point opposite the gage 

house. From this point it is carried across the canal along the bottom and up into the gage house and is connected to a glass tube by a 

rubber hose. The tube is fastened to a scale marked to 2 mm. spaces. 

The canal piezometers are similar to those of the weir, but have only 

one entrance pipe, which is in the center of the canal. The surface 

elevation of the water was read with the hook gage at the three points 

in fig. 15 marked "Standard weir bolt," "Croton bolt," and "Canal 

bolt," the elevation of each of which is known. The dial gage and 

the board gage G' show approxin1ately the head on the standard weir 

in feet and hundredths and enable the man operating the gates to 

keep a nearly constant head. A board gage ( G") opposite the" Croton. 

bolt" ( OB) shows approximately the depth of water in the canal. 
62 ACCURACY OF STREAM MEASUREMENTS. [NO. 95. 

SCOPE OF EXPERIMENTS. 

The experiment~; naturally divide themselves into five groups, which 

we have called series A, B, C, D, and E. The experiments of series 

A were made at a section 158 feet below the standard weir and 75 feet 

upstream from a model of the Croton dam the height of which was 6 

feet and the upstream face of which had a gradual slope and extended 

to within 29 feet of the meter station. This Inod·el dam formed a pool 

above it at the meter station and gave a zero velocity for 6 feet depth 

of water. The range of depths and velocities was therefore small. 

The water surface during the experiments was smooth, without boiling 

or swirls, with most of the foam made by the water falling over the 

weir moving down in two parallel lines 3 or 4 feet from each side. 

Three current meter:-3 were used in this series of experiments, viz, 

large Price meter No. 88, small Price meter No. 351, and the Cornell 

University Fteley meter. The latter w:ts always held with a rod, the 

small Price meter with a cable, and the large Price meter with a -cable 

in some of the experiments and with a rod in ot-her experiments. 

About 3-l- inches of n1ud had accumulated on the bottom of the canal 

above the model dam. After the first two experiments the mud was 

removed for a space of 4 or 5 feet above and below the meter station. 

For all other experiments the bottom was clean and smooth. 

The experiments of series B were made 234 feet below the standard 

weir after the model dam had been removed. They were with 

high velocities and shallow depths, the scarcity of water at the time 

restricting the depth soniewhat. In all these experiments except 

Nos. 6 and 8 the tail gates we.re open, so that there was no backwater. 

·The surface of the water was quite rough, being a succession of waves, 

without swirls or boiling. (See Pl. IV.) The same three meters were 

used as in series A. The Fteley and the large Price were held with 

rods-the small Price with a rod in some ~f the experiments and with· 

a cable in other experiments. 

The experiments of series C were made 280 feet below the standard 

weir, as part of the tests of accuracy of the discharge measurements 

of the New York State canals and feeders made during the summer of 

1900. They cover a range of depths from 6 to 9.5 feet and velocities 

from 0.23 foot to 2 feet per second. In most of the experiments of 

this series nearly all of the water w~s passed out of the canal through 

horizontal slits in the bulkhead. The-water surface was comparatively 

smooth, being a succession of long waves, without boiling or swirls. 

Two meters were used-small Price No. 363, operated by the sixtenths-depth and integration methods, and small Price No. 35L operated by the ordinary method. The former was held with aeable,'the 

latter with a rod. 

The experiments of series D were made 220 feet below the standard 

weir,·with Haskell meter No. 3 and small Price n1eter No. 363, each 
U. S. GEOLOGICAL SURVEY WATER-SUPPLY PAPER NO. 95 PL. IV 

CORNELL HYDRAULIC LABORATOR Y CANAL, SHOWING DISTURBED WATER SURFACE. DURING 

EXPERIMENTS IN SERIES B. 
MlJRPHY".] METHOD OF EXPERIMENTATION. .63 

held with a cable. The range of depth was fron1 5 to 9.5 feet, and the 

velocities from 0. 25 foot to 2 ~eet. The water surfu.ce was like that in 

series U-long waves, without boiling or swirls. Three methods of 

obtaining velocity were used-the ordinary, the six-tenths, and the 

integration. This series is not complete, the work being stopped by 

the freezing of the canal. The piezometers could not be used on 

account of the freezing of the pipes. The hook gage only was used 

to measure the head on the weir and the depth of water in the canal. 

The experiments of series E were made with two small Price meters 

and a Haskell meter, held with cables at station 220 feet below the 

standard weir. 'rhe depth in this series varied from 4.6 feet to 9.3 

feet, and the mean velocity from 1. 5 feet to 3 feet per second. It was 

designed to extend the results of the previous year to the higher 

velocities. The discharge measurements were made in pairs, as in 

series D, so as to compare the results of the meters with each other 

as well as the results of each meter with the corresponding weir discharge. The head on the weir and the elevation of water surface 

were obtained from readings of the portable hook gage. The water 

surface was quite rough for these higher velocities, being a succession 

of waves, without swirls. To quiet it and enable the surface elevation 

to he more accurately measured, in experiments 9 to 22 two planks, 

2 inches by 12 inches by 15 feet long, were placed across the canal 

about 3 feet apart and 154 feet from the weir, fastened at the ends so 

as to float on the surface and break the force of the waves. In experiments 23 to 50 three of these planks were used. The planks served 

their purpose very well, but distorted somewhat the vertical velocity 

curves. 

. METHOD OF EXPERIMENTATION. 

The first operation in each experiment was to adjust the entrance 

gates to admit such a quantity of water that with the desired depth of 

water at the meter stution the velocity would be about the desired 

rate. The tail gates were then opened or closed somewhat, as the 

case required, until the water reached the desired depth and remained 

steady. The standard weir gage was then read every thirty seconds 

and the canal gages (one or both) were read every five minutes during 

the time the meter observations were being taken. When the hook gage 

was used it was read six times in succession, as quickly as possible, at 

each of the three points in fig. 15 marked '"Standard bolt," "Croton 

bolt," and •' Canal bolt,'' ali·eady described. When the ordinary method 

of operating the n1eter was used the meter was held at from two to 

six points, depending on the depth, in each of from five to·eight verticals, and the number of the revolutions of the meter wheel in from 

one to two periods of from thirty to sixty seconds each was obtained. 

Usually it was two periods of fifty seconds each. In series C, ordinary 

method, one period of sixty seconds was used and the revolutions were 
64 .ACCURACY OF STREAM MEASUREMENTS. (NO. 95 • 

read on n. recorder. In all the other experiments, except those with 

the Fteley meter, the revolutions were obtained from indications of au 

electric buzzer. When the meter was operated by the six-tenthsdepth method it was held at about six-tenths depth below the surface 

in eight verticals, viz, 1, 3, 5,"7, 9, 11, 13, and 15 feet from the south 

side of the canal, and the revolutions were obtained for two periods 

of fifty seconds each. The meter was then held at the same depth in 

the same vet·ticals in the inverse order, i. e., 15, 13, etc., 1 foot from 

the south side of the canal, and the revolutions were again counted for 

two periods of fifty seconds each. When the integration method was 

used in series C the meter was moved in the following way: It was 

started at 1 foot from the bottom (center of meter 0.5 foot above bottom) and 1 foot fron1 the side of the canal, and was passed slowly to 

the surface at ±. 5 feet from the side, then to the bottom at 8 feet from 

the side, then to the surface at 11.5 feet from the side, and then to the 

bottom at 15 feet from the side. The time at the beg-inning and end 

was noted and the total number of revolutions were counted. The 

meter was then carried back over the same path at about the smne 

speed, and the time of passage and the number of re,rolutions were 

obtained as before. The mean time and the mean number of revolutions of these two passages across the canal are used as a sing-le experiment. 'Vhen this method was used in series A the meter was carried 

only once across the canal, and it was started and stopped at the bottom (center of meter 0.5 foot above bottom) and close to each side, 

and reached the surface 4 feet and 12 feet from the south side of the 

canal. When this method was used in series E the meter was nwved 

slowly from the surface to the bottom (center of meter from 2.5 inches 

below surface to 5. 5 inches above bottom) and back to the surface in 

each of the eight verticals in which the meter was held when the ordinary point method was used. The time of passage of the meter down 

and back again in each vertical was noted and the revolutions of the 

meter wheel were counted. 

REDUCTION OF EXPERIMENTS. 

The standard weir gage readings were averaged for the time of each 

discharge measurement, and the reading for zero head subtracted, 

giving the head on the weir in double centimeters. By-n1eans of a 

chart for converting head on weir into cubic meters per second and a 

computing machine the discharge in cubic feet per second was easily 

obtained. The depth of water in the canal was found by adding to 

the mean canal gage reading in feet the difference in elevation of the 

canal bottom and the zero of the scale. The discharge when the ordinary method was used was computed from the vertical velocity curve 

for that experiment (see figs. 23 to 28, pp. 75-77). The observations 

were usually taken in the eight verticals at 1, 3, 5, 7, 9, 11, 13, and 15 

feet from the south side of the canal, and at the same distance above the 
MURfHY.) RESULTS OF EXPERIMENTS. 65 

bottom. When observations in any vertical were missing, as in verticals 7 and 11 in series C, they were supplied by interpolation; The 

mean number of revolutions at the depth of eaeh observation for these 

eig·ht verticals was then found, converted into velocity by the rating 

table, plotted (as in figs. 23 to 28), and a mean curve drawn. The 

mean abscissa of this curve is. the mean velocity in the cross section; 

the discharge is the product of this velocity and the cross-sectional 

area. 

When the six-tenths-depth method was used a horizontal curve of 

velocity was drawn in a similar manner and the mean velocity was 

found from it. The mean velocity by the integration method was 

obtained by dividing the revolutions by the corresponding time and 

converting the quotient into velocity. 

DISCUSSION OF RESULTS. 

COMPARISONS OF DISCHARGE MEASUREMENTS. 

The following tables give the results of the discharge eomparisons 

of series A to D. The standard-weir discharge (third eolumn) is 

the 1nean for the time over which the meter observations (ordinary 

method) extended. It is assumed to be the same for the shorter 

period of measuring the discharge by the six-tenths-depth and the 

integration methods. This is not strietly true for the larger discharges, 

but it is near enough for practical purpose~;. The true velocity is 

obtained by dividing the weir discharge by the cross-sectional area at 

the meter station. The othe:r columns are self-explanatory. 

Compari~ons of (lischargc o·ve1· Cornell [h~iversit!f stand!.trcl wei1· with -rneasu1·ements by 

cu.rrent meters. 

SERIES A. 

~ J, Meter observations. 

Q) ;a 

s 1-<-· h'-' ~:~ ,_; ,C ·~ •...;Cf ~~ 1: ooo Variation. 

~; ~ :p <:.i<ll <lJ Q) 

A ~..--1.::.; .QS -.: Ordinary Integration Date. ~ >"O::Q) s o.~ '0~ .,_.!=loc <lJ • method. method. <lJ .... ~ Q~$-1 p.~~ - ,......., 

- o::,.c: ..c::'-'2 !·3 0 Q)0:: 

.o> 0 '8'-' ..., Q) 

<ll' "' '0 S53 Q-QQ 0 .s €'.S S e::~ .s ::I"' r Ql T'1 Ql -Q- z 00 A 8 ~. z Q 

---------------- -----------

Cn.jt. Feet Feet Cn . .ft. Feet C~t . .ft. 1900. ]Je?' sec. Feet. p.sec. (a) p. sec. ]Jf/'8eC. p. 8fC. per sec. Per· ct. May 5 ... 1 147.991 7.996 1.166 L.l'.88 •. 76 1.097 !38. 478 + 6.43 Do .... 2 65.024 7.167 0.573 .... do ... 29 0.447 50.714 ........... ................. +22.01 May 7 ... 3 78.4~1 7.258 0.683 Fteley .. 31 0.677 77.780 ............ ................ + 0.90 May 8.: 4 162.684 8.104 1. 268 S.P.351. 38 1. 267 162.46-1 1. 252 160.62 + 0.14 Do .... 5 100.379 7.542 0.841 .... do ... 20 0. 790 94.318 ............ ............... + 6.03 May 9 ... 6 193.624 8.369 1.462 .... do ... 35 1.435 190.109 ............. ........ 1+ 1.81 Do ••.. 7 131.178 7.845 1.056 .... do ..• 18 1.036 128. 6.')7 1. 031 128.04 + 1.92 Do .... 8 131.037 7.848 1.056 L.P.88 .. 18 0.982" 122.000 1. 006 124.!:18 + 6.90 Do .... 9 131.072 7.845 1.055 Fteley .. 18 1.148 142.570 .............. ................ - 8.77 May 15 .. 10 148.556 7.984 1.175 .... do ... 40 1.286 162.540 .............. ................ - 9.43 Do .... 11 119.947 7. 729 0.980 S.P.351. 32 0.939 114.887 0.978 119.66 + 4.22 May 16 .. 12 74.137 7.281 0.643 L.P.88 •• 36 0.533 61.432 ............. ................ +17.14 Do .... 13 93.457 7.484 0. 788 .... do ... 32 0. 744 88.110 .............. ............. + 5.72 Do .•.. 14 74.137 7.280 0.643 . ~-t:J~~ : : I ~~ 0.642 73.985 ............. ............... + 0.20 Do .... 15 93.386 7.484 0. 788 0.834 98.804 .............. .............. - 5.80 

aL. P.=large Price; S. !'.=small Price. The figures given are the meter numbers, 

IRR 95-0..J:--5 

Q-Ql -Q-

--

Per ct. .............. 

.. ............ 

.. ........... 

+1.26 

.............. 

.............. 

+2.32 

+4.63 

.. ............ 

.. ............. 

+0.26 

.............. 

............... 

.............. 

............. 
66 .ACCURACY OF STREAM MEASUREMENTS. [NO. 95. 

Comparison.s of discharge over Cornell University standard 1veir, etc.-Continued. 

SERIES B. 

Meter observations. 

Standard Depth Varia- No. of weir dis- of True Num- tion. Date. experi- charge water veloc- ber of Ordinary method. ment. (Q). in ity ( l) Kind of obser- Q-Q. canal at meter. va- -Q- at meter meter section. tions. 

section. r I 0 Q. -------------------------------

Ctt.jt. Feet Feet Feet C!~ . .ft. 1900. per sec. per sec. per sec. (a) 11er sec. per sec. Per ct. May19 ...•.......... 1 50.366 1.115 2.823 8. P. 35L 1G 2. 790 49.774 +1.11 Do .............. 2 50.260 1.115 2.823 Fteley .. 16 3.599 64.206 -27.75 Do .....•........ 3 50.154 1.110 2.824 L. P. 88. 1G 3.103 53.790 -7.26 

May~~::::::::::::::! 4 65.625 1. 299 3.157 Fteley .. 24 3.344 69.502 -5.91 5 65.625 1. 299 3.157 L. P. 88. 2J 3.085 64.118 + 2.30 Do ...•••....•... 6 66.8!16 2.000 2.091 Fteley .. 24 2.500 80.000 -18.09 Do .............. 7 21.616 0. 786 1. 719 L. P. 88. 16 1. 538 19.341 +10.54 Do .............. 8 66.731 2.029 2.056 .... do ... 24 1.900 61.682 + 9.07 Do .............. 9 33.060 0. 741 2. 766 Fteley .. 16 3.273 32.295 + 2.30 ~ay22 ...........••• 10 21.369 0.550 2.428 .... do ... Hi 2.945 25.916 -21.28 Do ...•.......... 11 94.410 1.885 3.130 .... do ... 24 3. 789 114.250 -21.01 Do .............. 12 94.410 1.885 3.130 L. P. 88. 24 3.102 93.556 + 0.90 Do .............. 13 57.854 1.198 3.018 Fteley .. 24 3. 720 71.305 -23.27 Do .. ; ..•........ 14 57.854 1.198 3.018 L. P. 88. 24 2.947 56.589 + 2.18 Do ....•.•••..... 15 43.761 0.953 2.870 8. P. 351. 16 2.698 43.055 + 1.62 Do ..........•... 16 43.761 0.953 2.870 Fteley .. 16 3.474 52.944 -20.98 Do .............. 17 29.598 0.693 2.671 8. P. 351. 16 2.425 26.876 + 9.19 Do .............. 18 29.598 0.693 2.671 Fteley .. 16 3.137 34.768 -17.47 Do .............. 19 18.932 0.464 2.553 8. P. 351. 8 2.290 16.983 -10.30 Do .............. 20 18.932 0:464 2.553 Fteley .. 8 2.932 21.744 -14.84 

aL. P.=large Price; 8. P.=small Price. The figures given are the meter numbers. 
Comparison of discharge orer Cm·nell University ~taudard weir with measurements by cw·rent meters. 

SERIES C. 

Meter observations. Variation. 

Nu::lbe' I s"::'~~ro I Depth of 

Small Price No. 351, Small Price No. 363. I Small Price 

True ye- ordinary method. Small No. 363. 

Price experi- discharge water in locity ( V) 

I 

ment. Integra- No. 351. t Q). canal at at meter Ordinary method. 

("QQ·} I "QQ· meter Q-Ql section. ro Qo tion 

section. method -Qv6 Q6 (Qtl· 

Date. 

Cu.jt.pe1· Cu.jt.per Ott. ft. per Cu .. jt.per ~ec. Feet. Ft. per sec. Ft. per sec. sec. Ft. per sec. sec. sec. Per cent. Per cent. Percent. 1 216.131 9.460 1.401l 1.446 219.836 1.465 22'2.980 220.393 - 1. 77 -4.11 ...:. 0.63 

1900. 

2 140.515 9.374 0. 932 0.969 146.060 0.985 148.528 143.099 - 4.13 -6.13 - 5;37 3 71.681 9.338 0.477 0.493 73.050 0.487 73.167 71.514 - 2.38 -2.08 - 1.59 4 38.254 8. 910 0.265 0.259 37.420 0.278 40.113 33.330 + 2.03 -6.00 -16.16 5 178.553 7.673 1.444 1.449 179.130 1.489 184.075 174.679 - 0,33 -3.09 - 5.17 6 125.298 7.640 1. 018 0.9!l9 122.974 1.047 128.880 120.789 + 1.85 -2.78 - 5.12 7 61.272 7.582 0.50'2 ............... ............ 0.522 63.771 . 61.327 . .......... -4.88 - 4.08 8 31.176 7.557 0.255 0.215 26.180 0.258 31.488 28:070 +16.01 -1.04 -22.10 9 50.310 6.005 0.515 0.494 48.208 0.540 52.696 46.451 + 4.17 -5.92 - 7.65 10 196.387 6.278 1. 940 1.890 192.799 1. 989 201.367 188.232 + 1.83 -1.46 - 4.86 11 132.414 6.399 1.283 1.251 129.078 1.318 135.991 123.816 + 2.52 -3.18 - 4.27 12 91.056 6.319 0.893 0.847 8ti.318 0.920 ~.,M

1 83.872 + 5.20 -5.08 - 2.96 13 65.319 8.476 0.478 0.464 63.325 0.492 67.146 60.459 + 3.07 -2.35 - 2.80 14 198.258 8.470 1.454 1.460 199.115 1.514 206.480 187.795 - 0.44 -3.71 - 6.76 15 125.301 8.508 0.915 0.890 121.921 0. 949 130.001 114.522 + 2.69 -3.75 - 9.54 16 31.223 8.455 0.229 0.201 27.364 0.240 32.674 25.186 +12.37 -2.47 -39.30 

"d 

~ --Ill 

.:::. 

a 

~ ~ r:D 

0 

z 

0 

r%j 

t:1 

H 

r:D 

a 

~ 

> :;d 

Q 

tz;J 

~ 

t:;l 

> 

r:D 

c:: 

~ 

e 

~ rp 

0':1 

~ 
Comparison of discharge over Gbrnell University standard weir with measw·ements by cw·rent meters-Continued. 

Date. 

1900. I 

~g ~ ~ ~~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ j 

Number I Standard of weir experi- discharge ment. , ( Q). 

Depth of water in canal at meter 

section. 

True ve- locity ( r) 

at meter · section. 

SERIES D. 

Meter ob;;ervations. 

Kind of meter. a 

Ordinary method. 

ro Qo 

Six-tenths 

~:lht~d (Qe). 

Integra- tion 

method 

(Ql)· 

Q-Qo 

-QVariation. 

Q-Qa 

--Q-- Q-Ql 

-Q-

---------------------f 1--_, ___ , __ _ 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

Ou . .ft.per 

sec. Feet. Ft. per sec. Ft. per sec. Cu. ft. per sec. Cu. ft. per sec. 233.262 9.505 1.528 S.P.363 ..... 1.519 231.976 ................... 233.262 9.505 1. 5:!8 Hask.3 ..... 1.484 226.380 ....................... 22!?. 731 9.317 1. 53.5 ..... do ...... ................. ..................... 239.120 117.673 b9.536 0. 7t8 ..... do ...... 0.832 b 127.421 b126. 498 117.673 b9.536 0.768 S.P.3G3 ..... 0. 794 b 121. 601 b119. 301 95.176 b9. 524 0. 622 Ha;;k.3 ..... 0.676 b103. 401 b 105.846 

95.176 b 9. 524 ...................... S.P.363 ..... 0.563 b99. 883 b 97.892 221. 74~ 7.245 1. 905 Hask.3 ..... 1.864 216.932 218.680 221.749 7.245 1. 905 S.P.363 ..... 1. 867 217.281 222. fl21 191.165 7.21.7 1.649 Hask.3 ..... 1.675 194.1R3 200.209 191.165 7. 217 1.649 S.P.363 ..... 1. 651 191.400 192.793 ll0.186 7.183 0.955 Hask.3 •.... 1.022 117.919 11R.802 110.186 ................... 0.955 S.P.363 ..... 0.955 110.188 110.8118 

56.717 7.113 0.496 {Hask. 3 ..... ..................... ........................ 53. 2-li S.P.363 ..... ···· ··a:7so· ..................... 58.270 57.071 5.154 '0.689 Hask.3 ..... 60.455 <12. 277 57.071 5.154 0.689 8. P. 363 ..... 0. 672 5.5. 651 57.308 

aS. P. =small Price. Hask. =Haskell. The figures given are the meter numbers. b Hook gage broken; depth not accurately measured. 

C11 . .ft.pa 

"'· Pccce>•f. P"cr"t-~I~uent. ~35. 082 +0. 55 . . . . . . . .. . -0. 77 239.968 +2. 95 .. . . . .. . .. -2.88 235. t\28 .. . . .. .. .. - 4. 09 -2. 66 ....................... -8.28 - 7.50 ...................... -3.34 - 1.40 ....................... -8.63 -11.21 ................ -4.93 - 2.84 228.340 +2.13 

:': ij:~ 1····::':~ ................... +2.01 202.647 -1.58 - 4.73 -6.00 .................... +0.20 - 0.84 .•••••.•.• 119.609 -7.01 -- 7.84 -8.55 . .................... .................... - 0.68 . ................. .. ............ - 6.14 ................... ............ - 2.73 62.277 -5.94 - 9.10 I -9.10 ................... +2.49 - 0.42 

~ 

00 

> 

a 

a 

~ 

:d 

> 

0 

~ 

0 

t'l:j 

ri1 

f-3 

~ 

tz;j 

~ 

~ 

I< 

tz;j 

> rJ). 

~ 

~ 

= ~ 

~ 

1 

~ 
COMPARISON 0:11' DIROHARGE MEASUREMENTS. 

eu from the foregoing tables that the meter discharge differs 

One 

er must 

hen we 

velocity 

rdinary 

g mean 

is seen 

It is se 

from the 

might sa 

be a ve 

examine 

we find t 

method. 

velocity 

that nea 

exceptio 

depth an 

charge. 

from the 

other me 

we have 

~ei r discharge all the way from 0 to 40 per cent 

y, without careful exan1ination, that the current Inet 

ry unreliable velocity-measuri~1g instrument; but w 

tl ese results carefully and plot thetn according to 

he case very different. Take first the results by the o 

"T'hese are plotted for .each meter in fig. 16, usin 

as abscissre and percentage difference as ordinates. It 

rl) all of these points fall on well-defined lines. T 

ns are those in which the depth is small and the er 

d position of meter have a large effect on the n1easur 

The discharge obtained with the Fteley meter differ 

he few 

rors of 

ed diss more 

ith the 

onstant 

, 1 rev-

( orresponding weir discharge than that obtained w 

te ·s. This is because it had never been rated. The c 

UF ed in reducing the observations with this meter-viz 

s-u ~ ... 1.16.1 

II I..._ 0 d 

,,... "'""' "68 ls"""' .......,, o.3.51 

10 1\ .-.:.. 0~ d 0 ~ 0 d () I 0 .,. 111 

t 

~· 111 

() 

•/() 

Zi> 

() 

FIG. 16.-Dia gr 

charge, fr 

discharge. 

om 

........ No 

net., !- d 

)-_ 0 yo 

vo 

'I'-- --l! 

0 

... ' .. J . V6/oclfy. fn.t p"/.,. .. ~t;~ it J .. m showing difference between meter discharge by ordinary method an d wen dismeasurements in Cornell University experiment canal. Line 0-0' repre sents weir 

olutiori 

observat 

per second at 1 foot velocity= 1. 072-was obtaine d from 

io 1s by students. It is not, however, n:mch in ~rror for this 

velocity, l ut is largely in error for other velocities. The rating 

obtained f mn these weir experiments is given in the table ori p age 81. 

For .the oLter three meters the percentage error IS small for velocities 

above 1 fG·dt per second. For the Price meters the error is positive 

and incre~ 3es rapidly as the velocity decreases. For the Haskell 

meter the :~rror is negative and increases, negatively, rapidly a.~ the 

,·elocity d~ creases. The error in rating, if we may call it such, is not 

so large as it appears from these diagrams, for a 10 per cent error in 

a small quLntity is only a 1 per cent error in a quantity ten times as 

large. TL ~ rating tables as derived from these curves and as found 

by movin~, ths meter through still water are given in the table on 

page 81. .8xperiments with depths of 0. 75 foot or less (Nos. 9 and 17 

to 20 of st: ·ies B) are not plotted in the diagram (fig. 16), as the prob-
70 AOOURAOY OF STREAM MEASUREMENTS. (NO. 95. 

able error is large; nor are experiments 1 to 4 of series C, because the 

upper and lower parts of the vertical curves are not well defined; nor 

II 

0 

c .,...-( ~ -- "i() I ~ 

lnt~r-

~"' I~ ~Jim metll<~ 

0 

0 e br:c f.--" kO""' ..., 44<> l*plh fnetm~ 4'~ d.,...h met/>0 

~ 

5 " J 0 ~ 

' NoJ 

FIG. 17.-Diagram showing difference between meter discharge by six-tenths depth and integration 

methods and weir discharge, from measurements in Cornell University experiment canal. Line 

G--0' represents weir discharge. 

experiments 4 to 7 of series D, because there appears to be an error in 

the hook-gage work of those experiments. 

In fig. 17 are plotted the percentage differences between weir discharge and discharge obtained by the six-tenths depth and the integration methods. It is seen that the meter discharge by these methods is 

•D 

010 

0 

•10 

.. 

--,.,..,_,__ 3SI 

04oo..i'1,.1'-V4n<!4~.J.tn.-:J?-.r 

W:,...4011"".U.""-stl 

.. ~t .. f• ~u u u 

Sm.lf'rkoA :.-... .., ... • •L 

~· M. /41F.I!..e::~" . .o , .... [0' l OjO 

I~ '-'"'' '"""' 1.3. U7/J ...... 

~ """'-f~~ ( N 

c - 0 

0 0 ~ 

1.4 ... ... ... ... ... FIG. 18.-Diagram showing difference between meter discharge with different 

meters and weir discharge in experi· 

ments of series E in Cornell University 

experiment canal. Zero line indicates 

weir discharge. 

greater than the weir discharge, being 

4 or 5 per cent greater for velocities 

above 1 foot per second. In the integration method, for small velocities 

the difference increases very rapidly as 

the velocity decreases. It is seen front 

figs. 16 and 17 that while the ordinary 

1nethod gives discharge 1 or 2 per cent 

less than the weir for velocities above 

.1 foot per second, the six-tenths depth 

and the integration methods give discharge 4 or 5 per cent greater than the 

weir. 

The results of the discharge measureInents of series E are given in the following table and are plotted in :fig. 18, 

which shows three sets of double comparisons. Experiments 1 to 20 give a comparison of simultaneous 

measurements with small Price meter No. 363 and Haskell meter 

No. 3, and also with the discharge obtained at the same time with the 

weir. Experiments 21 to 38 give similar comparisons for the two 

small Price meters and the weir, and experiments 39 to 50 give similar 

comparisons for Haskell and Price meters and the weir. 
MURPHY.) COMPARISON OF DISCHARGE 'MEASUREMENTS. 71 

Compari.son of discharge over Cornell Unit,ersiiy standa·rd weir with measurements by 

current meters. 

N·'· of ex perilltt'l1t. 

---

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

21 

25 

26 

27 

28 

29 

30 

31 

32 

33 

34 

35 

36 

37 

38 

39 

40 

41 

42 

43 

44 

45 

46 

47 

<18 

49 

50 

SERIES E. 

Depth of Tmeve-1 Standard water in Jocity at weir dis- Date. canal at: meter sec- meter sec- charge 

tion. tion. (Q). 

I 

C'n.jt. per 1901. Feet. Ft. per sec. sec. April L ... 9.075 1. 472 204.41 ... _ .. do .... 9.075 1.456 204.41 April2 .... 6.079 2.208 208.88 ..... do .... 6.079 2.187 208.88 ..... do •... 7.41'l3 1. 744 200.81 ..... do •... 7.453 1. 710 200.81 ..... do .... 5. 742 2.137 197.64 ..... do .... 5. 742 2.171 197.64 April5 .... 7.409 1.86!) 222.67 ..•.. do .... 7.409 1.883 2"22.67 ..... do .... 6.295 2.137 220.33 ..... do .... 6.295 2.177 220.33 ..... do .... 5.628 2.377 219.38 ....• do .... 5.628 2.438 219.38 ..••. do .... 5.294 2.611 221.96 ....• do .... 5. 294 2.602 221.96 

..... do .... 4.892 2. 764 222.81 ..... do .... 4.892 2.827 222.81 ..... do .... 4.617 2.936 224.75 

..... do .... 4.617 3.019 224.75 

April6 .... 4.808 2. 985 230.36 ..... do .... 4.808 3.006 230.36 April10 •.. 8. 744 1.670 230.75 ..... do .... 8. 744 1. 657 230.75 ..... do .... 7.874 1.846 229.28 

..... do .... 7.874 1.862 229.28 

--c··do .... 6.889 2.108 229.91 ..... do .... 6.889 2.073 229.91 Aprilll ... 6.129 2.340 227.16 ..... do .... 6.129 2.320 227.16 ..... do .... 5.483 2.596 225.01 ..... do .... 5.483 2.604 225.01 ..... do .... 5.185 2. 725 224.06 ..... do .... 5.185 2. 758 224.06 ..... do .... 5.003 2.816 222.60 ..... do .... 5.003 2.834 222.60 ...•. do .... 9.256 1.522 223.40 ..... do .... 9.256 1.538 223.40 

April12 ... 9.344 1. 486 224.63 ..... do .... 9.344 1.541 2"24. 63 ..... do .... 8. 934 1. 613 221.-39 ..... do .... 8.934 1.543 221.39 

..... do .... 8.297 1.646 221.39 

..... do .... -8.297 1. 700 221.39 ..... do .... 7.806 1. 775 221.49 

..... do .... 7.806 1.803 221.49 ..... 00 .... 7.266 1.879 221.21 ..... do .... 7.266 1.943 221.21 

..... do .... 6.439 2.132 221.03 ..... do .... 6.439 2.182 221.03 

M ··I Varia- eter 1s- tio n 

charge . ( Q _ Qw) (Qw)• -Q--- • 

I w • 

Cn.ft. per sec. Pe1' cent. 214.08 -4.73 212.33 -3.87 216.28 -3.54 214.22 -2.55 208.85 -4.00 204.77 -1.97 197.0'2 -0.31 200.15 +1.27 222.68 0.00 224.35 -0.75 -216.00 +1.96 220.03 +0.14 214.82 +2.08 220.33 -0.43 222.02 -0.03 221.27 +O.:U 217.32 +2.46 222.27 +0.24 218.32 +2.86 224.50 +0.01 

230.66 -0.13 232.30 -0.84 

234.68 -1.70 232.85 --0.99 233.61 -1.89 

235.64 -2.77 233.25 -1.45 229.38 +0.23 230.2.5 -1.36 228.28 -0.50 

228.59 -1.60 229.30 -1.91 

226.98 -1.30 

229.73 -2.53 226.37 -1.69 227.82 -2.34 

226.38 -1.33 

228.71 -2.38 

223.11 +0.68 231.37 -3.00 231.58 -4.60 221.53 +0.07 219.50 +0.81 226.70 -2.40 222.69 +0.54 226.19 -2.07 219.34 +0.85 226.81 -2.53 220.!3 -0.27 225.61 -2.07 

mr;erKind of encein 

meter meter. a dis- charges. 

Per cent. Hask. 3 ... } S. P. 363 .. 1 

Ha~k. 3 ... ~~ 

8. P. 363 ··[ Ha.'lk. 3 ... ~ 

8. P. 363 .. J Hask. 3 .. -\1 8. P. 363 .. ,{ 

Ha.<;k. 3 .• ·I} S. P. 3G3 .. 1 Hask; ~--·I} S. P . .:.ti3 .. 

Hask. 3.·-i} 8. P. 3G3 .. 1 

Ha-.k. 3 ... \\. 

8. P. 3C3 ·-IJ Hask. 3 ... } S. P. 363 .. I Ha'1k. 3 ... ~1 S. P. 363 .. f 

-

S. P. 351 .. } S. P. 363 •• 

S. P. 351 .. } 8. P. 363 .. 

S. P. 351..} S. P. 363 .. 

S. P. 351..} S.P.363 .. 8. P. 351.. l S. P. 363 .. I S. P. 351 .. I S. P. 363 .. { 

8. P. 3fi1 .. } S. P. 363 .. 

S. P. 351..} S. P. 363 .. S. P. 351 .. ~ 

S. P. 363 .. J 

0 . 

0. 

80 

99 

3 

8 

5 

2.0 

1. c~ 

o. 7 

1.8 2 

2.5 

0.3 

2. 

4 

22 

2.8 5 

1. GO 

0. 7 

o. 71 

0.8 8 

68 

6 

1. 

0.8 

0.3 

1.2 3 

5 

5 

0.6 

1.0 

0.9 0 

--- Hask. 3 ... } S. P. 351 .. 3.68 

..... do .... ), Hask. 3 ... J 4.67 

'iCP~~5i::} 3.21 

Hask: 3 ... { 2.61 8. P. 351 .. Hask. 3 ... 3. 8. P. 351 .. J 38 

Hask. 3 ••. } S. P. 351 .. 1.80 

---3.22 

aS. P.=small Price. Hask.=Haskell. The figures given are the meter nnmbers. 
72 ACCURACY OF STREAM MEASUREMENTS. [No.95. 

The prindpal results of the foregoing comparisons have been condensed in the foll?wing table: 

Table showing percentage variatl:on between 'Weir discharge and meter discharge, and 

between meter discharge by d~tferent 'instrwment.~ of e.tperiments in Series E. , 

Experiment,;. Kincl of meter. 

Difference between standard weir I Difference in discharge of si- discharge and meter discharge. multaneous meter measure- ments. 

----I------I-M~ax_. Min. Mean.a Range. / Max. Min. Mean. Ran~~e. 

Per ct. Per ct. 

1 to 20 ..... Haskell No. 3 ... -4.73 0.00 

Do. ... S. Price No. 363. -3.87 +0.01 

21 to 38 .... S. Price No. 351. -1.89 -0.13 

Do ..... S. Price No. 363. -2.77 +0.23 

39to50 .... S. Price No. 331. -4.60 -2.07 

Do ..... Haskell No. 3 ... +0.85 -0.27 

a Regarding signs. 

Prrct. 

-0.33 

-0.76 

-1.38 

-1.56 

-2.78 

+0.40 

Percent. 

-4. 73 to +2. 86 

Per ct. Pact. Per ct. Per ct. 

-3.87to+l.27 2.1l5 0.34 g~:: } 2.51 

-1.89to-0.13 .............................. .. 

-2.77to+0.23 1.68 0.31 {~gJg } 1.37 

~~::~::=~:~~ !---~.-~;- ---~--~~- {~~jr r·-~.-~; I 

b Disregarding signs. 

It is seen from this that in none of these fifty experiments does a 

meter discharge differ from a corresponding weir discharge 5 per cent, 

and in no case do two simultaneous meter discharges differ from each 

other 5 per cent. In experiments 1 to 20 the mean variation from the 

weir discharge is -0.33 per cent for the Haskell meter and -0.76 per 

cent for the Price meter, while the mean difference between corresponding meter discharges is 0.29 per cent. In experiments 21 to 38 

the mean variation from the weir discharge is 1. 38 per cent for Price 

meter No. 351 and -1.56 pe.r cent for Price meter No. 363, while the 

mean difference between corresponding meter discharges is 0.18 per 

cent. In experiments 39 to 50 the mean variation from the weir discharge is 2.78 per cent for the Price meter and 0.40 per cent for the 

Haskell metm~, while the mean difference between corresponding meter 

discharges is 3.22 per cent. 

The range of. variation of meter discharge from weir discharge is 

greater than that of corresponding meter discharges. This· is to be 

expee.ted, however, since there are a number of pos.sible errors in the 

former which are not in the latter. Errors in measuring head, depth, 

calibration of weir, velocity, and rating of n1eter affect tlie former, 

while only the two latter errors affect corresponding meter discharges. 

It is also seen that the mean of the difference between simultaneous 

discharge measurements Nos. 21 to 38 is only 0.18 per cent, and the 

extreme range in the-se eighteen consecutive measurements is only 1.37 

per cent. How much of this error is due to errors in the rating table 

and how much to errors in observing velocity we were unable to determine, as good facilities for rating were not at hand. We are, however, justified hy these experiments in the statement that the discharge 

of this canal can, with a small Price meter,. be measured to within less 

than 1 per cent when the mean velocity in the canal is from 1.5 feet 

to 3 feet per second. 
MUB.PHY.) CORNELL HYDRAULIC EXPERIMENTS. 73 

VELOCITY CURVES. 

Curves of equal velocity in the cross-sectional area of observation 

are shown in figs. 19, 20, 21, and 22. Four experiments are selected 

(one from each series) from the sixty-five experiments of series A to 

D by the ordinary method, to show the variation of velocity in the 

sections. They are self-explanatory. Fig. 20 illustrates a case of 

small depth, high velocity, and no back-water effect. The maxhnum 

velocity is at the surface, nearly midway between the banks. In figs. 

" ~ 

• j_ ~ - 1- '-' \ ~ I. r-- . . . ~ ~ 1..- .} ~ 

·~ '''"'" ""' .. '!'!4<- :? v 

.:: :::..-: n- . .~ #. ~~ ~ ::<::: .h~ ~ ~ " . 

8 "' " .. Wi th,Ft. Vllo 11y, I He. 

..... 'A 

:r ~ /'-

.v -..1'-~ ....... , . ii?l~ CV~I 

""""' lllcu•e ~~'"' t::ro 

FIG. 19.-Curves of equal velocity in experiment No. 11, series A. 

19, 21, and 22 the maximum velocity is below the surface and not 

midway between the banks. It is less at the center than 3 or 4 feet 

from either side. This is true of all the experiments of series A. · We 

tried admitting the water to the upper chamber of the canal in various 

ways, by opening some of the gates and closing or partly closing 

others, but the distribution of velocity appeared to be nearly indeI .!!l!li 1\ 1\ t--.L j ,~. 

~ "l\:: ~ -' =: ""'-.u.--' r~ .,...,/ ' !'-...!'.. ·~~~~ J, <$~ .............. 

·~ v .. ~ r-.b-... ,..;:;.:3 --~--"' 

~ ~~·~~ ~ ~~:;!:;v"' II ~ 4- fi ll N• 12 ,.- ..!.4- 18 ... u .M ... W1dth otna((t, y,{Dt:hy1 l"t. aN, 

~ ----~ I'-__ ,.. 

.. / 

·~·' v A v .... s· .,.... 

./ v s~~ 0:~1: E:""' fur 

FIG. 20.-Cni ves of equal velocity in experiment No. 12, series B, with large Priee meter No. 88. 

pendent o~: the openings through which the water was admitted to the 

canal. 

Horizon.nl velocity c~rves are shown in these same :figures (19 to 22), 

the velocity curve at sixrtenths depth below the surface being shown, 

and also , he curves for surface and bottom. In these figures the 

velocity n1:ar the north side of the canal is somewhat less than that 

near the ... outh side. This i:-~ true of all the experiments of series C 
14 AOOURAOY OF STREAM MEASUREMENTS. LNo. 95. 

and D. It is _due to the north side of the canal b~ing much rougher 

than the south side, the concrete of the north side having been cut 

away preparatory to its repair just previous to making the experiments of series C. 

~~ ~ 8 {,__, t$1 1$9.1 ~J~ j\, 1' 

_( 1\ tJ \ 140 

) s Cwv s~o ~ lrtwA "'"ty 

.. _\ ~ 1 

f. '-:5 t:Y~ I.~S /f!\ '{i ~~~ II 

:~ ~~ .... == "'" f.-/J I ;I / /I~ -~ ~~ "rz; flY 1.3.9 1.39 ~J, .av.-" <"'- ~ !-" ./ 7 _..¢ ~ 

" . ~ 6W.t0' 8 0 I I II 

"· :Ft Vel ell~ t.sec. 

18 -- ~ -- r-=: ----- \ ~,.. . ~ ~ \ 

:B j Iii Wfi 1\'\ . 

·; / _,....- "'\ \ B 

'-.. 

c \\ 

'" FIG. 21.-Curves of E!qual velocity in experiment No. 14, series C. The dots are for small Price meter 

No. 351; heavy black squares for small Price meter No. 363. 

Vertical velocity curves for these four series of experin1ents (A to 

D) are shown in figs. 23 to 28. Each of these curves is the mean of 

observations in the eight vertical~-! 1, 3, 5, 7, 9, 11, 13, and 15 feet from 

the south side of the canal. For series C and D, figs. 26, 27, and 28, 

"the observations obtained with small Pl.·ice meter No. 363 at six-tenths 

_, .., -...s.. I \&I ,a. ,L 1\ ..a ~ 

" '"" liH "" ""' \ /.M ,_ 

""" """ ""' - 1 WI I""' 

~ _Con """'" .... - C: ~ I I ~- ~/ l3.~ ~ _f~ ~ 13. 1/,. ·-· 

;'' :.J) ~~ ~ )-r-. '""'-..:2:.- .p ~5' 

~~v4~~ . 

...__ 

.g !.. ,/ \ .. ~ wk,n." 10 ~ 

·) 

14 .8~it~ 

~ AJ' ~ ~ ~ v. -- ---~ " ~cv v r---.... 1--- :"' L ~ ~ -=" c· . 

• v ,;,. ,.. ...... 

FIG. ~~.-Curves of equal velocity in experiment No. 20, series D. The dots are for Haskell meter No. 

3; heavy blac.k squares for small Price meter No. 363. 

depth are shown by the little squares. As a rule they fall outside the 

curve, meter No. 363 indicating a somewhat ~Teater velocity than 

meter No. 351. This fact is also shown hy the corresponding curves 

of figs. 16 and 17. The two sets of velocity curves (full and dotted) of 
MURPHY.] VERTICAL VELOCITY CURVES. 7 5 

l:fig. 28 were found from simultaneous velocity measuremen.t:;. Two 

iparties measured velocity in the same section at the same time. One 

:party, with the Haskell meter, started near the south side of the canal 

'and worked toward the north side; the other party; with :the P:rice 

meter, started at the north side and worked toward the south side. It 

is seen from these curveH (fig. 28) that the bottom velocities agree 

more closely than those at the surface. and that the Haskell meter 

No.I .NJL!! IJ! ...... 7 ....., 

(!!;,4 ~ ~~ ~ ~ ~ ~ ~ . ~ ~ 

t' :f tj If 1 ~ i i 

I I I I I L .J I .7 ..., 

z V' I ,,}, f I) I I !11/·l 1/ ) 

_.../ } / I / I I 

~ /,. I / / 

1.>-- ---~ ~ ~ ~ / 16./ / /v _,4 y v odt If. .no .9 I. ,4 7 Ia 

FIG. 23.-Vertical velocity curves obtained with current meters in experiments in series A. Nos. 1, 2, 

8,12, and 13 are for large Price meter No. 88; Nos. 4, 5, 6, 7, and 11 are for small Price meter No. 351. 

· give:-; a much larger surface velocity than the Price meter. We 

· should expect a little difference, since the revolving head of the Has-

. kell meter i:-; larger than the wheel of the Price meter, and its center 

, being farther below the surface it muHt revolve faster. But the difference in velocity il-J much greater than thiK little difference in depth 

of axis would indicate. (See p. 91.) 

4 'AI• 

~3 ~. ~ ~H' .. t> I . I 

s f, 1/ . 4 . ~ 1.1- .1. 

I. /-.. / I I !1. ct ~-l v / v t·~a " 7 2 1/ I / v. v ·' I ____ ....... 

// / ~"'" ·~ y rill'. I .. M. 

Fr.;. 24.-Vertical velocity curves obtained with Fteley current meter in experiments in ser~es A. 

The shape of these cut·ves evidently depends on the depth and 

velocity. For depths 1~ot exceeding 1 foot it is a nea1·ly straight line, 

with the maximum vel~city at the surface and the mean velocity at 

. mid depth. For deptl~s of 8 or 9 feet and sn1all velocities the curve 

· is very flat, with the maximum velocity at two-tenths to three-tenths 

depth and the mean velocity at sixty-five-hundredths to )';even-tenths 

depth below the surface. The radius of curvature decreases as tbe 

velocity increases. In all of these curves the least velocity is at the 
76 AOOURAOY OF STREAM MEASUREMENTS. [NO. 95. 

hottom. Nos. 6 and 8, ~;eries B, fig. 25, show the effect on the vertical 

velocity curve of checking the discharge at the lower end of the canal. 

For all the other curves of fig. 25 there is free discharge. The effect 

of checking the dh;charge at the lower end is to force the thread of 

maximum veloeity from the surface to a depth of two-tenths or mo-re: 

The table on page 77 gives the position of the threads of maximum and 

5 ,,._' 6_;: ~~~ N< ~~ I~ " ~ PiP -""a No. i!O 

----- v- ~ / / ...---; v v ~ 7"" 0 • 3 / A 19 

~~ ~ 

_, ~2 /10.,$ o./6 I 

~ ~ v / / / ~?' .s 2~ 6 

-- . J 

~ ~,...... 

.....-:~ ~ 3 

\~ vs / ~v or::::::::- ./ 

J z .!7 zg 

iii 8 No.6 2! ""'"-~l I~ ,t 2 ~ , .. ~ 2 d'f 2 " 

j V' I zA 6 3. 

I 

0 ~ rtii 

v v ~ / / / 9 .-o~~ 

---~ /__ v -- v :........-

--f::::: ~ f--~ (tyJI .sec. 

FIG. 25.-Vertical velocity curves obtained with current meters in experiments in series B. Nos. 1, 

15, 17, and 19 are for small Price meter No. 351; Nos. 3, 5, 7, 8, 1~, and 14 are for large Price meter 

No. 88; Nos. 2, 4, 6, 9, 10, 11, 13, 16, 18, and 20 are for Fteley meter. 

mean velocity taken from the curves shown in figs. 23 to 28. It is 

difficult to locate the threads with accuracy, since very little change in 

the shape of the curve would make a great cliange in the position 

of the threads. It is easily seen that the shape may be changed somewhat, and yet fit the observations nearly as well as the one drawn and 

give a discharge differing from it but little. For velocities of a foot 

I . 3 J 

~· 

I 8 • I I J /, 3 Y ./. 

FIG. :ttl.-Vertical velodty curves obtained with current meters in experiments in series C. Heavy 

round dots are for small Price meter No. 351; the square blocks are for small Price meter No. 363. 

or more per second, however, the threads can be located with a fair 

degree of accurac.y. The position of the thread of maximum velocity 

as found from series A is eighteen-hundredths depth below the surface; 

for series B it is one-tenth depth; for series C, thirty-eight-hundredths 

depth; and for series D, twenty-four-hundredths depth. For the rriean 
:$URPHY.) THREAD OF MAXIMUM VELOCITY. 77 

~f C arid D, in which the conditions are nearly tho same, it is thirty-

~ne-hundredths depth. The position of the thread of mean velocity 

as shown by this table is sixty-six-hundredths depth for series A, 

iji.fty-four-hunclredths depth for serie~ B, and sixty-six-hundredths 

.. ~~~ d ~ 

~ 

<I !!!' ND 9 ~ ~ ~~ ~~ ~ 

r"\ \ ['. -.._!'-, $ 

... . \ .I\ I \~ ~ "~1 J 

t! I u ) 11! / . . "i~ 

2 L,' e/. .)' ~ 

~ A"v lA" ~ I 

v ] kl' ~ __.v v v ~ ~..--.....- Yell~ ~ lL .......... v ....-

fiG. 27.-Vertical velocity curves obtained with current meters in experiments in series C. Heavy 

round dots are for small Price meter No. 351; the square blocks are for small Price meter No. 363. 

depth for series C and D. It is seen that the threads of mean and 

nmximum velocity are nearer the surface in series A than in series Cor 

p, although th~ depths do not differ much. This is probably due to 

the influence of the Croton model dam, the long upstream slope of 

9 '•~ ~-~t ~ ~ I 1 - Hask. '/No. - Sms/. Pd~ jN•J< .. I r \ 7 ' N~l< """" No.I(). Ntl .N49 

I I I I ·~ 

I "\ 17 ~ ' 0"==~ . I tS 

1 I II I I NDoi:S o.fS $ 1/ I I I ,'if' It'>~ lj I -L' I I .. ;, ,I~ I I I ,I/ // p je 

) // 1 V/ l7 ;· R. I I 

~~ If }o 0/ ) L_t ~ o/ !,' 

' ~ fA -~ f/ ./'/A ,Y,:- ~~~ r\Y<'Ioo n~ 

.s .? .8 u ... Mi .J " ,. us 11' ,. ,, 

1"IG. 28.-VerticJ velocity curves obtamed with Haskell meter No. 3 and small Price meter No. 363 in 

experiments i~· series D. Open circles are for small Price meter No. 363, point method; heavy black 

; dots are for askell meter No. 3, point method; heavy black squares are for small Price meter 

No. 363, six-te ~ths-depthmethod. 

~\ 

which has had the effect of foi.·cing the thread of maximpm velocity up 

to thirteen-hundredths depth. As the ratio of width to depth changed 

from 16 to 2 the thread of mean velocity moved from fifty-fourhundredths depth to sixty-six-hundredths depth below the_ surface. 
J"""'!-: 

' 

Table showing position of threads of max·imum and mean t~elocity in Cornell University experiment canal as found from current-meter discharge measurements made .in .May, November, and December, 1900. 

N f ~---;----------,--------,------1 I 

ex~e~i- ment. Velo.city I J?epth ~ ('rim.\ Ratio I Ratio ('.tl') I Yel~city . Depth I (dm) Ratio I Ratio (d') -

Vel~city Depth Ratio Ratio (d"') (d') Vel~c1ty . I Depth ~-R-;;i~-- (d"') (T). (D). 75/' D · (To}• (D). ]j • jj • (To)• (D). Jj • D · (l 0 ). (D). J5 • 

--- --------- ---------1---------------:------

Series A. Series D. Series C. Series D. 

Ratio 

(~)-

1 ...... . 2 ...... . 3 ...... . 

4 ....... 1 5 ...... . 6 ...... . 7 ...... . 

~ :::::::1 10 ...... . 11 ...... . 12 ...... . 13 ...... . 14 ...... . 15 ...... . 16 ...... . 17 ..... .. 18 ...... . 19 ...... . 20 ••••• :. 

Feet per second. 1.17 

0.57 

0.68 

1. 27 0.8'1 

1. 46 1. 06 1. 06 1. 06 1.18 

0.98 

0.64 

0. 79 0.64 

Feet. 8.00 

7.17 

7.26. 

8.10 

7.54 

8.37 

7.85 

7.85 

7.85 

7. 98 7.73 

7.28 

7.48 

7.28 

~~ 

~n 

~n 

~M 

~w 

~Th 

~M 

~m 

~% 

~~ 

~n 

~~ 

~M 

~M 

0. [~) 

0. 29 0.2.'l 

0.29 

0.49 

0.30 

0.45 

0.31 

0.43 

0.37 

0.36 

0.30 

0. 21 

0.39 

o. ~:I:::::::~~ J <:~::I::::~~~:: .......... 1 ......... . 

................................. 

------

0.8~5 0.343 

FeelJJer 

:oecond. 2.79 

3.60 

3.10 

3.34 

3.09 

~.50 

1. 54 1. 90 3.27 

2.95 

3. 79 3.10 

3 72 2.95 

2. 70 3.47 

2.43 

3.14 

2.29 

2.93 

Ff:f:t J!Cr Feet per 

1

1 

Feet. second. Fef:t. 11econd. Feet. 1. 1~ 1. oo o. 40 1. 45 9. 46. o. 65 o. 31 1. 52 9. 51 I o. 75 o. 29 1.1~ 1. 00 0. 49 0. 97 9. 37 0. 61 0. 32 1.48 9. 51 o. 80 0. 47 1.11 1.00 0.49 0.49 9.34 0.52 0.27 .......... 1 9.32 .................. .. 1. 30 1. 00 0. 42 0. 261 8. 92 0. 62 0. 28 0. 83 9. 54 0. 79 0. 42 1. 30 1. 00 0. 38 1. 4!) 7. 67 0. 70 0. 33 0. 79 9. 54 0. 84 0. 42 2.00 0.85 0.44 1.00 7.64 0.72 0.33 0.68 9.52 0.77 0.39 0. 79 1.00 0. 45 .......... 7.58 ..... ..... ..... ..... 0.65 9.52 0.80 0.34 2.03 0.85 0.37 0.22 7.56 0.60 0.28 1.86 7.25 0.82 0.36 0.7511 1.00 0.47 0.49 6.01 0.60 0.28 1.87 7.25 0.69 0.32 0.55 1.00 0.50 1.89 6.28 0.71 0.32 1.68 7.22 0.77 0.34 1.89 1.00 0.40 1.25 6.40 0.66 0.32 1.65 7.22 0.72 0.33 1.89 I 1.00 0.43 0.85 G.H2 0.60 0.31 1.02 7.18 I 0. 7'2 0.33 1 20 1. 00 0. 46 0. 46 11.48 0. 56 0. 27 0. 96 7.18 ' 0. 70 0. 36 1.20 1.00 0.49 1.46 8.47 0.65 0.31 .......... 7.11 ................... . 

8: ~~ t gg 8: :~ ..... ~·. ~: ...... ~: ~:. 8: ~~3 8: ~6 g: ~~ ~: ~~ 8: ~g 8:!1 0.69 1.00 0.50 .......... .......... 0.755 0.37 ..................................... .. 

gJ~ t ~g I gJg :::::::::: :::::::::: ::::: :::::r::::::::::: ::::::::: :::::::::: :::::::::: ::::::::: .. ........ 'D.9s5 ----o.457 ................... ·l---o.69[-------o.34 .................... ---o.7551 0. 3 

V =velocity found from the weir. 

V0 =velocity found with meter by ordinarylmethod. 

d 111=distance above bottom to thread of maximum Yelocity. d' =distance above bottom to thread of mean velocity. 

.... ~- ! ! ~ _ ..• -.. -·..: .:.. :.... 1 4 J 

-l 

00 

> a 

a 

c:: 

~ 

>. 

a 

-< 

0 

~ 

00 

~ 

~ 

t;j 

> 

~ 

~ 

t?;l 

> w 

c:: 

~ 

t;j 

~ tzj 

~ 

~ 

r:p 

z 

9 

~ 
The :fi1~st o£ the following tables gfves the mean, waxmiuni, and hottori1 ve1ocities in the expedmerits -ora 

series A, C, and D, also the ratio of bottom velocity to mean velocity and of mean velocity to mid-depth velocity. ~ 

It is seen that the ratio of mean velocity to mid-depth veloeity is much n1ore nearly constant, and hence is better to ~ 

use than that of ~ean velocity to bottom volocity. The second table gives the ratio of mean velocity to three-tenths·-

depth velocity, and of mean velocity to six-tenths-depth velocity in series A, 0, and D. The ratio at three·tenths 

depth is seen to be more nearly constant than that at six-tenths depth. 

r"elocitie8 at v£trious depths and 'Velocity ratios in Cornell Uni·versity experirnent canal as found .from standard weir a.nd current-meter discharge 

measurements. · 

Series A. Series C. Series D. 

No. of Depth Velocities ]n feet per sec.a Ratios. Depth Velocities in feet per sec.a Ratios. DDep~h Velocities in feet per sec.a Ratios. 

e~~~t (f:lef~ I I l' l' <fe~f.n - . T' l" (fe~:~ I I l' I V V r (b) l'.!.D .....!: - 'V F V (b) V1.D ~ - Y r l' (b) V•D __ b l'+ l'.!.D m b • , • V YiD m b • V ViD m L li V • 

--~------------------------- -------.----------

1...... I 8. 00 1.17 1. 26 0. 80 1. 24 0. 69 0. 90 9. 46- 1. 41 1. 45 1. 05 1. 44 0. 74 0. 98 9. 51 1. 53 1. 62 1. 29 1. 57 0. 84 0. 97 2 .. -... 7.17 0. 57 0. 59 0. 50 0. 56 0. 88 0. 98 9. 37 0. 93 0. 96 0. 83 0. 95 ' 0. 89 0. 98 9. 51 1. 53 1. 64 1. 33 • 1. 56 0. 87 0. 98 3...... 7. 26 0. 68 '0. 76 0. 60 0. 70 0. 88 0. 97 9. 34 0. 48 0. 50 0. 43 0. 50 lrO. 89 0. 96 9. 32 1. 54 ................ : ................... . 4...... 8.10 1. 27 1. 37 1. 01 1. 33 O.l:lO 0. 96 8. 92 0. 27 0. 29 0. 22 0. 29 1 0. 82 0. 94 9. 54 0. 77 .................................... . 5...... 1. 54 o. 84 o. 87 o. 64 o. 85 o. 76 o. 99 7. 67 1. 44 1. 54 1.12 1. 52 1 o. 78 o. 95 9. 54 o. 77 ..................................... . 6...... 8. 37 1. 46 1. 55 1. 22 1. 53 0. 82 0. 96 7. 64 1. 02 1. 09 0. 78 1. 06 1 0. 76 0. 96 9. 52 0. 62 .................................... . 7...... 7.85 1.06 1.10 0.92 1.08 0.87 0.98 7.58 0.59 ...... ········ ........ ······· .•..••.. 9.52 0.62 .................................... . 8...... 7. 85 1. 06 1. 09 0. 92 1. 07 0. 87 0. 99 7. 56 0. 26 0. 29 0.15 0. 28 0. 58 0. 93 7. 25 1. 91 2. 01 1. 65 1. 96 0. 86 0. 97 9...... 7. 85 1. 06 1.10 0. 92 1. 07 0. 87 0. 99 6. 01 0. 52 0. 58 0. 37 0. 57 0. 71 0. 91 7. 25 1. 91 2. 01 1. 61 1. 98 0. 84 0. 96 10...... 7.9811.18 1.24 0.83 1.20 0.70 0.98 6.28 1.94 2.17 1.42 2.07 0.73 0.94 7.22 1.65 1.77 1.42 1.69 0.85 0.98 11. •. . • . 7. 73 0. 98 1. 01 0. 79 1. 00 0. 81 0. 98 6. 40 1. 28 1. 41 0. 94 1. 37 0. 73 0. 94 7. 22 1. 65 1. 72 1. 44 1. 70 0. 87 0. 97 12 ...... 7.28 o.64 0.11 0.49 o.7o o.77 o.92 6.32 o.89 0.98 o.63 e.96 0.11 o.93 7.18 o.96 1.01 o.8o o.99 o.83 o.97 13...... 7. 48 0. 97 0. 89 0. 65 0. 88 0. 83 0. 90 8. 48 0. 48 0. 54 0. 40 0. 53 0. 79 0. 91 7.18 0. 96 1. 03 0. 76 1. 00 0. 80 0. 96 14...... 7.28 0.64 0.73 0.42 0.68 0.66> 0.94 8.47 1.45 1.60 1.04 1.58 0.72 0.92 7.11 ......................................... .. 

15...... 7.48 0.79 0.871 0.56 0.85 0.71 0.93 8.51 0.9210.95 0.67 0.95 0.73 0.97 5.15 0.69 0.711 0.59 0.68 0.86 0.99 16 ...... -----~---- ...... ........ ........ ...... .. ....... .... .... 8.46 0. 23 0. 26 0.15 ........ 0. 65 ........ 5.15 0.69 0. 72 0.62 0.68 0.89 0. 99 

' ----- ------ ----- . . ....................................... 0.795 0.958 .......... , ............................ 0.747 0.944 ...................................... 0.851 0.974 

a Correct velocities found from standard weir. b Velocity 2-k inches above the bottom. 

NOTE.- V=mean velocity; l';u=maximnm velocity; Vb=bottom velocity; VlD=mid-depth velocity. 

-< 

~ 0 

0 

::3 

1-4 

t;l 

riJ 

~ 

1-3 

tj 

1-4 

~ 

b:j 

tl 

t;l 

!Z 

1-3 

tj 

t;l 

~ ?2 

-::r 

~ 
80 ACCURACY OF STREAM MEASUREMENTS. [NO. 95. 

Velocity mtios ·in Cornell University experiment canal as .fonnd with current meters ·in 

-]fay, November, and December, 1900. 

Series A. Series C. Series D. 

No. of ex peri- Veloc- Depth Ratio Ratio Veloc- Depth Ratio Ratio Veloc- ment. I Rallo I Ratin ity (~). (~} ity (~). (f.:)· ity Depth (t'a) ( v6) tD). (D). (D). V: . ti;; • (t•.). Vo Vo ( !'o). ( !'o ). 

--- --- --------- - Ft. per Ft. per Ft. per sec. Feet. sec. Feet. sec. Feet. I 1 •...... 1.10 8.00 1.082 1.050 1.45 9.46 1. 022 1.009 1. 52 . .. , 

1

, .• ,. 1.012 2 ....... 0.45 7.17 1.062 1. 036 0. 97 9.37 1.029 1.017 1.48 ~:~~ -~~~~~- 1.002 3 ....... 0.68 7.'26 1.066 0.997 0.49 9.34 1. 037 1.022 . ............ 4 ....... 1. 27 8.10 1.060 1.014 0.26 8. 9'2 1.031 0.981 O.!l3 9. 54 1.031 0.988 5 ....... 0. 79 7.54 1.073 1.010 1.45 7.67 1.057 1. 0'21 0. 79 9.54 1.039 1.000 6 ....... 1.44 8.37 1.070 1.033 1. 00 7.64 1.073 1.025 0.68 9.52 r 1.034 1.000 7 •. -- .•. 1.04 7.85 1.040 1.003 0.50 7.58 ........... ........... 0.65 9.52 1.046 1.010 !:! ....... 0.98 7.85 1.034 1.013 0.22 7.56 1.091 1.082 1. 86 7.25 1.058 1.011 9 ....... 1.15 7.86 1.055 1.000 0.49 6.01 1.091 1.069 1. 87 7. 25 1.056 1.027 10- ...•.• 1.29 7.98 1.083 1.025 1.89 6.28 1.127 1.042 1.68 7.22 1.038 1.010 

11 ·-.-... 0.94 7. 73 1.050 1.021 1.25 6.40 1.094 1.045 1. 65 7.22 1.039 1. 018 12 ....... 0.53 7.28 1.103 1.043 0.85 6.32 1.090 1.056 1.02 7.:t8 1.060 1.023 13 ....... 0. 74 7.48 1.070 1.046 0.46 8.48 1.056 1. 043 0.96 7.18 1.070 1.017 14 ....... 0.64 7.28 1.146 1.001 1. 46 8.47 1.081 1.036 .. ............. 7.11 .. ......... ............. 15 ....... 0.83 7.48 1.155 1.030 0.89 8.51 1.025 1.042 0. 73 5.15 1.041 1.011 16 ....... ------·- ............. ............ ............. 0.20 8.46 1.139 1. 030 0.67 5.15 1.045 1.015 

----

1. 069 11. 035 

----

1.077 1.021 1. 0481 1.010 

V0 = velocity obtained by ordinary method. v3 and t•6 = velocity at three-tenths and at six-tenths depth below the surface. 

MEAN VELOCITY BY INTEGRATION IN VERTICALS. 

The mean velocity in the discharge section was obtained by the 

method of integration in the eight verticals 1, 3, 5, etc., immediately 

after making experiments 1, 3, 9, and 37 of series E. In the following table the velocity thus obtained is compared with that obtained 

by the ordinary point method in the experiment just preceding: 

Comparison of mean ·l•elocity obtained by the ordinary po·int ·method and by integration in 

·l•ertica.l.~ ·in Cornell Univers-ity e:11Jerhnent ca·nal. 

Velocity. 

Date. Point. I In;~a- met.hod methoo 

(lp)- (VI)-

Depth. Kind of meter. TJ,-l'i 

v p 

----1----

1901. April! ............................... . Apri12 ............................... . April5 ............................... . April11. ............................. . Peet. Ft. pe-r sec. 9. 08 Haskell No.3... 1. 468 6.08 ..... do.......... 2.208 7. 41 ..... do.......... 1. 883 9. 26 S. Price No. 351.. 1. 522 Ft. per' sec. 1.460 

2.225 

~- 9'21 1.568 

Per cent. 

+O.G 

-0.8 

-2.0 

-3.0 

It -will be seen that the agreement i:; close, the greatest differenee 

being 3 per cent. 

RATING METERS IN STILL AND IN MOVING WATER. 

The results of meter and standard-weir comparisons are given in 

the tahles on pages 65 to 68. With a few exceptions, already mentioned, these are shown graphically in figs. 16, 17, and 18, pages 69 

and 70. The straight lines 0-0' represent in each case the weir disc~arge and the curved lines drawn through the plotted points repre~ 
MURPHY.) METERS IN STILL AND IN MOVING WATER. 81 

!sent the percentage variation of the meter discharge fron1 the 

!corresponding weir discharge. The meter discharge is computed 

from a rating table prepared from ratings in still water. I-f we 

assume that the weir discharge is correct, then these curves show the 

percentage difference between a rating in still water and a I'ating in 

1

mo'ving water, and furnish the data for preparing a rating table for 

moving water from the one for still water. We have only to apply_ 

the correction to any velocity for any given number of revolutions 

per second, shown on the proper diagram, to obtain the velocity in 

moving water. This has been done, and the rating tables of the 

meters in still and in moving water are given in the following table. 

The velocity in moving water for any given number of revolutions per 

;second is greater for all speeds of the Price meters than thevelocity 

:in still water. For- the Haskell meter (a propeller instrument) the 

'velocity is less in movir..g water than in still water for low velocities, 

and probably about the same in moving water as in still water for the 

higher velocities. a The discharges might now be computed, using the 

lrating tables for moving water, and they would agree closely with 

the weir discharges. New vertical velocity curves have b~en found 

:for series A, and the mean velocity ascertained from them. The 

shape of the new curve differs little from the old one, as the range 

;of velocities for any curve is small. The new velocities obtained 

from the corrected curves are given in the second column of the 

,table. 

Rating tables of c·urrent meters in still 1vater and in 1noving 'Water in Cor·nell Unit1ersity 

e.'tperiment canal. 

I Small Price Large Price Haskell Revo- Haskell 1 

Revo- Fteley.b Fteley.b : lutions No.351.b No.88.b No.3.o lutions No.3.o 

per ~second. I 

v Vw v Vw v v., v Y., per second. y v w v v.,. , __ --------------------------

........... .......... ........ ...... ....... ...... . ...... . ....... ····-·· 1.10 1.30 1. 28 1.18 1. 07 

' 

...... ........ ....... ······· ....... ......... 1. 20 1.40 1.39 1. 29 1.15 0.10 0.284 0.318 ·o:54· ....... ........... ........... ........ 1.30 1.50 1.49 1.39 1.23 0.15 0.397 0.437 0.660 ........ ........... ............ ........... 1.40 1.60 1.60 1.50 1.30 0.20 0.510 0.552 0.70 O.&l4 ....... ............. ......... .......... 1.50 1. 71 l. 70 1.61 1.38 0.25 0.625 0.664 0.86 0.950 .......... ........ ............. .......... 1.60 1.81 1. 81 1. 72 1. 45 0.30 0. 741 0. 776 1.03 1.097 ......... .......... ............ .............. 1. 70 1.92 1.92 1. 82 1.53 0.35 0.857 0.887 1.19 1. 244 ......... ......... .......... . ....... 1.&l 2.02 2.03 1.93 1.60 0.40 0.972 0.998 1.35 1.392 ......... ........... ............ ......... 1.90 2.13 2.14 2.04 1.67 0.45 1.088 1.109 1.52 1. 550 .......... ........... ............ 2.00 2.23 2.24 2.14 1. 74 0.50 1.204 1.220 1.68 1. 709 0. 70 0.647 0.536 0.552 ............. ............ ....... .......... ............... 0.55 1.319 1.332 1.84 1.874 0. 75 0.698 O.fl89 0.598 ........... .......... ............ ........ ·-·····- 0.60 1.435 1.447 2.01 2.042 O.&l 0. 751 0.643 0.644 .............. ....... .. ....... ........ .............. 0.65 1.550 1.562 2.17 2.207 0.85 0.803 0.697 0.690 .......... ........ .. ........ .......... ............... 0. 70 1.660 1.677 2.34 2.373 0.90 0.85.5 0. 750 0. 735 ......... .. .. ---· ·····- ... -......... ............. 0. 75 1.782 1. 796 2.50 2.538 0.95 0.907 0.804 0. 779 ........... .............. ........... .. ....... .. ............. 0.80 1.897 1.915 2.66 2. 702 1.00 0.960 0.858 0.822 ............. ......... .......... ···-·· .. ............ 0.85 2.013 2.033 2.83 1.05 1.014 0.911 0.864 ............. ........... ......... ··---- ...... - ~ -- 0.90 2.129 2.150 2.99 3.0 4 1.10 1.068 0.965 0.00.') ............ .......... ........... .......... ............. 0.95 2.244 2.266 3.15 3.1 1.15 1.121 1. 018 0.946 .......... ····-- ......... .......... .. ........... ··m I 

1.00 2.36 2.38 3.32 3. 6 1. 20 1.174 1.072 0.987 ............ ...... r····· ...... ................ 

I 

a Recent experiments with a Fteley meter do not verify this statement. b Meter held rigidly 'With rod. o Meter held with caible~ 

NoTE.- V=veloctty-: in feet per second, from still-water ratfng; Vw=velocity, in feet per sec- ond, from moving-water rating. . 

IRR 95-04--6 
82 ACCURACY O:E' STREAM MEASUREMENTS. [NO. 95. 

A reason for the percentage increase in the variation of the meter 

discharge from the weir discharge as the velocity decreases is to be 

found in the rating table from which the velocities are computed. 

The experiment of November 1 shows that the small Price 1neter will 

measure a velocity of 0.23 foot per second, as the mean velocity found 

from the weir is 0.229 foot per second and the meter wheel revolved 

with regularity at all points where it was held. The observations in 

the rating do not extend to this velocity, however~ and do not warrant 

the preparation of a rating table giving velocities of less than 0.5 foot 

per second. 

In the three ratings of small Price meter No. 351 on May 9, 1901, 

shown in fig. 29, page 89, there are only four observations for velocities less than 0. 5 foot per second and none below 0.45 foot per second. 

The extension of the table to velocities less than 0.5 foot per second is _, 

probably made on the assumption that this part of the rating curve is 

a straight line. That this is very far from the truth can be seen from 

an inspection of the three curves of fig. 29. Another reason is that 

discharge shown by the Cornell University standard weir is probably 

from 1 to 3 per cent too large for low heads o~ the weir. Recent 

experiments seem to indicate this fact. These two causes, however, 

account for only a comparatively small part ef the difference between 

current-meter and weir discharge at low velocities which the experiments of series A and C, and others made since the writing of the 

body of this paper, indicate. The failure of the meter to indicate as 

high a velocity when held in a very slow-moving current, as when the 

meter is dragged through still water, is probably due to the stream 

lines becoming n1ore and more oblique to the axis of the canal. as the 

velocity decreases, and consequently their impact on the meter being 

less than when they moved n1ore nearly in the direction of the axis of 

the canal. 

ERROR IN USING AVERAGE OF BOTTOM AND SURFACE VEWCITIES FOR 

MEAN VELOCITY. 

The following table gives the mean velocJty and the average of the 

velocities 0.5 foot above the bottom and 0.5 foot below the surface for 

the experiments of series A, C, and D; also the error, in per cent, made 

by using the average of surface and bottom velocities instead of the 

mean velocity. ·It is seen that in all these experiments except t~o the 

mean velocity is greater than the half sum of the surface and bottom 

velocities, the difference varying from -2.2 per cent to +30.6 per cent . 

• 
I 

MtRPHY.] ERROR OF TOP AND HOTTOM M~THOD. 83 

~ble showing relation between mean ·velocity and cwerage of surface and bottom ?Jelocit1~es a.s fonnd frmn Cornell University standard 1t'eir and from current meters in Cornell 

e.rper-iment canRl. 

ment. v l" lr--

I :3eries A. Series C. Series D. 

y 

r-F 

-r- c~~-e~f- I y _ F 

__________ -

Feet per Feet per Feet per Feet per Feet per Feet per second. second. Per cent. second. second. Percent. - second. »econd. Per cent. 1 1.164 0.987 +15.3 1.409 1.412 - 0.2 1.528 1.436 +(i.2 

2 0.573 0.416 +27.5 0.932 0.954 - 0.2 1.528 1.436 +6.2 3 ................... .................... .................. 0.477 0.468 + 0.2 .................... ..................... 4 1. 268 1.190 + 6.1 0.265 0.231 +12.8 .................... .................... ..................... 5 0.841 0. 749 +10.9 1.444 1.364 + 5.6 .................... .................... ................... 6 1.462 1.384 + 5.4 1. 018 0.940 + 7. 7 ~ ...... -........... .................... .................... 7 1.056 0.965 + 8.6 0.502 . ""<i."i77"" ..................... 8 1.056 0.946 +10.4 0.255 +30.6 1.905 1.807 +5.2 9 .................... .................... .................... 0.515 0.435 +15.5 1.905 1. 779 +G.6 10 .................... .................. .................... 1. 914 1. 730 + 9.6 1.649 1.613 +2.2 11 0.980 O.S87 + 9.5 1.283 1.129 +12.0 1.649 1.500 +3.6 12 0.6-!3 0.476 +25.9 0.893 0. 759 +15.0 0.955 0.973 -1.9 13 0. 788 0.687 +12.7 0.478 0.422 +11.8 0.955 0.897 +G.l 14 .................... .................... .................... 1.454 1.311 + 9.8 .................... ---0~704"" ................. 15 ------·--- ................... .................... 0. 915 6. 784 +14.3 0.689 -2.2 16 .................... .................. .................... 0.229 0.179 +21.8 0.689 0.659 +4.3 

V =mean velocity found from standard weir. , V' =mean of velocities 0.5 foot above bottom and 0.5 foot below surface, as found by meters un- corrected. 

From the foregoing table, and from the table on page 79, in which 

is given the ratio of bottom velocity to mean velocity, it appears that 

bottom velocity is not a desirable quantity tq use in computing discharge, for it varies between too wide limit'3. In a stream with a stony 

or gravelly bottom the limits must be considerably greater than in the 

Cornell canal with its smooth bottom. Observations at mid depth or 

at six-tenths depth give better results. 

COMPARISON OF RES"GLTS BY THREE METHODS OF OPERATING METER. 

Three methods of operating meters have beep used in these experiments, viz, the ordinary 1nethod, the six-tenths-depth, and the "integration. A detailed account of the manner of operating the meter 

by each of these methods has been given on pages 63 to 64. The time 

required to n1ake a discharge measurement was from thirty to sixty 

minutes with the ordinary method, from twenty to thirty minutes 

with the six-tenths-depth, and from five to ten minutes with the 

integration. 

The results by the ordinary method in series A to D (fig. 16, p. 69) 

give for each meter a well-defined line, which agrees with the weh· line 

{0-0') within about 2 per oent for velocities greater than 1.5 feet per 

second, the Ineter discharge being less than the correspondiug _ weir 

discharge. 

The agreement with the weir discharge is closer in series Ethan in 

series A to D, being -0.03 per cent for the Haskell meter, -1.13 per 

cent for Price meter No. 363, and -1.88 per cent for Price meter No. 

351. The results by the six-tenths-depth method do not give as well-
84 ACCURACY OF STREAM MEASUREMENTS. (NO. 95. 

defined a line (fig. 17) for each meter as do those by the ordinary 

method, the meter discharge being from ! to 6 per cent greater than 

the corresponding weir discharge, and the mean being 3. 5 per cent for 

small Price meter No. 363. If the observations with the latter meter 

had been taken at sixty-four-huncfredths depth instead of at six-tenths 

depth the line representing the mean would coincide with the weir 

line 0-0', and the greatest percentage variations from the mea,n would 

be -2.5 per cent and +2.5 per cent. 

The results by the integration method do not give a well-defined 

line. The meter discharge is from 1 per cent to 9 per cent greater 

than the weir discharge for velocities greater than 0. 5 foot per second in the experiments of series C and D, and from 0 to 5 per cent 

less than the weir discharge for the experiments of series A. The 

following table gives the true velocity as found from the weir and 

the velocity found by tpe integration method for different speeds of 

the meter; also the ratio of difference between these velocities and the 

true velocity, expressed in per cent: 

Table sho·wing effect of var·iation of speed of meter ·in integration method. 

True Velocity 

No. of velocity Speed of of water 

ex peri- Date. Depth. by weir meter by me- V-V1 Kind 

ment. <n per per ter (V1) ----v- of meter. 

second. second. per second. 

-- --------- 1900. Feet. Feet. Feet. Feet. Per cent. (a) 

1 MayS .....•........•....... 8.10 1.268 0.101 1.268 0.00 S. P. 351. 2 •..•. do ...................... 8.10 1. 268 0.152 1. 235 + 2.60 Do. 3 ..... do ...................... 8.10 1. 268 0.270 1.200 + 5.35 Do. 4 ..... do ...........••......... 7.54 0.841 0.079 0.834 + 0.09 Fteley. 5 ...•. do ...................... 7.54 0.841 0.055 0.842 - 0.01 Do. 6 ·May9 ............•.•....... 7.85 1.056 0.056 1.028 + 2.65 S. P. 351. 7 .•... do ...................... 7.85 1.056 0.043 1.008 + 4.54 L. P. 88. 8 May 15 .............•....... 7.73 0.980 0.032 11.978 + 0.02 S. P. 351. 9 October 24 .....•••.......... 9.46 1.409 0.118 1.429 - 1.42 S. P. 363. 10 ..... do ................•..... 9.37 0.932 0.142 0.982 - 5.36 Do. 11 ..••. do ...................... 9.34 0.477 0.164 0.485 - 1.68 Do. 12 ..•.. do ...................... 8.92 0.265 0.107 0.308 -16.23 Do. 13 October 26 .................. 7.67 1.444 0.137 1.519 - 5.20 Do. 14 ..••. do •...•.......••••...••. 7.64 1.018 0.135 1.079 - 5.99 Do. 15 October 27 •.•............••. 7.58 0.502 0.143 0.522 - 3.99 Do. 16 ••.•• do ...................... 7.56 0.255 0.128 0.312 -22.35 Do. 17 ..... do ...................... 6.01 0.515 0.142 0.555 - 7.77 Do. 18 ..... do ...................... 6.28 1.940 0.180 2.000 - 4.64 Do. 19 ...•• do ...................... 6.40 1.283 0.154 1.338 - 4.29 Do. 20 ..... do ...................... 6.32 0.893 0.188 0.920 -· 3.02 Do. 21 October 29 ....•..........••. 8.48 0.478 0.151 0.492 - 2.93 Do. 22 October :n .................. 8. 47 1.454 0.29H 1.552 - 6.74 Do. 23 ..... do ...................... 8.51 0.915 0.258 1.002 - 9.51 Do. 24 November 1 ................ 8.46 0.229 0.185 0.319 -39.30 Do. 25 December 6 ................. 9.51 1.528 0.253 1.540 - 0.78 Do. 26 ..... do ...................... 9.51 1.528 0.284 1.572 - 2.87 Hask. 3. 27 December 7 ................. 9.32 1.535 0.243 1.576 - 2.66 Do. 28 DecemberS ................. 7.25 1.905 0.252 1.962 - 2.99 Do. 29 ..... do ...................... 7.22 1.649 0.295 1. 748 - 6.00 Do . 30 ...•. do ...................... 7.18 0.955 0.254 1.039 - 8.79 Do. 31 ..... do ...................... 5.15 0.689 0.179 0. 752 - 9.14 Do. 

aS. P.=small Price; L. P.=large Price; Hask.=Haskell. Figures given are the numbers ofthe meters. 
MURPHY.) RESULTS IN 1900 AND 1901. 85 I 

Ta.ble shmving effect of speed of meter on observed ·velocity as found by the integration 

method in e~l:periments of table on page 84. 

Experiments Nos. 9 to 25, omitting Nos. 1'2, 16, and 24. 

Speed of meter 

0.10 to 0.14. 

Feet per· second. 

0.118 

0.137 

0.135 

0.130 ................ 

..................... 

............. 

V-Vt s~:~~f ----v- 0.14 to 0.18. 

Percent. Feet per second. -1.42 0.142 -5.20 0.164 -5.99 0.143 -4.20 0.142 .............. 0.154 ............... 0.151 ............ 0.159 

Per cent. Feet per second. Pel' cent. -5.36 0.180 -4.64 -1.68 0.188 --3.02 -3.99 0.293 -6.74 -7.77 0.258 -9.51 

-4.29 0.253 -0.78 -2.93 0.234 -4.94 -6.33 . ............... ..................... 

Experiments Nos. 1 to 8. 

Speed of meter Y- Vt o.o5to -v- 0.15. 

Feet per second. Percent. 0.056 +2.65 0.043 +4.54 0.032 +0.02 0.101 0.00 0.079 +0.09 0.055 -0.01 0.061 +1.22 

Speed of meter V- Vt 0.15 to -----v- 0.30. 

Feet per second. Per cent. 0.152 +2.60 0.270 +5.35 ............. ................ ............... ................ .. ............. ................... 

0.211 +3.97 

This ratio is positive for all the experiments of series A, and is negative for those of C and D. This difference of sign is due to two causes: 

(1) The Ineter was moved faster in the experiments of C an4_ D than 

in those of series A; and (2} it was moved through only 14 feet of the 

width in series C and D and through nearly 15.5 feet of the width in 

series A, .and the additional 1.5 feet of width had a small velocity. 

It is seen fron1 the above table that for low velocities the error in 

velocity increases as the speed of the meter increases. The table on 

page 84 shows this effect for velocities from 0.5 foot to 2 feet per 

second · ' 

COMPARISON OF RESULTS OBTAINED IN 1900 WITH THOSE. OBTAINED 

IN 1901. 

Examining the plotted results in figs. 16 (p. 69) and 18 (p. 70), 

it is -seen that the meter discharge, compared with the corresponding 

weir discharge, is somewhat larger for the work of 1901 than for that 

of 1900 for velocities greater than 1.4 feet per second. This can not 

be due to change in rating of the meters, for an increase in the friction in a meter would reduee the observed velocity and make the 

meter discharge too small. There was considerably more seepage 

into the canal when the experiments of series E (1901} were made 

than at the time those of A, B, C, and D (1900} were made. There 

was also quite a little surface water entering the canal between the 

weir and the meter section in the experiments of series E. It is hardly 

possible, however, that this inflow between the weir and the ·meter 

section could amount to 2 per cent of the canal discharge. It must be 

borne in mind in this connection that the discharges obtained in 1900 

for velocities greater than 1.4 feet were in shallow water, and therefore are not so reli,able as those obtained in series E. 

EFFECT OF METHOD OF HOLDING METER IN WATER. 

In some of the experiments the meter was suspended from a cable; 

in others it was held in the water with a rigid rod. In the latter cases 
86 ACCURACY OF STREAM MEASUREMEN'!'S. (NO, 95. 

its axis was free to move about a horizontal axis; in the former cases 

it was free to move about a vertical as well as a horizontal axis. When 

used with a cable a sinker is necessary, which, being attached to the 

under side of the meter, keeps the axis of the revolving wheel farther 

frmn the bottom than is desirable in some cases. It is also difficult to 

keep the meter in any desired place when held with a cable, and it 

usually changes its ppsition considerably in a swi£t current. It was in 

order to measure the velocity close to the bottmn and keep the n1eter 

at a desired place during the observation that in m~ui.y of the experiments the meter was held with a rod. In ordinary river gaging, however, the Price and Haskell meters are held with cables and the meters 

are rated in still water suspended from a ear and cable. The queHtion 

then arises: "Is the rating tahle for a meter used suspended from a 

cable applicable to the same meter held with a rigid rod?'' 

On December 30, 1900, Mr. E. G. Paul made two ratings of small 

Price meter No. 351 in still water, one with the meter held with a rigid 

rod and the other with the meter held with a cable and a 5-pound lead 

sinker. In the following tables (pp. 87 and 88) are given the observations and computations of these ratings. The second column ("time 

in seconds") gives the average time required for the car to which the 

meter was attached to move over a run of 100 feet, and again over 

the saine course in the opposite direction; the third column gives the 

_number of revolutions observed in this average time; the seventh 

cohnnn gives for each of these cases the difference between the observed 

velocity and the velocity computed from the old rating table of April 

23, 1900, for the same metet· held with a cable.. The tenth column of 

the first table (p. 87) gives the difference between the observed velocities 

and those computed from the new rating table, which is based on meter 

rated in still water and held by a rigid rod. The portion of this new 

rating table, which was used in redueing the Cornell experiments, is 

given on page 81. By-comparing the corresponding quantities in the 

seventh and tenth columns of this table it will be seen how much more 

closely the values in the new rating table fit the observations than do 

those of the old one. The tenth column shows also how much the relation between the revolutions per second of this meter and the velocity as 

shown by these observations differs from the "most-probable" straight 

line, y=0.047+2.313x, y being velocity in feet per second and w revolutions of meter wheel pei· second. From the seventh column of the 

table on page 87 it is seen that the observed velocities are iarger than 

the computed velocities, indicating more friction in the mete.r on 

December 30, 1900, than on April 23, 1900. 

The "most probable" linear relation between m and y for this case 

of the meter held with a cable was found to be y=0.067+2.321a:1 The 

differences in the tenth column show that this line does not tit the 
MURPHY.) METHODS OF HOLDING METER.- 87 

observations. It crosses the curve given by the observations twice as 

y increases froml to 8 feet per second. The rating L<tble was prepared 

by using this line as a basis, applying corrections as indicated by the 

corresponding difference of the tenth column, so that the rating table 

will difference smoothly. The numbers in column 12 show how 

closely the observed velocities agree with those computed fron1 the 

new rating table with the meter held with a cable. 

It should be noted that the s1nallest observed velocity is about 0. 5 

foot per second in one case and 0.35 foot in the other case. 

Observations and computatim1s of a rating (~f small P1··ice meier No. 351 held by rigid rod, 

made at Chevy Cha.~e, Jfd.,. December 30, 1900. 

__ L ___ 1 __ 2_a_r_Id_3_. __ 1 __ 4.___ 5_. _l __ r._. __ 7_._ ~- _9_._ ~ __ n_._ 

Length of run, 

No. of 100 feet. l!fi6~s Ob- Comobser- Revo- per served puteu 

vation. T' e lntion~ second velocity velocity Im • ofme- (x). (y). (yl).a 

Seconds. 

ter. 

Feet per se!'ond. 

Difference 

(y-yl). 

Residual 

(t•). 

1 9.25 43.00 

42.50 

43.00 

43.00 

42.2.") 

42.00 

42.00 

42.00 

41.75 

41.75 

41.00 

41.00 

40.50 

39.50 

39.00 

36.90 

4.648 

Feet per second. 

10.811 

b9.524 

6.250 

10.1-115 

9.405 

6.231 

4.414 

2.797 

2.183 

1.867 

1.823 

1.461 

1.174 

0.944 

0.891 

0.669 

0.522 

0.569 

0.351 

Ft. per second. 

-.004 

+.119 

+.019 

+.030 

+.060 

+.039 

+.020 

+.012 

+.010 

--.004 

21.604 50.245 +. 0;)9 . 003481 2 10.5 3 16.0 4 22.5 5 35.0 6 45.0 7 53.0 8 5!.5 9 68.0 10 85.5 11 106.5 12 113.0 13 154.0 14 197.0 15 220.0 16 293.0 

b4.048 

2.688 

1.911 

1. 207 0.933 

0. 794 

0. 774 0.614 

0.488 

0.385 

0.363 

0.263 

0.201 

0.177 

0.126 

15.572 

4.4-14 

2.857 

2.222 

1.887 

1.835 

1.471 

1.170 

0.939 

0.885 

0.649 

0.508 

0.455 

0.341 

36.724 

-.005 

-.006 

-.020 

-.014 

-.014 

-.010 

7.2~ 

3.652 

1.457 

0.870 

0.630 

0.599 

0.377 

0. 2'3~ 

0.148 

0.132 

0.069 

0.040 

0.031 

0.016 

1G.800 

8.493 

3.448 

2.073 

1.498 

1.420 

0.903 

0.571 

0.362 

0.321 

0.171 

0.102 

0.081 

0.043 

::7. o:-:s s6. 531 

-.014 

---.022 

+.018 

+.017 

+.003 

-.003 

+.004 

-.006 

+.001 

-.002 

-.006 

-.004 

--.001 

-.003 

a Computed from rating table prepared from rating of April23, 1900. 

bOmitted in computing ~ x and~ y. 

.00019() 

.000484 

.000324 

.0002&9 

.00000!) 

.000009 

.000016 

.000036 

.000001 

.000004 

.000036 

.000016 

.000001 

.000009 

NoTE.-Observation equation, y-a-bx=l•; normal equations, a~ a.'+b ~ x2=:l; xu, na+b :S X=~ 11· For these observations these_ become 15.572 a+37.088 b=86.531, 15a+15.572b=36.724. The solution: 

of these gives b=2.313 and a=.047. The mean error of a single observation is .../~ t•~ =.019. Theprob- n-1 

able error of result is 6.745 .../ ~ t'

2

1

)=.00::t n~n-
88 ACCURACY OF STREAM M.EA8UREMENTS. [NO. 95. 

ObservatiiJrts and r.mnptttations of a rating of small Price meter No. 351 held by cablf', 

made at Chevy Chase, Md., December 30, 1900. 

1. 2 and 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 

---------------- Length of run, 100 feet. Revo- Ob- Com- Com- No. of lutions served puted Differ- Resid- puted Differ- obser- Revo- per veloc- veloc- ence x2 xy ual. veloc- ence yation. Time. lutions second ity ity (y-y'). (z•). ity (y-y"). 

of me- (x). (y). (y').a (y").b 

ter. --------------- -------------

Sec- Ft. per Ft. per Ft. per Ft. pel' 

onds. second. second. second. second. 1 10.5 42.00 4.000 9.524 9.300 +.224 ............. ·21:20o· .............. ............. 2 12.5 42.50 3.400 8.000 7.900 +.100 11.560 +.042 7. 98 +.02 3 16.5 42.50 2.576 6.061 5.967 +.094 6.636 15.613 +.015 6.04 +. 0'21 4 21.5 42.75 1.990 4.651 4.588 +.063 3. 960 9.256 -.034 4.68 -.029 5 2&.0 42.50 1.635 3.846 3. 767 +.079 2.673 6.288 - .. 015 3.837 +.009 6 29.0 42.50 1.465 3.448 3.383 +.065 2.146 5.051 -.020 3.443 +.005 7 31.0 42.25 1.363 3.226 3.151 +.075 1.858 4.397 -.004 3.290 +.017 8 41.0 42.50 1.037 2.439 2.411 +.028 1. 075 2.529 -.034 2.451 -.012 9 50.0 42.50 0.850 2.000 1.990 +.010 0. 723 1. 700 -.039 2.024 -.024 10 61.0 42.00 0.688 1.639 1.624 +.015 0.473 1.128 -.024 1.655 -.016 11 70.0 42.00 0.600 1.429 1.430 -.001 0.360 0.857 .030 1.454 -.025 12 80.5 41.25 0.512 1.242 1.226 +.016 0.262 0.636 -.013 1. 256 -.014 13 90.5 40.00 0.442 1.105 1.072 +.033 0.195 0.488 +.012 1. 098 +.007 14 105.5 39.00 0.370 0.949 0.908 +.041 0.137 0.351 +.024 0.938 +.011 15 125.0 38.00 0.304 0.800 0. 759 +.041 0.092 0.243 +.028 0.790 +.010 16 140.0 37.00 0.264 0. 714 0.671 +.043 0.070 0.189 +.035 0.697 +.017 17 171.0 36.00 0.215 0.585 0.556 +.029 0.046 0.126 +.019 0.585 -.000 18 184.0 36.00 0.196 0.543 0.507 +.036 0.038 0.106 +. 02'2 0.541 +.002 19 211.0 35.75 0.169 0.474 0.452 +.022 0.029 0.080 +.015 0.479 -.005 

---- ----

18.076 43.151 32.334 76.239 

I 

a Computed from rating of April23, 1900. b Computed from rating of December 30, 1900. 

NOTE.-Most probable straight line given by these observations, y=.067+2.321x. 

The following table shows the percentage difference of velocity for 

each 0.05 revolution for these two ways of holding the meter. It is 

seen that a given number of revolutions per second of this meter indicates a higher velocity when it is held with a cable than when it is held 

with a rigid rod, and that this percentage difference decreases as the 

velocity increases. In other words, in a given velocity the meter will 

revolve faster when held with a rigid rod than when held with a cable. 

It must be remetnbered that the va]ues given in this table for velocities less than about 0.5 foot per second are only approximate, since 

the observations do not extend below 0.35 foot per second. We may 

say that if the rating tab]e for this meter held with a cable be used to 

reduce observations made with the meter held With a rigid rod, the 

results will be in error from 1.3 per cent to 8.5 per cent for velocities 

from 1.5 feet to 0.5 foot per second. 
MURPHY.) METHODS OF HOLDING METER 89 

Table :~howing percentage d~fference ·in 1•elocity a.~ .~houm by srnall .Price meter No. 351 

·when rated in st·ill 'Water on a rigid rod and on a cable. 

Speed of r. r Y.-r. Speed of I r l y 

Y.-Y. 

meter. c --r~ meter. r • ~ ----~--

R.per sec. F. per sec. F.per sec. Per cent. R.per sec. IF. per sec. F.per sec. Per cent. 0.15 0.397 0.433 9.1 0. 60 1. 435 1. 455 1.4 

0.20 0.510 0.550 7.8 0.65 1.550 1.568 1.2 0.25 0.625 0.666 6.6 0. 70 1. 666 1. 682 1.0 

0.30 0. 741 0. 781 5.4 0. 75 1. 782 1. 796 0.8 

0.35 0.857 0.894 4.3 0.80 1.897 1. 910 0. 7 0.40 0.972 1.006 3.5 0.85 2.013 2.024 0.5 0.45 1.088 1.118 2.8 0.90 2.129 2.138 0.4 0.50 1.204 1.230 2. 2 0.95 2. 244 2.252 0.4 0.55 1.319 1.342 1. 7 1.00 2.36 2.37 0.3 

Y .=velocity with meter rated on a rigid rod. J'e=velocity with meter rated on a eable. 

Small Price 1neter No. 351 was again rated three times on May 9, 

1901. It was held (1) with a cable, using an 18-pound Hinker; (2) with 

a rod, the meter being free to tip; and (3) 

with a rod and the meter not free to tip. 

Space will not permit the· insertion of the 

observed data or the computations, but 

the re'sults are plotted in fig. 29, using R= 

revolutions per second as abscissre and 

Ii= .J;=ratio of velocity to revolutions as 

ordinates. It is seen that these rating observations give a separate curve for each 

of these cii8es. The value of I{ for any 

value of R for one curve is very different 

from that for the other curves for velocities les(3 than about 3 feet per second. For 

example, for R=0.3, I-1=2. 755 for case 1 

(curve AE), 2.585 for case 2 (curve BE), 

and 2.485 for case 3 (curve DF). The coefficient is largest when the meter has the 

most freedom of motion and least when it 

has no freedom of motion. As the velocity 

for a given number of revolutions varies 

directly with.Ii, the velocity decreases as 

the freedom to tip about a horizontal axis 

and to swing around a vertical axis de-

., 

1 

~ 

~ 

:8 ·t 

.\ 

.7 \ 

~ 

~\\ 

_\\ \ ~ lt 

I~ '' ~ 1'-. ....... :--..... -....... 

trewio Nona/»'"~ 

FIG. 29.-Curves showing relation between rev:olutions of meter and ratio 

between velocity of water and revolutions of meter from three ratings 

of small Price meter No. 351 at Chevy 

Chase, Md., May 9, 1901. Crossed 

circles are for observations with meter held with cable, an 18-potmd 

sinker being used. Heavy black 

dots are for observations with meter 

held with rod and free to tip. Open 

circles are for observations with meter held with rod and not free to tip. 

creases. Or, stated in the other way~ in a current of a given velocity 

the revolutions increase as the freedom of motion decreases. - Each 

of these cases therefore requires a separate rating table. 
90 ACCURACY OF STREAM MEASUREMENTS. [No. 95. 

SURFACE VELOCITY EXPERIMENTS WITH FLOAT RODS AND WITH 

CURRENT METERS. 

It was noticed during the weir and current-meter comparisons that 

the shape of the vertical velocity curve near the surface obtained with 

a small Price n1eter was quite different under certain conditions from 

that obtained with ,the Haskell meter under the same conditions. This 

peculiarity can be seen in the simultaneously obtained curves of fig. 30. 

The Haskell meter indieates a higher surface velocity than the Price 

meter. By surface velocity obtained with a meter is meant that 

obtained when the revolving part of the meter is entirely under water 

all of the time and yet as close to the 1-Hll'face as possible. For the three 

meters used in these surface velocity observations the distance of the 

FIG. 30.-Vertical velocity curves from simultaneous experiments of series E with small Price 

meter No. 363 and with Haskell meter No.3. Large black dots are for Price meter, open circles 

for Haskell meter. 

center below the surface was a~ follows: Small Price meter No. 351, 

from 2.5 to 3 inches; Fteley No. 107, from 3 to 3.5 inches; Haskell 

No. 3, from 4 to 4.5 inches. 

In order to investigate this matter further the surface velocity of a 

part of the canal was measured simultal).eously with floats and with 

two current meters. The floats used were 6-inch cubes of wood loaded 

with lead so as to have an immersion of 5! inches. Surface floats of 

wood 6 inches by 6 inches by 1 inch thi~k were also used. These were 

started near the center of the canal 18 feet above the upper wire and 

timed over a run of 60 feet. Any tha~ passed the lower wire within 2 

feet of either side were not used in computing velocity. The meters 

were held 10 feet below the lower wire, the Haskell at 5 and 7 feet 

from the south side of the canal, the Price at 9 and ll feet from the 
MURPHY.) FLOAT RODS AND CURRENT METFRS. 91 

south side, and the revolutions were counted for period~ of forty 

second.s. The results of the experiments are given in the following 

table: 

Compa·rison of surface twlocity mea81tred 'With float rods (tnd ·with current wwter.<:. 

Small Price meter No. :151. Haskell meter No. 3. 

Number Velocity Number Velocity Number Velocity Numbe< I V•lodty of float of 40- of float of 4o- with observa- with second with observa- with sec_?nd meter tions. floats. periods. mt_•ter. tions. floats. penods. · 

------

Feet per Feet per Ped per Feet per 

second. 8f('U11d. .~f'cond. 8CC01!d. 

11 3.12:.! 10 2. 794 13 3.083 13 3.171 12 3. 076 12 2.806 12 3.144 12 3.187 13 3.030 13 2.81/l 10 3.135 10 3.165 ------------------------

36 3.076 35 2.806 35 3:121 35 

1 3.174 

During the foregoing observations the depth of water in canal was 

6.0± feet, its mean velocity 2.8 feet, and the discharge 275.3 cubic 

feet per second. The float velocity that is compared with the Price 

meter velocity is obtained from the floats passing the lower wire frmn 

2 to 8 feet from the south side of canal;· that which is compared with 

the Haskell meter velocity is found from the floats passing the lower 

wire from 8 to 1± feet from the south side of canal. It is seen that in 

each experiment the float velocity is greater than that of the Price 

u~eter and less than that of the Haskell meter. The mean float 

velocity for the three experiments is 8.8 per cent greater than the 

velocity with the Price meter and 1. 7 per cent less than that with the 

Haskell meter. · 

It was thought that possibly this failure of the stnall Price meter to 

give correct. surface-velocity indications was due to wave motion of 

the meter. Another experiment was therefore made with the floats 

and with the meter held with a rod and not free to tip. Fteley electric 

meter No. 107 was also used in place of the Haskell meter. The floats 

were started at many points in the width of the canal and were timed 

over a run of 50 feet. Those that came within 2 feet of either bank 

were not used in computing the velocity. The meters were held 2± 

feet below the lower wire at points from 0 to 7 feet from the center, 

and the rmTolutions were counted for 50-second periods. 

The -mean surface velocity sho.wn by the small Price meter from 

thirty -two 50-second periods i8 1. 967 feet, and the eorresponding float 

velocity obtained from ten floats pa.ssing from 2 to 8 feet from the 

south side of canal is 2.146 feet. The corresponding surface velocity 

shown by the Fteley meter is 2. 07 4 feet, and by the floats from 8 to 

14 feet from the south side of canal, 2.137 feet. The float velocity is 

8. 3 per cent greater than the Price meter velocity and 2. 95 per cent 

greatet.· than the Fteley meter velocity. The difference between the 
92 ACCURACY OF STREAM MEASUREMENTS. [No.95. 

float and the Price meter velocities is about _the same as in the previous 

experiments. 

During this experiment the Price meter was held 3. 5 :feet :from the 

south side of canal, with its center 2-! inches below the surface for 

seven 50-second periods, and again with its center 4. 5 inches below 

the surface for about the same length of time. The mean velocity at 

2! jnehes depth was 1. 884: feet, and at 4. 5 inches depth it •was 2.035 

feet. The float velocity at this point was 2.137 feet. The"-iBidicated 

velocity increased 7.± per cent as the meter was lowered lf ,iaehes. 

The float work in this experiment is not very satisfactory. 

On May 20 vertical-velocity-curve data were taken with small Price 

meter No. 351 and with Haskell meter No. 3 for different mean velocities, with a view to determining the magnitude of this error at different velocities and depths below the surface. The Haskell meter was 

· held with a cable 1 foot south of the center of the canal and 244: .feet 

from the weir; the Price meter was held with a cable 1 foot north of 

the center of canal. The following data were obtained: 

Velocit'ies near the su·rface of Cornell Uni·verB'ity e.vperiment canal as found 'lvith snwll 

Price meter No. 351, and urith Haskell meter No. 3. 

Number of run. 

Small Price meter No. 351.a j Haskell meter No. 3.b 

Depth below surface, in inches. Dept1j:~~clt:~rface, 

2.5- 4.5 6.5 8.5 4. 5 6.5 I 8.5 

--------------1---------------------

Second ...................................... 0.482 0.490 0.482 0 0 

Third ........................................ 0.556 0.595 0.575 0.592 0.615 

Fourth ...................................... •o. 936 0.958 0.958 0.942 1.015 1.032 

Fifth ........................................ 1.297 1.281 1.320 1.299 1.348 1.325 

Sixth ........................................ 1.480 1.457 1.389 1.434 1.450 1.39'-l 

Seventh ..................................... 1.611 1.556 1.533 1.552 1.572 

a Meter held with cable 1 foot north of canal center and 244 feet from weir. b Meter held with cable 1 foot south of canal center and 244 feet from weir. 

0 

0.602 

1.010 

'"i:4i2 

Each run lasted about half an hour, during which time the mean 

velocity remained constant. These results indicate that for velocities 

less than 1.5 feet the difference between the velocities indicated by 

these meters is small from the surface to a depth of 8.5 inches. 

In the upper right-hand corner of fig. 30 is a vertical velocity curve 

prepared ;from thirty-five 50-second observations taken in forty minutes 7 feet from the south side of the canal, at a station 220 feet from 

the weir, with small Price meter No. 351. It shows a decrease of 8.5 

per cent in the velocity 2-! inches below the surface. 

From these float and current-meter surface velocity experiments we 

conclude that a small Price meter will not measure velocity correctly 

when its center is within 0.5 foot of the surface, if the velocity be 

greater than 1. 5 feet per second, and that this error increases :from 0 

at about 0. 5 foot below the ~urface to 8 or 9 per cent at 2. 5 inches 

below the surface. 
MURPHY.] OORNELL LABORATORY EXPERIMENTS. 93 

LOW VELOCITY CURRENT METER AND WEIR COMPARISONS. 

The current-meter and weir-dischatge comparisons described_ on 

pages 58 to 80 see1n to indicate that for velocities less than about {).5 

foot per second the discharge given by the meter is less than that given 

by the weir, and that this difference increases as the velocity decreases. 

With a view to examining this point further, small Price meter No. 

375 was rated on October 26, 1901, and the Fteley meter No. 107 on 

November 1, in the 10-foot canal at Cornell University. A chronograph ~as used to indicate the time and revolutions. The rating in 

each case was carried to velocities less than 0.2 foot per second; for 

these lower velocities the motion of the car was not very steady. On 

October 25, November 1 and 20 comparative measurements of the 

discharge of the 10-foot canal were made with these two meters and 

with the standard weir, using the 0.6 dept4 method. The results are 

given in ~he following table: 

Low t'elociJ,y current 1neter and standard ~veir discharge comparisons. 

Small Price meter No. 375. Fteley meter No. 107. 

Date. Mean velocity. Date. Mean velocity. 

Depth r;,.-Ym Depth. V,.-Vm water. Weir 

V,. 

Meter 

r m ---v;- v,. Ym ~ 

---- ------

1901. Feet. Feet. Feet. Per ct. 1901. Feet. Feet. Feet. Per ct. October 25 ....... 7. 79 .564 .468 +17.0 November!. ..•. 8. 79 1.257 1. 277 - 1.6 Do ........... 7.62 .401 a.166 +58."8 Do .......... 8.58 1.098 1.129 - 2.8 Do ........... 7. 70 .508 a.390 +23.2 Do .......... S.S6 .951 .957 - 0.7 Do ........... 7.90 .630 .527 +14.7 Do .......... 8.24 .872 .907 -4.0 Do ........... 8.02 .712 .646 + 9.1 November20 .••• 7.07 .154 .127 +17.5 Do ........ ~•- 8.12 . 776 .715 + 7.9 Do .........• 7.45 .361 .322 +10.8 Do ......... -.. 8.25 .863 . 826 + 4.3 Do .......... 7. 72 .529 .522 + 1.3 Do ........•.. 7.95 .666 .611 + 8.9 Do---------- 7.95 .674 .693 + 2.9 

November 1 ...•. 9.05 1.454 1.427 + 1.8 Do .......... 7.31 .286 .263 +11.5 Do ........••. 8. 79 1.257 1.259 + 0.0 Do .......... 7.08 .169 .142 +16.0 Do ........... 8.58 1.098 1.080 + 1.7 Do ........... 8.36 .951 .890 + 6.4 Do ....• ..... 8.24 .872 ··"30 + 5.1 

aNo measurable velocity in some parts of section. 

The results for the Fteley meter are plotted in fig. 31, and those for 

the Price meter in fig. 32. 

Some of these discharge measurements were made just previous t<? 

the rating of the meters, and the remainder only a short time after. 

They indicate, as in the other comparisons, that the meter discharge 

obtained in this canal by this n1ethod is less than the corresponding 

weir discharge for low velocities. Whether this difference was due to 

imperfect rating of the meter, to the method of measuring the discharge, to the condition of the water in this canal, or to the meters 

themselves. was then to be considered. It was frequently noticed that 

the rate of rotation of the meter wheel was very irregular in this canal 

when the velocity was small. 
94 ACCURACY OF STREAM MEASUREMENTS. [No.95. 

The following table shows the irregularity of motion of the water 

in the 10-foot canal as compared with that in the 3-foot entrance to 

the 6-foot ean_al: 

Table showing irregztl.arity of motion of ·ulQ.ter in 10-.foot canal and 3-joot entrance to 6-joot 

canal, Cornell Unil•ersity hydraulic laboratory. 

Speed in 10-foot canal. Speed of meter in 3-foot canal. 

Fteley meter. I Fteley meter. Small Price meter. Fteley meter. 

Revolu- Time. Revolu- Time. Revolu- Time. Revolu- Time. tions. tions. tions. tions. 

---

Seconds. Seconds. Secomts. Seconds. 5 32.0 5 20.9 3 24.0 8 27.0 l'i 23.4 5 27.0 3 25.0 8 27.0 5 22.9 5 22.7 3 24.3 8 27.2 5 25.1 5 25.0 3 24.0 8 27.3 5 28.5 5 24.9 3 24.7 8 27.5 5 23.9 5 24.9 3 24.1 8 26.8 5 23.0 5 26.9 3 24.6 8 28.0 5 29.0 5 26.1 3 24.4 8 27.9 5 28.3 5 24.3 3 24.0 8 27.0 5 28.7 5 23.7 --- 8 27.2 5 31. l 5 28.0 24.34 5 48.5 5 22.5 27.19 5 25.5 5 . 21.5 V=0.327 5 34.4 5 21.6 5 27.0 5 25.9 5 32.5 fi 25.3 

28.99 24.4.'5 t•=0.230 11=0. 253 

It is seen that for a velocity of 0.23 foot per second in the large 

canal, the variation i~ from 21 per eent below to 67.3 per cent above 

the Inean, and for a velocity of 0. 253 foot per second the variation 

from the mean is from 14.5 per cent below to 14.5 per cent above the 

mean. In the entrance to the small canal the variation is only from 

1.5 per cent below to 2.9 per cent above the mean for a mean velocity 

of 0. 327 foot. 

If this irregularity of motion of the water is due to conflicting currents which strike the eurrent n1eters obliquely, the difference between 

meter and weir discharge may be mainly due to this cause. There is 

some reason, however, for thinking it may, in part at least, be due to 

the imperfect rating in still water. This Fteley meter No. 107 is one 

of the two meters used in the tests of low-water stream measurements 

·de:;cribed on pages 100 to 105. During the progress of this work it 

was rated at Chevy C};lase, Md., by Mr. Stewart and the writer. This 

rating shows a change of about 1 per cent in velocities from 0.6 to 1.4 

feet per second, and a much larger percentage change for very low 

velocities. This increase in friction of the meter shown by th~ two 

ratings was not anticipated. There was an interval of fourteen months 

between the ratings, but the meter had not been used much, and only 

in the laboratory. The conditions during the secondratingwere quite 

diffe1·ent frmn those of the first, and, on the whole, not so favorable 

for accurate work. In the· first rating the water was clear, still, and 

warm. A chronograph being used, time and revolutions could be read 
MURPHY.) CHANGES IN METER RATING. 95 

to tenths. The motion of the car was_ somewhat unsteady. In the 

second rating the water was llllucldy, cold, and had a small irregular 

velocity, and there was some wind. The motion of the car was steadier 

than during the first rating. The distance passed over by the car 

for whole number of revolu~ions was read to 0.5 foot. The rating 

table obtained from the secopd rating was used in computing the 

meter discharge of 4 feet woo4}en flume in test of low-water stream 

measurements, and these results show a close agreement of meter and 

Velocit~ in feet per second.' 

.1 .2 .3 .4 .5 .. 6 .7 .8 .9 1.0 1.1 1.2 1.3 

1. 4 

1.3 

1.2 

v 

f IZ 

l/ 1.1 

1.0 

rd 

.:: .9 0 

0 

~ 

"" ~ .8 A 

~ 

.8 • 7 "Ei 

0 

l> 

Q.) .f> ~ 

.5 

.4 

.3 

-~ 

~~c~ ,1 t· 

/:/.."-!• 

~/0~· d\e-

~ ('{} 

_d \()"'' 

Vr~o· 

_b .lJ V, v\ \e e-

~~·1 \"' 

-

~ f e_v o Still-water rating 

• Moving-water rating 

.2 

.1 

0 

h 1'/ 

L-"/ I 

J 

r)'" 

FIG. 31.-Diagram showing results o~ rating in still and moving water, Fteley meter. 

Cippoletti weir discharges eve~ll for low velocities. The first rating, 

on the face of it alone, 'is mor~ accurate than the second; and· as it is 

not uncommon for a meter to ~bange its rating that amount in that 

time, the evidence is not conch~sive. 

In view of the fact that current meter and weir discharge measurements differ so widely for low velocities, whether due to the mete1· or 

to the condition of the water, the discharge should not be measured 

with a current meter in a section where the mean velocity in any considerabre part of it is less than half a foot per second. 
96 ACCURACY O.Jf STREAM MEASUREMENTS. .(NO. 95. 

CURRENT METER AND PITOT TUBE COMPARISONS. 

With a view to obtaining some data bearing on the adaptability of 

a Pitot tube for stream measurements, the writer obtained a tube of 

the Darcy-Ritter type, somewhat like that in fig. 2, and measured 

with it the discharge of the 6-foot canal in the Cornell University 

hydraulic laboratory. He also made some relative ratings of a Pitot 

tube of the point and wall pressure type, and two current meters, 

in the entrance to this 6-foot canal. The velocity in this canal was 

small, and the tube was not a good one, or, at least, was not in good 

condition. The results, therefore, are not given. They serve only to 

Velocity in feet per second . 

. 1 . 2 . 3 . 4 . 5 . 6 . 7 . 8 . 9 1. 0 1. 1 1. 2 1. 3 1. 4 1. 5 

2 

I / ,~ o'~ 

~b/ 

~l ~ 7 !{~ e, ~ 

~ 0~ c•'& • . \\~ 0~ 'V 

~~ o Still-water rating 

• Movmg-water rating I ~( 

~ v I <f'e 

f>,,~ (~ I 

/ / r~ I 

6 

5 

0 

FIG. 32.-Diagram showing results of rating in still and moving water, small Price meter. 

emphasize the fact, noted by others, that this instrument is poorly 

adapted to measurement of flow in open channels, and is vastly inferior 

to the current meter for this purpose. 

APPLICATION OF RESULTS TO ORDINARY RIVER GAGING. 

It has been shown that the discharge of the Cornell University 

canal can be measured with a small Price current meter by the ordinary point method with an error of not more than 1 per cent under 

favorable conditions. This degree of accuracy, however, can seldom 

be attained in ordinary river gaging, as the conditions are not so 
MURPHY.) .AOOURAOY OF RESULTS. 97 

favorable for accurate work. The bed of the Cornell canal is hard, 

smooth, and regular in shape; the bed of a river is frequently of soft 

material, into which the meter will settle, or is gravelly, stony, and 

irregular in shape. There are no shallow parts in the canal the depth 

and velocity of which it is difficult to meaRure with accuracy, but 

frequently there are one or n1ore of these in a river discharge section. 

There is a good measurable velocity in all parts of the canal for all 

depths, while in a river there are frequently parts in which the velocity 

is too small for accurate measurement. The change in velocity from 

one point to another in a discharge section is frequently greater in a 

river than in the canal, on account of obstructions. Fluctuations of 

the surface elevation are also larger in a river than in the canal. On 

these accounts it is to be expected that ordinary river discharge 

measurements may be several per cent less accurate than those of this 

canal. 

In river gaging work, however, it is not alone accurate- discharge 

measurements that are required, but it is the accurate measur6ment 

of the volume passing the gaging station each day and each month. 

The accuracy of daily and monthly flow of a stream depends on the 

accuracy of the discharge curve, or the relation between th~ total 

dischargP- and the river stage, and on the accuracy of measurement 

of the fluctuation of river stage. The latter is quite as Important as 

the former, and improvement in it should keep pace with improvements in the former. 

ACCURACY OF RESULTS. 

The discharge of the Cornell University standard weir is computed 

from Bazin's formula. It is not possible, however, to measure the head 

on the weir in exactly the same way that Bazin measured the head on 

his weir, so that this formula is not strictly applicable to this weir. 

From experiments made at the Cornell hydraulic laboratory, nowever, Prof. G. S. Williams believes that the actual dischat·ge of the 

Cornell weir will not differ from that computed by Bazin's formula 

by more than 1 per cent for heads up to 1.5 feet, nor more than 3 per 

cent for heads up to 2. 5 feet. 

The results given in the tables have been obtained with five current 

meters operated in three ways by several observers. In several of the 

experiments simultaneous measurements were made with two meters, 

so that we have several checks on the work. We have not carried 

any of the computations beyond the third decimal place, believing 

'that the length of a meter observation, the method of obtaining fractional parts of a revolution of the meter wheel, the uncertainty in the 

exact location of the vertical velocity curve, and the pulsations in the 

water do not warrant even this degree of accuracy. In closely studying the results some little inacc1 tracies will be found, as all the results 

lRR 95-Q4-7 
98 ACCURACY OF STREAM MEASUREMENTS. (NO. 95. 

are not obtained in exactly the same way, though they are believed to 

be substantially correct. 

In comparing the results of these experiments with results obtained 

by other experimenters it n1ust be remembered that we have used 

smaller velocities in many of our experiments than were used by them. 

In Fteley and Stearns's comparisons (p. 58) the smallest mean velocity 

is 1. 7 feet, in Henry's (p. 50) the smallest is 3 feet, in Bazin's (p. 43) 

the smallest is 1. 25 feet, in Francis's (p. 54) it is 0. 5 foot, and in Marr's 

(p. 49) 2.4: feet. For these and higher velocities our meter results by 

the ordinary metho:l agree elo1-1ely with those given by the weir. We 

are unable to find any comparisons by other experimenters for velocities less than 1 foot per second, except a few by Francis with rods and 

those at Cornell with rods (p. 57.) The large disagreement between 

meter and weir is for the low veloeities, a field into which apparently 

few experimenters have entered. 

CONCLUSIONS. a 

The conclusions to be drawn from thel:!e experiments may be briefly 

summarized as follows: 

(1) Discharge measured with current meter by the ordinary (point) 

method agrees with that given by the Cornell standard weir within 2 

per cent for velocities above 1.5 feet per second. (See tables on pages 

65 to 6~ and 71.) 

(2) For velocities less than 1. 5 feet per second the discharge found 

with the Price metet·s is le~s than the corresponding weir discharge, 

and the· difference increases rapidly as the velocity decreases. (See 

tables on pages 65 to 68.) 

(3) For velocities less than about 1.5 feet per second the discharge 

found with the Haskell meter is greater than that of the weir, and the 

difference increases as the velocity decreases. This differenee is 6 per 

cent for a velocity of 0. 75 foot per second. (See fig. 16.) 

( 4) The discharge of the ·Cornell canal can be measured with a small 

Price meter, ordinary point Inethod, with an error of not more than 

1 per cent under favorable conditions, a velocity observation lasting 

fifty seconds being taken in each 2. 3 square feet of discharge area. 

(5) When the most accurate results are desired the meter should be 

held with a rod and not given freedom to tip . 

. (6) Velocities of 1.5 feet per second and upward obtained with a 

small Price meter when its center is closer to the surface. than 0.5 foot 

are too small by from 0 to 9 per cent. This error, however, decreases 

from maximum at the surface to 0 at about 0.5 foot depth. 

(7) The small Price meter will measure velocities of 1 foot per second and less more accurately than either the large Price meter or the 

a See also pp. 137, 138, 150, 151, and 160. 
MURPHY.] OONOLUSIONB. 99 

Haskell meter. It appears from these experiments that the smallest 

velocity that these meters will measure with a fair degree of accuracy 

is 0.5 foot for the large Price meter and the Haskell meter and 0.22 

foot for the small Price meter. (See fig. 16.) 

-(8} The small Price meter should be frequently rated, and it should 

be used with much care if accurate results are required. 

(9) The six-tenths-depth method gives discharge from 2 to 6 per 

cent in excess of that by the weir, depending on the ratio of width to 

depth. (See fig. 17.) 

{10} The integration n~ethod as a rule gives results in excess of 

those given by the weir, the difference increasing with the speed of 

the meter and decreasing as the velocity increases. (See fig. 17 and 

tables on pages 84: and 85.) By using special care in moving the 

meter at a slow speed and a uniform rate it may be possible to obtain 

better results by this method than those shown by these experiments. 

A device like Harlacher's {page 38) for giving the meter a uniform 

motion will increase the accuracy somewhat. We do· not believe, 

however, that the little saving of time of this method over that by 

the mid-depth or the six-tenths-depth will warrant the us~ of any such 

device. The method is useful only as a rough check on one of the 

other methods. 

(11} The thread of maximum velocity is at the surface for depths 

less than 2 feet and unobstructed flow at the lower end of the canal. 

For depths of 5 feet or more and discharge checked at the lower end 

of the canal this thread is from two-tenths to four-tenths depth below 

the surface, the mean for thirty-one experiments being thirty-onehundreds depth. (See table on page 78.) 

(12) The po~ition of the thrertd of mean velocity varies from fivetenths depth for small depths to seventy-three-hundredths depth for 

the larger depths. For the thirty-one experiments hy the ordinary 

method of series C and D it is sixty-four hundredths depth below the 

surface. (See table on page 78.) 

{13} The surface velocity is always greater than the bottom velocity 

with center of meter 0. 25 foot above bottom. (See figs. 23 to 28.) 

{14} The ratio of bottom velocity to 1nean velocity varies from 0.6 

to 0.9, being 0.8 for the experiments of series A, 0. 75 for series C, and 

0.85 forseries D. (See table on page 79.} 

{15} The ratio of mean velocity to mid-depth velocity varies from 

0.90 to 0.99, the mean of forty experiments being 0.95. (See table on 

page 79.) 

(16) The average of the velocities 0.5 foot above the bottom and 

0.5 foot below the surface is frmn -2.2 per cent to +30 per cent less 

than the mean velocity shown _by the weir. (See table on page 83.) 

{17) A small Price 1neter wHl revolve faster in moving water of a 

given velocity when held with a rigid rod than when held with a 
100 AOCURAOY OF STREAM MEASUREMENTS. (NO, 95. 

cable. (See table on page 89.) Hence the same rating table will not 

answer :for both. 

(18) The bottom velocity varies between so wide limits that it is not 

a desirable quantity to use in computing discharge; the mid-depth or 

the six-tenths-depth is better. 

TESTS 01!' LOW-WATER STREAM MEASUREMENTS. 

A knowledge of the summer flow of streams is very important, for 

on the minimum flow depends mainly the value of the stream for 

water-supply and power purposes. This smnmer flow is very small 

in some streams, in others it is nothing; even the larger ones become 

very shallow during the low water season. The importance of a 

knowledge of the smallest summer flow of streams has caused numerous measurements to be made of small amounts of water :flowing, 

usually, in a broad shallow channel. On account of the expe-nse of 

constructing a measuring weir on a stream the current meter is the 

instrument used for measuring minimum as well as ordinary flow. 

Frequently this mininum flow can not be measured at the gaging 

station on account of the small velocity. It is necessary to go up or 

down stream :from the gaging station, and find a place where the depth 

is at least half a foot, bed not too rough, and the velocity :from 0.5 to 

1.5 :feet per second. Some Western streams have a minimum flow o:f 

0. 75 to 4 second-feet, a gravelly or sandy bed, a minimum depth of 6 

to 12 inches, and a velocity of 0.5 to 1! feet per second. The velocity 

is computed from observation with a current meter held as near to 

the bed, and then as close to the surface as possible, (its center is 

usually :from 0.15 to 0.20 feet :from bed and surface). The mean velocity 

in a vertical is taken as the hal£ sum of the bed and surface velocities. 

In order to test the accuracy of current-meter work done under 

these conditions, the following series of comparisons of current-meter 

and weir diseharges were made in the hydraulic laboratory of Cornell 

University during January and February 1903. They were planned 

to cover the conditions of quantity of water, depth, velocities and 

roughness of bed, that the writer met in his work in Nevada and in 

California. 

Fig. 33 shows the 6-:foot canal in the Fall Creek hydr£tulic laboratory of Cornell University. Water is admitted to it through two 

gates 14 :feet upstream from the bafile B, and can be measured by the 

sharp crested weir F. In this canal was built, as shown, a rectangular 

wooden flume 4 feet wide, 2 feet deep, and 20 feet long, with smooth 

bottom and sides. C is a 4 by 4 inch timber which serves as a breakwater to destroy the energy of the falling water. D is a bafile made 

of 1 by 8 inch timber placed horizontally 2 inches center :from center. 

G is a bafile like D but with strips 1 by 3 inches placed vertical to hold 

back the water and give the.required depth :for any discharge and per-
MURPHY.) LOW ·WATER S'l'REAM MEASUREMENTS. 101 

mit the water to pass out through all parts of the cross section. B is a 

bulkhead carrying a 2-foot Cippoletti measuring weir. The hook gage 

for showing the head on the weir is ·5 feet upstream from the weir. 

The current-meter IneasurP.ments were made at E, 4 feet from the 

.... A 

f 

~ 

-t ~Hook gage 1 

I I+- - 6'- --I 

it, 

I 

B 

I ·~:~:_,,~~~:r.!i'i~~,;~~~\~'~~~~~ 

I J .., 

I 

+ 

I J c 

I ~ D 

I 1 

I 

I 

!::: 

I !<-- 4'--

I 

1 

I 

I 

I 

I E 

1.._ 

~ -----F---- i--

c., 

l G 

i.'!:;~!H;' i :l:;W• ~;:,:t :, H ~:~. \ t~ ~~:' 

,....-

Baf'f'le 

c ippoletfi weir 

Breakwater 

Baf'Tie 

1:1 

Meter 

station 

Sta.weir 

Baf'f'le 

FIG. 33-Plan and sections of flume. 

lower end of the flume. The 1neters were held with a rod clamped in 

proper positions to two 2 by 4 inch strips fastened to the sides of the 

canal. 

Three series of discharge 1neasurements were made with two meterb. 

In the firstsel'ies the bottom and sides of the flume were smooth, the wood 
102 ACCURACY OF STREAM MEASUREMENTa. 

being planed hemlock 2 inches in thickness. In the second series the 

bed was mixed gravel, and had approximately the shape shown in :fig. 33. 

Five of these wooden forms wer.e fastened in the bottom of the flume 

3 to 4 feet apart, and gravel placed between then1. This gravel bed 

is shown in Pl. V. In the third series the bed was as in series 2, but 

with rounded stone 2 to 3!- inches in diameter scattered over the bed, 

these stones being the coarse material of pit gravel. 

The current meters used were a small Price meter No. 396 (see Pl. I, 

p. 20)~ held with a rod and free to tip. The other was the eight-vaned 

Fteley meter (see fig. 5, p. 22) used in the experiments described on 

pp. 93-95. 

In the first series the small Price meter was held with its center 

0.15 foot from the bottom and 0.15 foot from the surface for periods 

of 50 to 100 seconds, and the Inean velocity in a vertical was taken as 

the half sum of the surface and botton1 velocities. The mean velocity 

in a vertical was found in the same way with the Fteley meter, but its 

center was held 0.2 foot from the bottom and 0.2 foot from the surface. The verticals in which velocity was measured were 0. 5 foot 

apart, the end ones being 0. 25 foot from the sides of the flume. 

In the second series the velocity was measured in verticals from 0.5 

to 1 foot apart. On tTanuary 28, 29, and 30 the meters were held as 

close to the bottom and surface as possible, viz, 0.15 foot in the case 

of the small Price and 0.2 foot in the case of the Fteley. On February 10, instead of holding the meters as close to the bottom as possible, they were each held with centers 0. 3 foot above the bottom. 

In series 3 both meters were held as near to the surface as possible, and with center 0.3 foot above bottom in each case. 

The order of work was usually as follows: The gate was opened in 

order to admit about the quantity of water desired and the bafile G 

was adjusted so as to give the required depth at the meter station. 

When the flow was steady the h~ok gage waR read, the depths were 

measured, velocity was measured with one meter (requiring 7 to 14 

observations of 50 to 100 seconds each), depths were again measured, 

the hook gage was again read; then the velocity was measured with 

the other meter, the depths were measured again and the hook gage 

was read; the gate was then changed, and two more discharge measurements made. In some of the experiments the depth was changed 

without changing the discharge. 

The quantity of _water used was so small that the velocity of approach to the weir was small and the head eould be read with accuracy. 

The depths at the meter station were measured with a sharp-edged 

thin scale, made for the purpose, marked to hundredths of a :foot. 

For depths less than 0. 7 foot ihe depth could be read to 0.002 :foot 

for a depth of 1 foot. The surface was rough, being a succession of 

small, irregular, dashy, waves. 
U. S. GEOLOGICAL SURVEY WATER - SUPPLY PAPER NO. 9 5 PL. V 

F L UME, WEIR, METERS, ETC. 
MUP.PHY.] LOW WATER EXPERIMENTS. 103 

The :following table gives the results o:f 3() meter-discharge measurements and the corresponding weir discharges, arranged hi the order 

of depths o:f water at the meter stc<ttion :for series 1, with smooth 

sides and bottom. The weit· discharge i J taken :from " The Use of 

Water in Irrigation," by Elwood Mead and C. T. Johnson, United 

Sta~es Department of Agriculture, Table 1, page 49. This table is 

computed from the formula Q=3.3i LJti, L being the length of weir 

crest in feet, h the head in feet, and Q the discharge in cubic feet per 

second: 

Cmrent meter and Cippoletti 1veir discharge comparisons in 4:foot wooden flume with 

smooth bottom and sides. 

w i Dis-~Veloc-/ Die'- I Dis- Q -Qr Q -Q Dis- Q -Q No. Date. he:J Depth. charge ity charge,charge ~Q ~Q charge ~Q r . Qw rw Qr I Qp w w Qr w 

---------------------------------------

1903. Feet. Feet. Cub.jt. Fed. Cub.jt. Cub.jt. Per cent. Per cent. Oub.jt. Per cent. 1.. Feb. 14 0.270 0.286 0.945 0.822 ....... 0.981 .......... - 3.8 ............... .. 2 .. Jan. 22 .250 .400 .842 .532 0.862 ....... -2.4 .......... 0.852 - 1.2 3 ...... do: ... 250 .400 .842 .532 ........ 868 .......... - 3.1 ................ . 4 .. Feb. 14 .270 .400 .v45 .588 .947 ....... --0.2 .......................... . 5 ...... do .... 270 .400 .945 .585 ........ 954 .......... - 1.0 ................ . 6 .. Jan. 22 .324 .460 1.242 .677 1.253 ....... -0.8 .......... 1.244 -- 0.1 7 ... : .. do... .324 .460 1.242 .677 ....... 1.231 .......... + 0.9 ................ . 8 .. Jan. 24 .205 .461 .625 .336 ....... .606 .......... + 3.0 ............... .. 9 ...... do... .205 .462 .625 .336 .635 ....... -1.6 .......... .598 + 4.3 10 .. Jan. 23 .362 .477 1.466 .758 ....... 1.473 .......... - 0.5 ................ . 11.. Jan. 26 .185 .499 .536 .267 ....... .530 .......... + 1.0 ................ . 12 ...... do... .185 .499 .536 .267 .536 ....... 0.0 .......... .494 + 7.8 13 ....•. do.~. .187 .502 .545 .270 ....... .5H .......... + 0.8 ............... .. 14 ...... do .... 187 .510 .545 .270 .538 ....... +1.3 ........... 494 + 9.4 15 ...... do... .187 .516 .545 .263 .566 ....... -3.8 .......... .521 + 4.4 16 .. Jan. 23 .423 .535 1.853 .860 1.884 ....... -1.7 .......... 1.862 - 0.5 17 ...... do .... 423 .537 1.853 .858 ....... 1.883 .......... ·- 1.6 ................ . 18 .. Jan. 24 .170 .561 .472 .208 .459 ....... +2.8 .......... .384 +18.6 19 ...... do... .170 . 561 . 472 . 208 ... _... . 406 . .. ... . . . . b+13. 8 ................ . 20 •• Jan. 26 . 238 . 581 . 782 . 334 . 782 . . . . . .. +0. 0 .... . . .... . 732 + 6.4 21.. Feb. 14 . 410 . 581 1. 768 . 756 . . . . .. . 1. 798 . .. . . . .. . . - 1. 7 ................ . 22 .• Jan. 26 . 238 . 581 . 782 . 334 . . . .. . . . 780 ......... _ + 0. 3 ................ . 23.. Feb. 14 .410 . 582 1. 768 . 756 1. 725 . . . .. .. +2. 4 .......................... . 24 .. Jan. 26 .187 .585 .545 .242 .572 ....... a-5.0 .......... .516 + 5.2 25 .. Jan. 23 .499 .603 2.374 .966 ....... 2.327 .......... + 1.9 ................ . 26 ...... do ... .499 .603 2.374 .966 2.448 ....... -3.1 .......... 2.424 - 2.1 27.. Jan. 26 . 258 . 609 . 88:~ . 359 . 869 . . . . . . . + 1. 6 . . • .. • . • . . . 827 + 6. 3 · 28 .. Jan. 23 . 566 • 664 2. 868 1. 076 2. 916 . . . . . . . -1:.7 . . . .. .. . . . 2. 889 - 0. 8 29 ...... do... . 566 . 665 2. 868 1. 076 . .. . . . . 2. 8.')7 . . . . .. . . . . + o. 4 ................ . 30 ...... do... .658 .745 3.595 1.199 ....... 3.440 .......... a+ 4.3 ................ . 31. ..... do... . 660 . 748 3. 610 1.198 3. 729 .. . . . . . -3.3 . . . .. . . . . . 3. 693 - 2. 3 32 .. Feb. 14 .555 . 770 2. 785 .891 ....... 2. 752 .......... + 1.2 ··-···· ........ .. 33 ...... do. . . . 557 . 770 2. 800 . 903 2. 678 . . . .. .. +2. 1 .......................... . 34 .. Jan. 23 .362 .841 1.466 .758 1.495 ....... -2.0 .......... 1.483 - 1.2 35 •• Feb. 14 .722 .997 4.131 1.027 4.050 ....... +2.0 .......................... . 36 ...... do... . 732 1. 010 4. 217 1. 036 .. . .. . . 4. 212 . . . .. .. . . . + 0.1 ................ . 

a Depth varied during measurement. b Not velocity enough in some parts of section to start meter. 

NoTE.-The Fteley meter discharge is computed from observations 0.2 foot below surface and 0.2 foot 1!-bove bottom. The Price meter discharge is computed from observations 0.15 foot below surface 

anQ. 0.15 foot above bottom. 

Qw=weir discharge. Qr=Fteley meter discharge. Qp=Price meter .discharge. Computed from 

ra.tmg November 2, 1901. l'w=velocity at meter station computed from Qw. 

The Fteley meter discharges giv~n in column 11 are computed from 

a rating of this meter Novmnher 2, 1901. As it had been used very 

little it was supposed that its rating had not changed much, but the 

new rating February 4, 1903, at Chevy Chase, Md., shows a change 

of about 1 per cent in velocity from 0.6 to 1.2 feet, and a larger change 

for the smaller velocities. Some of this change is due to increased 

friction of the meter and some to different conditions in the two 

ratings· (see pp. 94, 95). 
104 ACCURACY OF STREAM MEASUREMENTS. [NO. 95. 

With three exceptions, viz, Nos. 19, 24, and 30, the meter discharge 

computed from the new rating table approximates to the weir dis 

charge. The per cent variation of meter from weir discharge is from 

-3.8 to +2.4 for the Fteley, and from -3.8 to +3.0 for the Price. 

Of the three exceptions noted, No. 19 is due to the very small velocity 

in some parts of the water section, the Ineter wheel not turning part 

of the time. The other two exceptions are due to an irregular variation in depth at meter station, as ice formed on the baffle (G) and 

obstructed the flow. 

The results of the 26 meter-discharge meastuements and corresponding weir-discharge measurements for the mixed gravel bed are given 

in the following table. On January 28, 29, and 30 the meters were 

held as close to the bed as possible, the center of the small· Price being 

0.15 and the Fteley 0.20 foot above bottom. On February 10 both 

meters were held with centers 0. 3 foot above bottom. It is seen that 

the meter discharge is less than the weir discharge. For the small 

Price at 0.15 foot from bottom the variation is from +2.8 to +19.2 

per cent, and at 0.3 foot from bottom the variation is frmn + 1.3 to 

+7.6 per cent. For the Fteley meter held 0.2 foot above bottom the 

variation is from + 1.() to +6.1 per cent, and when held at 0.3 foot 

above bottom the variation is from -0.7 to -2.5 per cent. A wider 

range of variation of meter from weir discharge is to be expected in 

a section of varying depth, for there are shallow parts at each end of 

section in which the velocity can not be accurately measured. 

Current-mete~· and Cippoletti 1.oei·r-di.schm·ge comparisons in 4-foot flume 'ltrith mi:I:edgral'el bed. 

No. Date. Weir Depth. Q V I Qr Q Qw-Qr Q .. -Qp head. w w P Q,. Qw 

~---1----1---- ---------1------------

1903. 1. ........ Jan. 28 

" Jan. 30 

1::::::::: -~~~0 ~- 5 ......... Feb. 10 6 ............. do .. . 7 ......... Jan. 30 8 ......... Jan. 28 9 ............. do .. . 10 ......... Jan. 29 11. ............ do .. . 12 ......... Feb. 10 13 ............. do .. . 14 ......... Jan. 29 15 ............. do .. . 16 ............. do .. . 17 ............. do .. . 18 ............. do ... 19 ......... Jan. 30 20 ............. do .. . 21. ........ Feb. 10 22 ............. do .. . 23 ......... Jan. 29 24 ............. do .. . 25 ......... Feb. 10 26 .............. do .. . 

Feet. 

0.207 

.270 

. 207 

.207 

.417 

.417 

.411 

.264 

.264 

.271 

.271 

. 500 

.500 

.346 

.346 

.346 

.458 

.458 

.547 

• 553 

.569 

.569 

.458 

.458 

.686 

.691 

Feet. 

0.381 

.439 

.509 

.515 

.642 

.642 

.647 

. 712 

.713 

. 723 

. 724 

. 764 

. 766 

.828 

.830 

.830 

.840 

.842 

.844 

.849 

.875 

.875 

1.008 

1.010 

1.050 

1.050 

Cub. feet. 

0.634 

.946 

.634 

.634 

1.813 

1.813 

1. 775 

.914 

.914 

.950 

.950 

2.381 

2.381 

1.370 

1.370 

1.370 

2.087 

2.087 

2. 724 

2. 774 2.890 

2.890 

2.087 

2.087 

3.826 

3.867 

Feet. 

0. 793 

.954 

.515 

.511 

1.081 

1.081 

1.044 

. 470 

.470 

• 480 

.480 

1.111 

1.111 

.571 

.571 

.571 

.860 

.855 

1.112 

1.082 

1.124 

1.124 

. 670 

.671 

1.170 

1.170 

Cub.jeet. Ottb.jeet. Per cent. Per cent. 0.606 .......... + 4.7 .......... .864 .......... + 8.5 0.624 .......... +1.6 ........ .. .......... .518 .......... +18.4 1.826 :......... -0.7 ......... . 1. 789 .......... + 1.3 .......... 1.620 .......... + 8.8 .892 .......... +2.4 ......... . .......... .886 .......... + 2.8 .900 .......... +5.3 ......... . .......... . 768 .......... +19.2 2.440 .......... -2.5 ........ .. 2.200 .......... + 7.6 1.150 .. .. .. .. .. +16.1 .......... 1.168 .......... +14. 7 1.286 .......... +6.1 ......... . ....... ... 1.847 .......... +11.5 1.985 .......... +4.8 ......... . • .. .. . • . • . 2. 542 • • • .. . .. • • + 6. 7 2.667 .......... +3.8 ......... . 2.923 .......... -1.2 ........ .. ...... .. .. . 2. 726 .. ... .. ... + 5.6 1. 986 • . .. • • • . .. +4. 8 ......... . .......... 1.776 .......... +14.9 3.916 .......... -2.3 ........ .. 3.728 .......... + 3.5 

Discharge on January 28, 29, and 30, computed from velocity observations, 0.15 foot above bottom and 0.15 foot below surface with Price meter and 0.2 foot above bottom and below the surface with Fteley- meter. Discharge on February 10, computed from observations, 0.3 foot above bottom, and 0.15 foot below surface with Price meter and 0.2 foot below surface with Ftelev meter. 
ACCURACY 0.1!' MEASUREMENT. 105 

It appears-that the roughness of the bed has a greater influence on 

1

1 he Price than on the Fteley meter. In the case of the Price meter 

1

1 he variation of 1neter from weir measurement increases as the velocity 

(lecreases. 

The following table gives the results of 11 comparisons of meter and 

,,veir discharge for a gravel and stony bed. The center of each meter 

"vas held 0.30 foot above bottom, except at the sides, where the depth 

""'"'as not sufficient to permit it. The variation for the Price Ineter is 

:"-om 0.0 to + 8.4 per cent (with the exception of No. 1), and for the 

:

7 teley the variation is from - 5. 6 to + 3. 9 per cent. 

t)urrenl-meter and Oippoletti ~veir discharge comparisons in 4-foot flume with gravel and 

stone bed. 

No. Date. Head. Depth. Q,.. v., I 

Q,..-Qr Qw-Qp 

Qp Q,.. Q,. 

-------------------------------

1903. 1. ........ Feb. 12 2 ............. do ... 3 ............. do ... 4 .... : .... .... do .. . 5 ............. do .. . 6 ............. do .. . 7 ............. do ... 8 ............. do ... 9 ............. do .. . :"l' ............. do ... ~·1. ............ do .. . 

Feet. 

0.264 

.676 

.676 

.470 

.470 

.675 

.675 

.fi90 

.590 

.676 

. 676 

Feet. 

0.442 

. 720 

. 720 

. 764 

. 764 

.821 

.827 

.928 

.928 

1.057 

1. 063 

Cttb . .ft. 0.9H 

3. 743 3. 743 2.170 

2.170 

3. 735 

3. 735 

3.052 

3.052 

3. 743 3. 743 

Feet. Cub. jt. Cub. jt. Per cent. Per cent. 0. 956 . . . • . . . . • . 0. 791 . . . . • . . . . . a + 13. 4 1.906 .......... 3.426 .......... + 8.4 1. 906 3. 627 . . . . . . • . . . +3. 1 ..••••.•.• 1.018 2.292 .......... -5.6 ........ .. 1.018 .......... 2.171 .......... + 0.0 1.590 3. 784 .......... -1.3 ........ .. 1.576 3.457 .......... + 7.4 1.096 .......... 3.009 .......... + 1.1 1.096 2.965 .......... +2.9 ........ .. 1.132 3.595 .......... +3.9 ........ .. 1.124 .......... 3.543 .......... + 5.3 

a Depth too small to measure velocity at edges. Small Price meter discharge, computed from observations, 0.30 foot above bottom and 0.15 foot r elow surface. 

Fteley meter discharge, computed from observations, 0.3 foot above bottom and 0.2 foot below 

""Urface. 

It appears from these tests that the method in use of measuring the 

;<tow of small streams with current meter held close to thQ bed and to 

·•be surface, and using as the mean velocity the half sum of top and 

" ')ttom velocity, gives results agreeing closely with those given by a 

,,...,.eir if the bed is smooth, depth fron1 0.4 to 1 foot and velocities of 

0.4 to 1.5 feet per second. For a gravely bed the meter should be 

r-~ld with its center 0.25 to 0.35 foot above the bed. 

f:TUDIES OF ACCURACY OF MEASUREMENT OF STREAM 

FLOW. 

The object of the following studies was to determine, or at least 

{brow light upon, the accuracy of river-gaging work, and to improve 

l'he methods. The Cornell University experiments show the degree 

of accuracy where conditions are artificial and controllable. But it is 

]:mpossible to control the flow of rivers for the purpose of measurement, and it is impracticable to construct measuring weirs in order to 

fest the accuracy of current-meter work; so some criterion of accuracy 

of work must be adopted other than the standard weir. The writer 

J-~s adopted the two following criteria: (1) He has compared velocity 

obtained at chosen stations by different methods with that obtained 
106 ACCURACY OF STREAM MEASUREMENTS. [NO, 95. 

from vertical velocity curves at the same place. (2) He has compared 

discharge obtained by the common methods with that obtained from 

the station rating cut·ve. In other words, the departure or variation 

of any measured discharge from the mean discharge for that river stage 

is a measure of its accuracy. It may be asked why not use the verticalvelocity-curve method in all cases. For two reasons: (1) It requires 

too much time and expense, and (2) the stage of some rivers changes 

too rapidly to permit its use in all cases. A change of a foot or more 

per hour is eonunon on some steeams. The velocity from one bank of 

a stream to the other usually varies so much that it is necessary to 

measure it in many verticals, and if it is measured in more than one 

or two points in each vertical so much time is consumed that there 

may be a considerable change in stage and a large error introduced. 

It is very desirable that the point of mean veloeity (distance below 

water surface) be known, so that the meter can be held there and the 

velocity in a vertical found in one observation. The vertical velocity 

curves show the position and amount of the mean velocity, hence their 

importance. If the shape of these curves were constant and known in 

advance, the point of mean veloeity would be known. The shape 

vades, however, with roughness of bed, shape and depth of channel, 

and river stage. · 

Many of the gaging stations are located at bridges to avoid the 

expense of a cable equipment. The piers interfere with the natural 

flow, thus making accurate discharge measurements i1ear them difficult. These stw:lies are expected to throw light on the 1~elative accuracy of discharge measured from a bddge with piers and a station 

where the flow is unobstructed. 

The following streams were selected for these studies: Chittenango 

Creek, a small stream with unobstructed flow at the carriage bridge, 

in Chittenango Village, N. Y.; Chenango and Susquehanna rivers, 

streams of moderate size, with flow unobstructed at bridges in Binghamton, N. Y.; Oswego River, of something over moderate size, 

with unobstructed flow at the cable station near Battle Island, N. Y.; 

Skaneateles Lake outlet, on which is a measuring weir; and the flume 

of the Truckee River General Electric Company, at Farad, California. 

These stations are· described and illustrated in the discussion of the 

work done at each. 

WORK ON CHITTENANGO CREEK AT CHITTENANGO, N.Y. 

This stream rises in the southwestern part of Madison County in 

the east-central part of New York State, and flows northwest into 

Oneida Lake. Thence its waters find their way, through Oneida a.nd 

Oswego rivers, to Lake Ontario. On it are Cazenovia Lake and Erieville reservoir, which regulate its flow to some extent. 

The station is at Main Street Bridge, Chittenango, about 18 miles 
MURPHY.] MEASUREMENTS ON CHITTENANGO CREEK, N. Y. 107 

from the 1nouth of the creek. The bridge is at a bend in the stream, 

and at an angle of 60° with the creek. The bed is mixed coarse and 

fine gravel. The cross section of the stream, on July 15, 1901, is 

shown in fig. 34. The gage is a board marked to feet and tenths, 

....;1 

<1) 

~ 

.s 

-:5 

g. 

0 10 

Width in feet. 

30 40 50 60 

A2Hr-------+----~~+--------4--------~------~~------~ 

.-. Velocity at EX"o depth. July 15, 1901 

• Vertical velocity curves 

FIG. 34.-Cross section of Chittenango Creek. 

fastened vertically to the right abutment on the upstream side of the 

bridge. 

Measurements were made from the upper side of the bridge on July 

15, 1901, with small Pdce meter No. 377, and April 2, 1902, with 

small Price meter No. 375. Some of the results are given in the following tables. Fig. 34 shows the cross· section at the time of the first 

0 

+3 <::: 

b 1---5? 

+2 

b '1---=: 

f 

/ ~ 

-2 

a 'f----" 

Velocity in feet. 

2 0 2 0 1 ') ~ 0 2 0 2 

rl ¢: <::: ¢: ¢: it' 

~ 0::: <> <> Ot---~ <> Of--_3 11 or--"' ~---~ !--=--...,:> or-=-=--= 

I -7 I--~ 

j I v } j J J 

I al! ) all J al! J :L/ 

l ·l,Jt a!---/ v a~ a!-----' 

1/ 

FIG. 35.-Vertical velocity curves of Chittenango Creek. 

measurement, the velocity curve at six-tenths depth, and vertical 

velocity curves at 10; 20, 30, and 40 feet, respectively, from the initial 

point. Fig. 35 shows the velocity curves obtained in these verticals 

on July 15, 1901, and April 2, 1902. The two sets of vertical velocity 

curves are plotted side by side, so as to compare curves at same places 
108 .AOUUR.AOY OF STREAM MEASUREMENTS. (NO. !!5 . 

for different stream stages. Between these dates a flood scoured out 

the bed of the stream at this place, making the increase in depth much 

greater than that shown by the change of stage. b b' is the change in 

stage, a change from a gage reading of 1. 80 feet to 2. 33 feet. a a' shows 

the increase in depth due to scour of bed. The two curves at any point 

are seen to resemble each other very closely. The mean velocity at 

six-tenths depth is seen to be somewhat less than that obtained from 

the vertical velocity curves for the first set of measurements and 

the reverse is true for the second set of measurements-that is, the 

thread of mean velocity has lowered somewhat as the depth of water 

increased. On April 2 the discharge obtained from the vertical velocity curves was 2.9 per cent less than that obtained by the six-tenths 

depth method. Not enough vertical velocity curves were taken July 

15 to enable the discharge to be computed, but from those that were 

taken, one can see that it would be slightly greater than that by 

six-tenths depth method. For some intermediate stage between the 

dates of these measurements the discharges by these two methods will 

agree. 

Results of discharge measurements of Chittenango Creek, Ch,ittenango r'Wage, N. Y. 

Gage Mean Meter used Date. Method used. Areas. Discharge. (small readings. velocity. Price). 

1901. Feet. Sqtw·rejeet. Feet. Cubic feet. 

July 15 1

6

0 depth •..•••.....•.........•. 1. 80 85 0.63 53 No.377. 

1902. 

Apr. 2 ..... do ..••••.................•.. 2.33 151 1.40 2.12 No.375. 

Apr. 2 Vertical velocity curve:; ....... 2.33 151 1. 36 2.06 Do. 

Yertical ~·eloci.ty C'IH'l'e data, Chittenango Creek, Chittenango, N. 1: 

10 feet from initial point. 20 feet from initial point. 

Date. Vel. ihD. Vel.v.v.c. D. d+D. Vel. 1'\,-D. Vel.v.v.c. D. d+D. ---------1·-------·----------' -----

1901. 

July 15 ...................... 0.678 0.695 2.6 0.59 0.667 0.660 1.5 0.60 

1902. 

Apr. 2 4. 71 1. 7081 1.670 1 3.2, ..........•..•........ 1. 460 1.520 .55 .61 

30 feet from initial point. ! 40 feet from initial point. 

Date. 1----c------,----.--1----..,· ~--.------,-----

-------~--JV-er-1....,..~-o_D. Vel.v.v.c. _D_._ d+D.IVel.flrD. Vel.v.~.c. _D_. _ d+D. 

1901. 

July 15 ...................... 0.678 0. 710 1.5 0.54 0.644 0.670 1.5 0.55 

1902. 

Apr .. 2 ................•...... 1.657 1. 750 3.0 .57 1.494 1.470 3.1 .61 

WORK ON SKANEATELES LAKE OUTLET. 

Skaneateles Lake is fifth in size of the group of lakes in central 

New York that drain into the Seneca Ri yer and thence into Lake 

Ontario. The water surface of the lake has an area of 12.75 square 
MURPHY.] MEASUREMENTS AT SKANEATELES LAKE OUTLET. 109 

miles, and the drainage area above the foot of the lake is 73 square 

miles. 

In 1893 the city of Syracuse constructed a masonry dam across the 

outlet at the foot of the lake, converting the lake into a storage reservoir, and since that time has used a considerable part of the discharge 

from the watershed for a municipal water supply. 

ELEVATION 

~----'?'-----~ . r 

~ 011111111111111111111112 :~ 

TYPICAL SECTION 

FIG. 36.-Plan of Willowglen weir. 

In 1894 what is known as the New Willowglen measuring weir was 

built on the outlet by the city of Syracuse, about 1.5 miles from the 

foot of the lake. The plan, elevation, and section of this weir are 

shown in fig. 36. It has a sharp crest 27 feet in length, with end contractions. The head is measured from a measuring po~t 5.2 feet 

ups~ream from the crest. The channel a hove the weir is straight and 
110 AOOURAOY OF STREAM MEASUREMENTS. [NO. 95. 

ha8 an average depth at the weir of 1.5 feet. The velocity of approach 

varies from 0 to about 2 feet per second. 

Francis's formula for flow over sharp-crested weirs, with con1plete 

contractions, has been used to compute the flow over this weir. It is 

not strictly applicable, howe.ver, as the ·depth of water below the crest, 

and the distance from the ends of the weir to sides of channel approach 

are too small to permit the contraction to be complete. The discharge 

is probably slightly greater than co,mput.ed by Francis,s formula. 

Three h1easurements of the discharge of this outlet were made from 

a temporary hridge August 29, 1901, with small Price meter No. 377, 

about 500 feet above the measuring weir in a straight reach of the 

stream. 

Width in feet. 

0 4 6 8 10 12 14 16 18 20 '''1 24 26 2R 30 32 

0 Yolo~9ty \ I 1/ ~ I 

\ I 

v J I I / v 10 

30 

I I 

v 1 r_; 1\ ~ / ~ J -- / 

~ I ./ -

V~;.::: .& Velocity at SAo depth. Aug. 29 

:---K eVe7ical r'ocl cuTes 

1 :----"' 40 

FIG. 37.-Vertical velocity curveR, Willowglen, N. Y. 

In two of these the mean velocity was obtained from measurements 

at six-tenths depth; in the third it was found from vertical velocity 

curves. Fig. 37 shows the cross section of the stream at the place of 

Ineasurement, also the curve of velocity at six-tenths depth and the 

vertical velocity curves. The bed is smooth, being clay, sand, and 

fine gravel. The results are given in the following table: 

Results of dischm·ge measurements on 8kanea.teles Lake outlet, lVillowglen, N. Y. 

Date. Method used. Head 

weir. on Section area. velocity. 

Mean I Discharge 

by meter. Discharge by weir. ~ 

Qw-Qm 

-----1-------------------1------

1901. Aug. 29 Aug. 29 Aug. 29 

T6il D ........................ . V. V. curves ............... .. I6ll"D ........................ . 

Sq.jt. 68.9 

68.9 

68.9 

Feet. 

1.272 

1.340 

1.334 

Sec.jt. Qw. Sec.ft. Qm. Per cent. 87.7 «88.86 +1.4 9'2.3 «89.37 -3.2 91.9 «89.37 -2.8 

«Computed from tableiurnished by R. .E. Horton. 

The discharge by meter calculated from the vertical velocity curves 

is seen to be 3.2 per cent greater than that given by the weir formula 

used. This is about what would be expected, as the contraction not 

being complete on the crest and ends of the wei~·, the discharge should 

be larger than with complete contraction. 
MURPHY.] MEASUREMENTS ON THE TRU OKEE RIVER. 111 

The effect of the banks in modifying the shape of the vertical velocity 

curves is shown by the curves at 5 and 28 feet from the initial point. 

The effect of bed and bank here is to lower the thread of maximum velocity instead of 

raise it. 

WORK ON TRUCKEE 

RIVER AT FARAD, 

CAL. 

The headworks and 

flume of the Truckee 

River General Electric 

Company are shown on 

Pl. VI. Water is taken 

from the Truckee River 

at Floriston, Cal., and 

brought to the power 

house at Farad in a 

wooden flume about 10 

feet wide, 7 feet deep, 

and 8,500 feet long. :s 

Vertical velocity curves 0: ; 

were obtained at two 

places in this flume, one ~ 

590 feet from lower end 

and 150 feet below a 

curve, the other 220 feet 

farther downstream, beyond the influence of the 

curve~ 

At the s e c t i o ns of 

measurement, the sides 

of flume are smooth. 

There are four cleats on 

each side covering the 

four joints, ea~h cleat 

4 by ! inches. The 

mean width at the upstream section was 10.09 

feet and mean depth 

5.98 feet. At the 

Depth in feet. 

t~ to z ,;... 

downstrealll section the FIG. 38.-Curves in upper section, Farad flume, California. 

~nean width was 10.09 feet and the mean depth 5.96 feet. 

V eloc~ty n1easurements were made at six points at each of the six 

verticals, 0.5, 2.0, 4.0, 6.0, 8.0, and 9.5 feet from north side of flume. 
112 ACCURACY OF STREAM :MEASUREMENTS. (No. 95. 

The location of these points, the curves of equal velocity, and the 

mean vertical velocity curve for upper section are shown in fig. 38. 

Depth in feet. 

0 

The upper part of the 

vertical velocity curve, 

a' b, is evidently in error. 

There was no wind at 

the time of measurement 

or any othe.r cause of 

velocity retardation near 

the surface. It is due to 

a peculiarity of this make 

of meter. For velocities 

greater than about 2.5 

feet per second it indicates too small a velocity 

1----+--Hr---+-t-t---T--+---+---t--+----1~ 01 when he] d near the surface. (See p. 90.) The 

points {centers of the lit-

~+--e---++-+-e--l+--e-----ft----<e---+-~r---+--t-e--;.t~ ~ tie circles) defining each 

~ vertical velocity curve, 

~as well as those on curve 

~ t:;· a b c, all fall on a well-

[ defined curve. The veoo • locity was very uniform t14--t~~t--4t::::::t=:~::::t=~-r-::::;?-7f11 at each point. The thread 

of mean velocity is at 

lt--'v-~t::::=:::l=::::::::;:::::o'r=-J:?"-] '"' 0. 7 6 of the depth below 

the surface, · and the 

thread of maximum ve- o I======F~~=======t====t=::zt=====::t======ll! locity at 0. 50 depth. 

FIG. 39.-Curves in lower section, Farad flume, California. 

Fig. 39 shows the 

mean vertical velocity 

curve, and the curves of 

equal velocity in the lower section. The thread 

of maximum velocity is 

near the center of the 

canal at 0.42 depth, and 

the thread of mean velocity at 0. 73 depth below the surface. 

The discharge of the flume at the upper section was 209 second-feet, 

at the lower 205 second-feet, a difference of about 2 per cent of the 

latter. 
U. S. GEOLOGICAL SURVEY WATER - SUPPLY PAPER NO. 95 PL: VI 

A. TRUCKEE RIVER FLUME. 

B. CAR AND CABLE AT OSWEGO RIVER GAGING STAT ION, BATTLE ISLAND, 

NEW YORK. 
MUll.PHY.] .MEASUREMENTS ON THE CHENANGO. 113 

WORK ON CHENANGO RIVER AT BINGHAMTON, N. Y. 

This stream rises in Madison County, N. Y., and empties into Susquehanna River at Binghamton, N. Y. The gaging station is at 

Court Street Bridge, Binghamton. The channel here is straight for 

FIG. 40.-Contour of bottom of Chenango Riv~r at Court Street Bridge, Binghamton, N.Y. 

about 1,000 feet on each side of the station; has a width of about 300 

feet at low watet· and 340 feet at high water; and is broken by three 

piers. The bed is gravel and cobblestone with large, rough stone 

Width in feet. 

I. P. 20 40 60 80 100 120 140 160 180 200 220 2-tO 260 2~0 ilOO :~:..:J 

~ 3 ~ 

.s 4 

.cl 

~5 A 

6 

\ I, 

\ 

\ 

\ 

\' . ""'e' ' \ ~ "'-\ 

'r ~ 

Velocity curves ~o depth 

- A July 8, ~a~e 5. 78 feet G JulyZ9,gage 5.21 feet _l I I I 

r--.... _ --e. !r ...... io--£,. l~ .... 

\.. 

_\ 

"-.._) 

L 

l 

I 

'"' ,.... ....... "--a._ ;:( "'\ ',._... _ .... 1--e- ...... - 1/:r-1. 

l'\ ,.~r >v\ \~., 1:",.1/f I -.&. ... ~· .. 

i\ I 

J \ I 

\ ( """ 

\.. f---/ ~ 

FIG. 41.-Cross section of Chenango River at upper side of Court Street Bridge, Bingham-

- ton, N.Y. 

around the piers. Fig. 40 shows the contour lines of the stream bed 

for some distance above and below the bridge, and the location of the 

piers. It is seen from this figure and fig. 41 that the bed is irregular 

IRR 95-04--8 
114 ACCURACY OF STREAM MEASUREMENTS. [NO, 95. 

as well as rough. This is due to the filling around the piers, and to 

the riffie a short distance below the piers. The bed is permanent, and 

there is a good measurable velocity at all ·river stages. The station 

is 2,500 feet from the Susquehanmi, and is subject to backwater from 

it at certain stages. Although the channel is broken by three piers, 

the bridge projects beyond the piers on each side, and the sections of 

measurement are continuous. 

The gage is of the wire-weight type, located on the upper side of 

the bridge, about half way across it. The initial point is on the west 

face of the east abutment. 

The surface slope of the stream was determined by measuring with 

a steel tape and 3-pound lead from points of known elevation at the 

station and on Ferry Street Bridge, 1,500 feet upstream from it. 

Velocity measurements were made from the upper and lower sides 

of the bridge, with a view to comparing discharges and vertical 

velocity curves on eaeh side. On the lower side, however, the piers 

produeed so much disturbance of the water (eddying) that good results 

could not be obtained, especially for the higher stages. 

The heel being rough, it must be expeetecl that there will be some 

discrepaneies in depth, as shown by the vertical veloeity eurves. The 

instrument, when on bottom, may rest on top of a stone, or may slip 

down between two of them, and thus a movement of a few inches 

show a differenee of 0. 2 to OA of a foot in depth. If the meter could 

be held rigidly with a rod its position would always be accurately 

known, but when held with a eable, as it necessarily must be from a 

high bridge, there is always some uneertainty as to its exaet location, 

and there will be discrepancies in difl:'erent measurements of the 

depths. The soundings were carefully made twice at each side of the 

bridge when the river was low. These, and the change in the river 

stage, were used in computing areas of cross section. 

Twenty-two diseharge measurements have been made at this station. 

From July 2, 1901, to August 15, 1902, nineteen of these were made 

by the six-tenths-depth method, and three· by Harlacher's method. 

For obtaining discharge, the velocity was measured in verticals 10 

feet apart, except near the center of each bridge span, where there 

was little change in velocity, and where they are 15 to 20 feet apart. 

Each observation was usually for two periods of :fifty seconds each. 

Fifteen sets of vertical velocity curves were obtained, each set containing usually 8 curves, at distances 100, 120, 140, 190, 210, 230, 275, 

and 290 feet from the Initial point. These curves are not used in computing discharge, as they were not taken sufficiently close together 

near the piers to enable mean velocity in section to be computed, but 

they are used to show amount and position of mean velocity in a 

vertical with which to compare velocity at six-tenths depth. 
MURPHY.) MEASUREMENTS ON THE CHENANGO. 115 

The results of the discharge measurements are given in the following 

table: 

Discharge measurements, Chenango Ri11er, Binghamton, N. l~ 

No. Date. :Method. Gage Area Dis- Mean Place. 

reading. section. charge. velocity. ----1--------------1---------------

1901. Fret. Sq.jt. Cub. ft. 

1 July ., 0.6 depth -----·------------·-----··· 2 July 8 ..... do .............................. 3 July 11 ..... do ........... .................................. 

4 July ·9 ..... do ............ ················-- 5 -~~- do ::_ ..... do-.............................. 6 ..... do .............................. 

7 Aug. 19 ..... do··-··························- 8 .... do ... ..... do .............................. 9 Oct. 19 ..... do ........... ·················-- 10 .... do ... ..... do ........................ · ...... 

1902. 11 Mar. 27 ..... do ............................. . 12 Mar. 28 ..... do ............................. . 13 Mar. 29 ..... do .. _ ........ _ ................. . 14 July 1 Harlacher's .. _ ..... __ ............. . 15 .... do... 0.6 depth ............... _ ...... _ ... . 16 July 3 Harlacher's ............ _ ..... _ .... . 

~~ 'jiil~q i5" -~~~ ~~~~-: :::::::::::::::::::::::::: 

19 Aug. 2 Harlacher's ....................... . 20 Aug. 3 0.6 depth ............... _ .......... . 21 Aug. 14 ..... do ............................. _ 22 Aug.15 ..... do ............................. . 

5.64 

b5. 78 

5. 71 

5.21 

5.21 

5.49 

5.48 

e5.82 

e 5.81 

8.I5 

8.2I 

8. 75 8.44 

8.41 

7.I6 

7.I6 

!6.56 

f9.IO 

!9.04 

!6.20 

!6.08 

689 

764 1,666 

617 

602 

469 

681 

5-!7 

775 

646 

I, 3M 

I,489 

I,590 

I 56-! I:534 

I, 155 I,I55 

995 

I, 795 

I, 775 

877 

841 

848 

1,119 

768 

942 

405 

425 

577 

566 

927 

987 

4,20I 

4,377 

5,205 

4,439 

4,8I5 

2,611 

2,688 

2,093 

5,426 

5,543 

I,608 

1,341 

a Upper side Court Street Bridge. bThis reading is probably wrong; it should be 5.88. cCable above bridge. · dLower side Court Street Bridges. 

eReading too large on account of backwater. 

!Corrected by -0.09 foot for stretch of wire gage. 

Feet. 1. 23 

1.46 

0.46 

1.53 

0.61 

0.90 

0.85 

1.0-1 

1. 20 

1.53 

3.04 

2. 94 

3.27 

2.83 

3.14 

2.26 

2.33 

2.I3 

3.02 

3.12 

1.83 

I.48 

(d) 

(a) 

(d) 

(a) 

(a) 

(a) 

(a) 

(a) 

(a) 

(a) 

(a) 

(a) 

The gage reading of measurement No. 2 is evidently in error. The 

velocities are all larger than the corresponding ones of No. 10. The 

correct reading is probably 5.88; that is, there is a mistake of 0.1 foot. 

Discharge in Recond-feet. 

0 500 1 000 2 000 3000 4 000 !l,OOO 6 000 

I~ 

~ l.-< r1 __j!.-rz 

l.----J_--

__,!1.- ./ I v [{ 

2~ v .~ 

~ f:t2 ~hange ln mean velocitY. fOr changes in gage heights 

s.-.; I I I 

ao t.jO f:[O :J.O VelocitT f'eet 

FIG. 42.-Station-rating curve, Chenango River, Court Street Bridge, Binghamton, N.Y. 

The quantities in columns 4 and 6 are plotted in fig. 42, which ~bows 

the station-rating curve. From this curve the following station-r:,tting 

table has been prepared: 
116 ACCURACY OF STREAM M.EASURE·:MENTS. (NO. 95. 

8tatiou-rali11g table, Ohenauyo Ril•n·, Court Street B1·idge, Binghamton, N. 1". 

Gage reading. Discharge. I 

1----------------1--------

Fed. Second:fecl.l 6.9..... ... . . ... .. . . . 2,490 

I

. 7.0.................. 2,6:!5 

~:~:::::::::::::~:::: ~:~~I 

i ~t::::::::::::::::: ~:~~. 

Fed. Second:feef. 8.6 .................. 4,\lliO 8.7 .................. 5,100 8.8.................. 5,2.'i0 8.9.................. 5, 400 9.0...... ............ 5,550 9.1... .. ..... .. . .. ... 5, 705 

Uage reading. I Discharge. 

Fed. I &cond-feef. 

g:~ : :: :: : : :: :: : : : :: :::I j~g 5.4 ............. -..... ! .510 5.5 .............. -- ... ! 625 5.6... ................ 755 5.7.-. .. . . . ...... .. . .. i\85 

Gage reading. Discharge. 

H ::::::::::::: !:!~! 9.2................ .. 5, 8ti0 9.3. ...... ... . . . . . . .. 6,015 9.4 .... .. ............ 6,170 9.5.................. 6,325 

5.1'1. .. . .. . .. .. . . . .. ... 1,015 5.9................... 1,145 6.0..... ...... ... . . . . . 1,275 6.1. .. . .. . ....... .. . .. 1,410 6.2..... .. . . .... ... . . . 1,545 7.9.................. 3,905 9.6. ...... .. .. . . . . ... 6,475 6.3 ............. ...... 1,6SO 8.0.. .. . . . ... . . .. . . . . 4,050 9.7 .................. 6,625 6.4................... 1,S1.'; 8.1. .. . . . . . . .. . . . . . . . 4, 200 9.8.. .. . . . . ... . . . . ... 6, 775 6.5 ........... -. . . . . . . 1, 950 8.2. ............. .... 4,350 9.9.................. 6,925 

1

8.3.......... .. . . . . . . 4,500 

8.4 ...... ········ .... 4,650 8.5... ... . . . . . . . . . . .. 4,800 

6.6 .. ... . .. . . ... . . .... 2,085 10.0................. 7,075 6.7 ............. ...... 2,220 6.8 . . . . . . . . . . . . . . . . . . . 2, :3.55 

From the two preeeding tables, the following, showing the differenee 

between the mea~ured diseharge and the di~charge given by the stationrating table, has been prepared: 

Comparison ~~f mew-:ured and mean di.schm·ges, Chenaugo Ril•er, Binghamton, Jv". r. 

Discharge. 

Date. No. Gage 

reading. By By rating measure. cnrve. 

1901. Feet. 8econd:fcet. Secmuljeet. 

July2 ................................ fl.64 848 i-107 JulyS ................................ a5. 78 1, 11\l 989 July9 ....... · ......................... 3 5. 71 942 1,028 

July29 ............................... 5 5.21 40.5 420 Do ............................... 6 5.21 425 420 August 19 ••.......................... 7 5.49 577 613 Do ....•••........................ 8 5.48 566 602 October 19 ............................................... 9 b5.82 927 1,041 Do ............................... 10 b.5.81 987 1,028 

1902. March 27 ............................. 11 8.15 4,201 4,275 March 28 ............................. 12 8.21 .(,377 4,365 March29 ............................. 13 8. 75 5,205 5,175 

July 1 ................................ 15 8.41 4,815 4,665 

July3 ................................ 17 7.16 2,688 2,849 

July15 ............................... 18 6.56 ~~- 098 2,031 

August3 ............................. 20 9.04 5,543 5,612 

August 14 ............................ 21 6.20 1,608 1,545 

August15 ............................ 22 6.08 1,341 1,383 

1903. July1 ................................ 14 8.44 c4,439 4, 710 July3 ................................ 16 7.16 c2, 611 2,849 

August2 ............................. 19 9.10 c5,426 5, 705 

a Should pmbably be 5.88. bReading too large ou account of backwater. c By Harlacher's method. 

Discharge difference. 

Cubic feet. Per cent. 

+ 41 + 5.1 +130 +H.2 - 86 - 8.3 - 15 - 3.5 

+ fi + 1.2 - 36 - 5.9 - 36 - 6.0 -114 -10.9 - 41 - 4.0 

- 74 - 1. 7 

+ 12 + 0.3 

+ 30 + 0.6 +150 + 3.2 -161 - 5. 7 

+ 67 + 3.3 - 69 - 1.2 

+ 53 + 3.4 - 42 - 3.0 

-271 - 5.7 -238 

I - 8.3 -279 - 4.9 

Omitting No. 2 on account of a probable error in_ the gage reading, 

and No. 9 on account of the influence of back water, we see that the 

variation of the diseharges from the mean discharge is from -8.3 to 

+5.1 per eent. 

The 15 vertical velocity curves for each of the 8 verticals are made 

up from velocity observations at from 3 to 5. points in each vertical, 
MtJRi>iiY.j MEASUREMEN'I'S ON THE CHEN .A.~~GO. 117 

the extreme ones being about 0. 5 foot above bottom and 1 foot below 

the surface. Each observation covered 4 periods of 25 seconds each. 

The nearest whole number of revolutions in each period was recorded -

except the last one, in which the nearest tenth was also recorded. 

The velocities computed frmn these observations were plotted on section paper, and a smooth curve drawn to reprP.sent the mean vertical 

velocity curve. These points gave, as a rule, a well-defined curve 

except near the bottom, where the bed was rough. From these curves 

the velocity at each two-tenths of the depth and at the sudace was 

taken and tabulated. The data for each vertical was grouned, and 

.s 

0 

! 1. l At /00 reef from I. P. 

- ~/6 ,, 

- ~ 

I 

I 

-~ 

Velocity in feet. 

3 

.I I At 140 reef rrom l P. 

4 

__§.. 

__..§., I 

I 

41 - 7 

--2..,1 

...£ p:·/ 

-~ /( 'II J ,, .. _p 

-; II VJ ~ 

; # 1 

3 

L v // v 1/ If I 

VJ v 'J If 

I II 1/ 2 

0 

3 

.1 ·I 1 . At /90 reet rrom I. P. 

~ -~ 

~It 

l/7 

~ 

- ¥1 

~ 

7 

7 

1 ~ 

J 1) I I//; / 

v 

FIG. 43.-Groups of vertical velocity curves, Chenango River, Binghamton, N.Y. 

• 

I 

those for each two-tenths of depth and surface were combined for the 

curves in which the gage heights did not differ by more than 0.5 foot. 

The resulting six sets of vertical velocity cur'ves on the upper side, 

and three sets on the lower side of the bridge are shown on figs. 43 

and 44. These sets of curves should now be studied in connection 

with figs. 40 and 41, which show position of piers and irregularity of 

bed. Perhaps the first thing that is noticed is the similarity-with 

one exception--of the curves in any group. Curve No. 6 in each 

group is different from the others, and indicates a di8turbance of the 

ordinary conditions. The reduced surface velocity indicates back-
118 [No. 95. 

"1ater, but as no slope measilrements wete taken that afternoon it can 

not be ciefinitely stated that this is the cause. Another noticeable 

feature is the falling of ail the sttrface velocities except No. 6 on a 

well-defined curve which resembles a parabola. Another is that the 

maximum velocity is at or near the surface. Another, that as the 

depth decreases and as the velocity decreases, the vertical velocity 

curve approaches a straight line. For shallow depths this line is 

more inclined than for great~r ~epths. 

3 0 0 At 120 f'eet f'rom l P 

!) 6 I 

I 

8 .'! 

AI ~ 

rJ/ 

~~ VJ 

t I 

.s 

t Jl l 

v /1 v; 1 

Velocity in feet. 

2 3 0 

At210f'et f f'rom .P. 

6 J 

-rL 

v 

.2 ;-, 7 

AP21'51') 

2, 

_L 7~ -4 -?~ 

I 1 

~ i 1 I 

3 1 2 3 

f f'romi.P. A!'P9~ f'eef f'I"Dm I. P. 

6 61 

-~ _.§.. A 

v 

4/ /j I 

v I I IJ --*' ..L v 4Y. t ~ j, 

t I IIJI 

lA I; !!)' 

LL ~ v ), I v 1/1 / 1(0 - 2 

~ I i 'I f-lj II f./ 

0 I If! I 

FIG. 44.-Groups of vertical velocity curves, Chenango River, Binghamton, N. Y. 

The lower parts of these curves are not well defined on account of 

roughness of bed; the depths varied and the velocity was irregular 

and loc.al. The following table shows the change in mean velocity. in 

verticals for-changes in river stage: 

Ta.ble showing change ·in mean !'elodty in 'l'erl'icals 'With changes in r-i·ver stage, Chenango 

Ri1'er, Court S~t·eet Bridge, Bingharnton, N. 1':. 

Gage Distance of vertical from initial point. 

Date. ~~~ 100 feet. 120 feet. 140 feet. I 190 feet. 210 feet. 230 feet. '1:75 feet. I 

1 

290 feet. 

-1-9-01-. -I-F1-ee-t.-- ---------~--- ---------~---

July 30 .. . 5. 21 0. 68 0. 91 1.11 0. 90 0. 83 0. 75 0. 62 0. 42 Aug. 20... 5. 43 . 97 1. 19 1. 31 1. 09 . 95 . 74 . 77 . 53 July 9 .. .. 5. 64 1. 49 1. 66 2 09 1. 68 1. 52 1. 41 1. 29 . 94 Oct. 19a.. 5. 80 1. 36 1. 53 1. 78 1.42 1. 31 1.15 1.12 .84 

1902. 

Aug.15 ... Aug.14. .. July 3 .... Mar. 28b •. Mar. 27b .. Mar. 28 .. . July 1 ... . Mar. 29ft .. Aug. 2a •• 

6.15 1. 72 1. 97 6.27 2.17 2.18 7.18 2.49 2.65 8.02 3.38 3. 74 8.14 .................. ................... 8.17 2.93 3.23 8.40 3.04 8.85 3.60 3.83 9.07 3.22 3.33 

aAffected by back water. 

2.30 

2.61 

3.10 

3.91 

3.90 

3.51 

3.59 

4.10 

3.65 

1.90 1. 90 1.71 1.40 1.98 2.09 1.90 1. 77 1.51 2.57 2. 70 2.30 2.48 2.11 3.92 4.05 3.84 ~ .................. ................... 4.11 4.12 .................. ................. ................... 3.19 3.01) 2.58 3.06 3.11 3.08 2.61 3.00 2.42 4.19 4.35 

3.17 3.01 3.15 ··--·a:os· 2.79 

h From lower side of bridge. 
MURPHY.) MEASUREMENTS ON THE CHENANGO. 119 

These mean velocities and corresponding river stage has been plotted 

for each v~rtical, giving curves like that £or 140 feet from initial 

pobt, as shown in Fig. 45. The velocity does not increase as fast a.s 

the river stage. The following. table shows the changes in the ratio 

'fJ for river stages: . 

Table showing change in rat·io d-+-D in 1•erticals with clzamge 1:n river stage, Chenango Riz•er, 

Cowrt Street Bridge, Binghamton, N. r. 

Gage 

reading. 

---

Feet. 

5.21 

5.43 

5.64 

6.15 

6.27 

6.64 

7.18 

8.17 

8.40 

a9.07 

b8.02 

8.14 

8.85 

! 

Distance of vertical from initial point. 

100feet. 120 feet. HOfeet. 

--- --~ --

0.5! 0.64 0.60 .53 .59 6') 

.56 .65 .61 .56 .58 . 61 .64 .61 .&! .57 .59 .67 

.61 .64 .63 .59 .63 .64 .67 . 70 a. 70 (! .67 a .69 

--------- .586 .616 .636 

b • 57 b • 60 b • 63 ........ ........ b.69 b . 57 b . 66 b . 64 

.P..7 . 63 .6n8 

190feet. 

--~ 

0.57 

.60 

.61 

.64 

.67 

6') 

.59 

6'} 

.63 

a .64 

---

. 616 

b .62 

b .59 

b .66 

210feet. 230 feet. 1275 feet. 290feet. --~ --- ---

0.68 0.58 0.56 0.55 .63 .58 .57 .56 .63 .60 .58 .53 .66 .58 .60 .67 .67 .67 .63 .65 .66 .64 .57 . 70 .67 .65 .57 6'} .61 .61 .63 .67 .63 .67 .55 a .63 a.67 a.65 a .61 

------------ .657 .625 .614 .577 

b.63 b.53 .............. .. b.63 ...................... .. b .67 ....................... . 

.623 _.643 ...................... .. 

a ResnltR affected by backwater and not used in computing means. b Results from lower side of bridge. 

It is seen that this ratio increases somewhat as the depth increases 

£or the shallower depths when the stage is constant, and also increases 

slightly as the. river stage increases. Fig. 45 shows results for the 

verticall40 feet from initial point. 

The following table show:s changes in the ratio ~~~· in verticals for 8 

changes in river stage, T: being the yelocity 0.5 foot below the surface: 

Table .<~howing change in mHo r;n-+-rs ·i.n rertical.s for change-s in ·ri1•e1· siagP, Cmtt·t St-reet 

Bridge, Chenango RiNT, Binghmnton, N. r. 

Gage 

rending. 

---

Feet. 

5.21 

5. 43 5. 64 a5.80 

6.15 

6.27 

6.64 

7.18 

8.17 

8.40 

a9.07 

b8.02 

. 8.14 

8.85 

Distance of vertical from initial point. 

100 feet. 120 feet. 140feet. 190 feet. 1210 feet. 230 feet. 27fi feet. 290feet. -------.-----------------

0.80 0. 77 0.83 0. 90 0.86 0.80 0.84 0.83 .\JO .80 .83 .94 .85 .78 .86 .81 .90 .83 .89 9') .93 .89 .89 .89 a.91 a.85 a.86 a.91 a.90 a.76 a.86 a.91 .82 .81 .85 .83 .86 .88 .82 .90 .84 .89 .84 .88 .90 .87 .88 .89 .81 .90 .89 .88 .82 .90 .88 .89 .84 .88 .86 .92 . 92 .91 .86 .85 .87 .89 .87 .88 .81 .87 .90 .89 . 92 .89 . 91 .84 . 90 .82 a.93 a.88 a.89 a.89 a.83 a.SS a.86 a.81 

------------------------

.871 .821 .876 .882 .897 .833 .880 .855 

b,85 b,88 b.90 b.93 1>.94 b.91 ............... . 

.... .... ........ b.921 b.93 b.94 ...................... .. ':>.86 b.89 b.93 b.94 b.98 ...................... .. 

-----------------------

. 855 . 885 . :m . 933 . 953 ...................... .. 

a Results affected by backwater and not used in computing means. b Results from lower side of. bridge. 
120 ACCURACY OF STREAM MEASUREMENTS. (No. 95. 

The values of this ratio and the corresponding gage heights have 

been platted for each vertical. They all show this ratio to be nearly 

constant. There is a slight increase of the ratio for increasing river 

stage. Fig. ±5 shows results for verticall±O feet from initial point. 

.') 

4.0 

3. 5 

) 

o/ ) 

1.5 / 1.0 

p: . f) 

~ 

0 

~ .8 ~ 

~ .7 

I 

~ 

c 

-0 0 

E ·~ "' -

0 

Gage height in feet. 

8 9 

~8 

v 

0/ (a) 

~ 

, _p 

0 - 0 (h) 0 

0 

- F 

0 

..D-- -- ---- (C) 0 0 0 

::<'IG. 45.-Diagram showing results in vertical 140 feet· from initial point, Court Street 

Bridge, Binghamton, N. Y. 

The slop~ of the surface in the vicinity of the gaging station was 

obtained by measurements with a steel tape from points of known 

elevation at the gage and at Ferry Street Bridge. The data obtained 

are given in the following table: 
MURPHY.] MEAStJ'REM:E:MTS ON TflE CHENANGO. 121 

Slope of Chenango River, Binghamton, N. l~, from Court street to Fen·y Street Bridge, 

1,500feet. 

Date. Hour. 

1902. 

March 28 ............................... 7.30 a:m ... . · Do .................................. 10.45 a.m ..• Do .......................... o ••••••• 5p.m ...... . March 29 ..............•................ 7.30a. m ... . Do .................................. 11.4.') a.m .. . 

Gage reading. 

July 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.14 p.m ... · 

Feet. 8.02 

8.05 

8.32 

8. 70 

8.91 

8.46 

8.40 

8. 07 

7.30 

6.68 

6.59 

8.62 

7.88 

6.28 

6.26 

6.19 

6.09 

Do ................................•. 3.45 p.m ... . July 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5.') a. m ... . July 3 . . . . . . .. . . . . . . .. . ... . . . . . . . . . . . . . 1. 30 p·. m ... . July 15 ................................. 5.10 a.m ... . Do .................................. 1p.m ...... . August 3 ................................ 6 a.m ...... . August 4 ................................ 5.40 p.m ... . August 14 •••••.•••••••••.••...•••..•.•.. 2.40 p.m ... . Do................... . . . . . . . . . . . . . . . 6.3.'i p. m ... . 

August 15 ..................... :... . . . . . 5.30 a. m ... . August 16............................... 1"2.12 p.m .. . 

Elevatious.a 

Elevation 

Court Ferry difference. street. street. F-C. 

c. F. 

Feet. Feet. Feet. -5.09 -4.72 0.37 

---5.06 -4.68 .38 

-4.79 -4.40 .39 

-4.40 -4.01 .39 

-4.20 -3.80 .40 

-4.70 -4.31 .39 

-4.75 -4.37 .38 -5.06 -4.68 .38 

-5.82 -5.52 .30 

-6.38 -6.15 .23 

-6.46 -6.22 .24 

-4.40 -4.09 b.31 

-5.16 -4.89 b.27 

-6.74 -6.55 .19 -6.77 -6.57 .20 

-6.83 -6.64 .19 

-6.97 -6.81 .16 

a Elevations referred to Binghamton Citr datum. Elevations of B. M. furnished by E. F. Weeks, 

Assistant City Engineer. . ' bMeasurements made durmg backwater. 

NoTE.-From July 3 to July 15, 190'2, the gage wire appears to have shortened about 0.09 foot. 

These data are plotted in fig. 46, using surface elevations .at Court 

Street Bridge as ordinates, and fall of the surface in 1,500 feet as 

Fall of surface in feet. 

0.1 0.2 0.3 0.4 o.n -4r------------r------------T-----------~------------,------------, 

B 

--5 

....; 

Q) 

~ 

.s 

~ 

0 

:;:: 

o:l -6 ... 

Q) 

Q) 

Q) 

0 

~ ::I 

w 

-7 

-8~----------~----------~----------+-----------~--------~ FIG. 46.-Diagram showing change in surface slope for change in river -stage, Chenango 

River, Court Street Bridge, Binghamton, N.Y. 

al>scissas, giving the curve A B. The slope increases with the depth, 

but the rate of increase is not as great as that of the depth. The points 
122 ACCURACY OF STREAM MEASUREMENTS. [NO. 95. 

a and a.' obtained during the effect of backwater, show that there is less 

slope. and smaller change in slope when there is backwater at a station. 

WORK ON SUSQUEHANNA RIVER AT BINGHAMTON, N.Y. 

Susquehanna River rises in Otsego County, in the east-central part 

I 

I 

N 

I S 

of New York, and flows southwesterly and southerly through 

New York, Pennsylvania, and 

Maryland, into Chesapeake Bay. 

The gaging station, where the 

work to be described was done, 

is at Exchange Street Bridge, 

Binghamton, N.Y. The channel 

is st1:aight for about 500 feet 

above and below the station, has 

a width of about 300 feet at low 

water and about 450 feet at high 

water, and is broken by three 

piers. The_ bed is gravel and 

small stone, with large stone 

filled around the piers. Fig. 47 

shows the contour lines of the 

bottom, and the location of the 

piers. Fig. 48 shows the cross 

section on the upper side of the 

bridge. The shape of the section 

is good except for the filling 

around the. piers; the bed is permanent, and the velocity large1 

especially for the hig·her stages. 

About 900 feet above the station 

is the clam of the Binghamton 

'Vater Power Company. Its effective head is 6 feet. The thread 

of the stream strikes the piers 

somewhat obliquely, producing 

eddies. 

The old wooden bridge at the 

station was condemned shortly before this station was established, 

and it was decided to place the 

gage, which is of the wire-weight 

FIG. 47.-Contours of su~quehanna River bed at Ex- form, on washington Street 

change Street Bridge, Binghamton, N.Y. ·Bridge, about 1,900 feet below 

the station. A temporary gage was, however, established at the 

station, and the watet· surface referred to it for convenience. The 

new bridge was erected in the spring of 1902. 1 t has only one 
MEASUREMENTS ON THE SUSQUEHANNA. 123 

pier, which is about 200 feet from the east abutment. Around it are 

two rows_ of s~ort piles and a quantity of large stone. The upper 

parts of the old piers have been removed, but the ~-:~tone filling around 

them remains, leaving the river hed irregular and rough. 

The method of measuring discharge and of obtaining v~rtical velocity curves was the same as at the Chenango River station, and need not 

Width in feet. 

I.P. 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300• 320 340 360 

"\~ lro..,, 1'-<~r- -.... , /~ t 

_I!(" !{' 1:: ' I 1

1 1 ~~ \ , ' I '" ...,..- --- . -........... .... T: 'A-..6 --- ,.._-.!>-- -A-._ ll.{v __ .. - ,., rj I 

~ i!l:: ----- .... :---............. _ _..,./, f I ,y--' '&A- ~:~.,;, I 

. .e. I #' I 

~-...... · ... , ........ -// ! AI'" -~-- -41: •I ~~ :::0: :-• , s'' /' II ~ --- ~- -- --a' ;- -.a-::--- , __ .tf}f/ ," .,' t:~--- ~ .. _ I ~ \ ,, v \'e -- 'EI, I ,f' Ill .... , 

Ill). ' 

'-e __ / -· --l!lo ... ;· ~ 

<b ... , I 

' ...... , ... 

I I~ ... I ---~ ---- ,_ ___ ... -*' ... 

I ... ,,/ -V - -Velocity curves 6

/io depth~ A Au!).20 gage(temporary) -.63ft\ / \ __... -4) Aug. 23 gage (temporary) + .31 ft 

G Aug.Zc (p.m) gage(temporary)+.73 ft \J ~ v m Aug.2c(arn) gage(temp'y.) + 1.10 ft. ' - .) 4>Aug.21 (pm.)gageltemp'y.) "'2.7.3ft 

f I I I I I FIG, 48.-Cross section of Susquehanna River at lower side of Exchange Street Bridge, 

Binghamton, N.Y. 

again be described. The current was so swift here that it was difficult 

to keep the meter in place, and the discharge is computed in some 

cases from v~locity measurements 1 foot below surface, and the ratio 

of mean to surface velocity found from the vertical velocity curves. 

The following table gives the results of the discharge measurements. 

Those made in·1902 were from the upper side of the new bridge: 

Dil5cha·rge ·merr.~llrement.s, 8nsqttehanna Riz•er, Binghamton, N. Y., Exchange l~~reet -B1·idge. 

No. Date. I Method '"""· G-age A~a. IDI~h-e. Mean Gage, 

reading. velocity. Wash. st. 

1901. Squm·ejed. Second-feet. 1 July 3 0. 6 depth ......... -0.60 891 947 1.06 2.13 2 July10 ..... do ............ - .27 1, 0'20 1,425 1.40 2.28 3 July30 ..... do ............ - .83 847 b608 7') 1. 99 4 Aug.20 ..... do ............ - .65 909 942 1.04 2.09 b Aug.20 ..... do ............ - .6i> 923 952 1.03 2.10 6 Aug.21 ..... do ............ +2.73 1,989 7,2-14 3.65 4. 63 7 Aug.21 Harlacher's ....... +3.00 2,066 7,803 3.77 4.87 8 Aug.2'2 0.6 depth ......... +1.10 1,439 3, 752 2.61 3.23 9 Aug.22 ..... do ............ + .73 1,324 2,983 2.25 2.94 10 Aug.23 ..... do ............ + . 31 1,189 2,176 1.83 2.64 

1902 11 July 2 Harlacher's ....... +2.16 1,813 5,386 2.97 4.09 12 July 2 0.6 depth ........ _ +2.09 1, 790 5,839 3.26 4.04 19 July 2 Surface ratios ..... +2.06 1,794 5,680 3.17 4.10 12~ July 2 V. V. curves ...... +2.09 1, 790 5,420 3.03 4.04 13 July 3 Harlacher's ....... +2.46 1, 916 6,559 3.42 4.39 14 July 4 V. V.cnrves ....... +1.87 1, 717 5,230 3.28 2.96 14 July 4 0.6 depth ......... +1.87 1, 717 5,626 3.28 3.86 15 July14 ..... do ............ + .77 1,320 3,064 2.32 2.96 16- ·Aug. 3 Harlacher's ....... +3.31 2,206 8,156 3. 70 5.15 17 Aug. 3 ~urface ratios ..... +3.31 2,187 

s.rum I 3.95 5.15 18 Aug. 4 Harlacher's ....... +2.65 1,971 6,599 3.34 4.60 19 Ang.-4 Surface ratiot> ..... +2.65 1,952 6,902 3.53 4.60 20 Aug.15 0.6 depth ...... ". .. + .24 1,140 2,105 1.85 2.60 21 July16 ..... do ............ +.OS 1,103 1,920 1. 74 2.50 

a Upper side of old bridge. b Two small gates in mill closed during measurement. c Lower side of old bridge. 

dUpper side of new bridge. 

Place. 

---

(a) 

(a~ (a 

~~~ 

~~~ (a) 

(c) 

(C) 

(d) 

(d) 

(d) 

(d) 

(d) 

(d) 

(d) 

(d) 

~d) 

(:~ (d) 

(d) 

(d) 
124 ACCURACY OF STREAM MEASUREMENTS. 

These discharges and the corresponding temporary gage readings 

are plotted in fig. 49, which gives the station-rating curve for this 

.s 

0 

4 

3 

-1 

Discharge in second-feet. 

1,000 2,000 3,000 4,000 5,000 6,000 7.000 8,000 9,000 10,000 

Y< I 

~ ~ .J If ~~x-

~ 12 

y v v 

v ~ 

~ zo / 

v. / Change in mean velocity 

;) 5 with chanje in gage 

I 

0 LO z.o Veloc,ry I 3.0 teet ~0 

Fig. 49.-Station-rating curve of Susquehanna River at Exchange Street Bridge, Binghamton, N. Y. 

station. From this curve the following station-rating table has been 

prepared: 

Station-rating table, Susquehanna River, E.rchange Street Bridge, Binghamt_on, N. Y. 

Gage readI 

Discharge. Gage read- Discharge. Gage read- J)iscbarge. ing. ing. ing. 

. Feet. Second-feet. Feet . Second-feet. Feet. 8cr011 d-feet. -1.0 525 (1. 7 2,955 0.4 6,390 - .9 642 .8 3,140 .5 6,620 - .8 760 .9 3,335 .6 6,850 - .7 879 1.0 3,530 . 7 7,085 ·- .6 1,000 .1 3, 780 .8 7,325 - .5 1,124 .2 3,930 ·.9 7,565 -.4 1,250 .3 4,130 3.0 7,805 - .3 1,378 .4 4,330 .1 8,045 - .2 1,510 .5 4,530 .2 8,290 - .1 1,tl45 .6 4,730 .3 8,540 .0 1, 790 . 7 4,9ao .4 8,790 +J 1,935 .8 5,130 .5 9,045 

2,090 .9 5,330 .6 9,300 .3 2,252 2.0 5,530 .7 9,560 .4 2,415 .1 5, 740 .8 9,820 .5 2,592 .2 5,950 .9 10,080 .6 2, 770 .3 6,170 4.0 10,350 

From this table and the one g1vmg results of discharge measurements the folJowing table, giving the percentage difference between 

the measured discharge and that shown by the discharge table, has 

been prepared. With three exceptions this variation is less than 5. 5 

per cent. The largest variation is for the smallest river stage, and is 

due to the closing of the g·ates of the mill at noon while the measurement was under way. No. 14 is too large, due to the meter being 

carried downstream, and not being at 0.6 depth. The results by 

Harlacher's Inethod, No. 7, 11, 13, 16, ~nd 18, indicate, as in the case 

of the Chenango River station, that the coefficient 0. 85 in the formula 

Q=0.85 ~,..Is Fis too small, and should be 0.88. 
MURPHY.] MEASUREMENTS -ON THE SUSQUEHANNA. 125 

Ca,mparison of measured and mean di.scha1·ge, Susq1uhanna River, Exchange Street Bridge,' 

Binghamton, N. 1~ · 

Discharge. Discharge difference. 

Date. 

1901. July3 ..... ________________________ _ 

July 10 .. ----- .... --------.--- ... --- July 30 .. --------.------------.----. August 20. ____ . ------------ __ ..... . 

Do----------------------------- August 21.---- __ ----------- ... ____ _ August 22.----------- ..... _____ .... 

Do----------------------------- August 23 ... --- ..... ----------- .... 

1902. July2 _____________________________ _ 

Do-----------------------------

Do----------------------------- July4 ............................. . 

Do----------------------------- July 14. ______ ... _ ------- __ . _ .. __ . _ August 3 ___ ............. __________ _ 

August 4-------.--------- ______ .... August 15 ____ . ------------- __ .. ___ _ August 16 .... ------·· ..•.. _____ .... August 21. _____ ......••.. _________ _ 

July 2 ................ _ ...... _ .. _ .. . JulyS ............................. . August 3 ....... __ . _ ............... . August 4 ..................... __ ... . 

No. 

3 

4 

5 

6 

8 

9 

10 

12 

121 

122 

14 

141 

15 

17 

19 

20 

21 

7 

11 

13 

16 

18 

Gage. 

Feet. 

-0.60 

- .27 - .83 - .65 - .63 +2. 73 +1.10 

+ .73 + .31 

+2.09 

+2.09 

+2.16 

+1.87 

+1.87 

+ .77 +3.31 

+:!.65 

+ .24 + .08 +3.00 

2.16 

2.46 

3.31 

2. 6.5 

Byu~~as- By curve. 

Seconcl-jeet.- Seconcl:fet.'l. 

947 1, 000 1, 425 1,416 

608 725 

942 940 

952 965 

7,244 7,155 

3, 752 3, 730 2, 983 3,011 

2,176 2,268 

5, 839 5, 720 5, 420 5, 720 5, 680 5,866 

5, 626 5, 270 5, 230 5, 270 3 064 3,084 8:633 8, 565 6, 902 6, 96.5 

2,105 2,152 

1, 920 1, 906 

7, 803 7,805 

5, 386 5,866 5 660 6,488 8:156 8, 565 6, 599 6, 965 

Secondfeet. 

-53 

+ 9 -117 

+ 2 - 13 

+ 89 

+ 22 -- 28 

-92 

+119 

-300 

-186 

+356 

-40 

-20 

+68 

- 63 - 47 

+ 14 - 2 -480 

+ 71 --409 

-366 

a Due to closing the gates in bill at noon. b Due to meter being carried downstream and not at 0.6 depth. 

Per cent. 

-5.3 

+ .7 a-16.1 

+ :2 - 1.3 + 1.2 + .6 - .9 -4.0 

+ 2.1 -5.2 

- 3.1 b+ 6.6 

.8 

7 

+ .8 - .9 - 2.2 

+ .7 

.0 - 8.2 + 1.1 -4.8 

-5.2 

Vertical-velocitv-curve data were obtained in 12 verticals as described 

on p. 117. Thesevwere plotted~ vertical velocity curves drawn, and the 

velocities at ,eaeh one-fifth of the depth and at tl;1e surfaee tabulated. 

The eurves in each vertical in which the change in river stage did not 

0 1 2 3 4 

Af /00 fut from I. P 

..LI 

Velocity in feet. 

1 2 3 4 

At 125 f'eet rrom I. R 

5 1 2 3 4 5 

FIG. 50.-Vertical velocity curves, Susquehanna River, Exchange Street Bridge, Binghamton, N.Y. 

differ by more than 0.5 foot were then united by combining .the velocities at each fifth of the depth. Some of the resulting groups of curves 

are plotted in figs. 50 and 51. Nos. 4, 5, 6, and 7 were taken from 

the upper side of the new bridge, which is 18 feet upstream from the 

upstream face of the old bridge. 
126 ACOURACY OF STREAM MEASUREMENTS. [No. 95. 

Velocity in feet. 

0 1 2 3 4 0 1 2 3 4 1 2 3 4 2 3 

At/70f'eetf'roml P. At Z45 feet from /. P. Ati!~ reef rrom /. P. At-335 rt. t'rt:Tm I. R 

-L -L 

3 

2 

-

Q) 

$ 0 

;?I I .§.. / .§.. I 5 5 s I 

~ J 7 II ~~rr 1 I J 

_:! -~~ .!t., 

_z :jL z/ I _J 

.!:! I 

~ " -1 IJ tt I jl/ 411 1/ - .:: 

:s 

~ 

Q) 

'"' -2 Q) II f. I/ I /, fLJ biJ 

~ VI I 7 tJ l 711 ~ 

\!) 

-3 

-4 

-5 

J 

~ 'j / ;{ I t ~~ v 

___!1, 7-' /JV I I //; 

-1' I' 

FIG. 51.-Vertieal velocity curves, Susquehanna River, upper side of Exchange Street 

Bridge, Binghamton, N.Y. 

Gage height in feet. 

-1 0 +1 2 3 4 

3.5 

3.0 

/8. 

/ 

't:l / 

/ .:: 

0 

0 

~ 2.5 

'"' Q) 

A 

-

Q) 2.0 $ 

.s 

t-

·s 1.5 

..9 

Q) 

:;.... 

a 

/ v 

/ 

/ 

1.0 .-7 

p: .5 

~ .9 0 

:p 

~ ' 0 

A c 0 p c 0 0 

~ 

.8 

. 7 

- '-£ 

q c . - ... 'tl . 6 i D' • • • • 4 

~ ' 

FIG. 52.-Diagrams showing change in velocity and in ratios ~· ~= for changes in river stage. 

4 

5 
MURPHY.) MEASUREMENTS ON THE SUSQUEHANNA. 127 

It is seen that the curves in fig. 50, out of the influence of the pier, 

are very regular in shape, and the surface velocities give a well-defined 

curve, the greatest velocity being at or near the surface. 

Those in fig. 51 are not far from the piers, except that at 335 feet from 

initial point, which is near the shore. These are not so regular in shape, 

and the surface velocities do not fall on a well-definPd curve. The points 

marked by triangles show surface velocit}T for the river stage indieated, 

but not taken when the vertical velocity curve was obtained. 

Sm:face slope of Susquehannn Rirer, Binghamton, N. r., from Exchange Street Bridge 

to Washington Street Bridge, 1,850 feet. 

Elevation water sur- face. 

Date. --------1 Difference Washing-, Exchange elevation. ton Street Street Bridge. Bridge. --------------------------------------r------------1------ 1902. July2 ............................................................ . July 14 ........................................................... . August 3 .......................................................... . Do ............................................................ . Do ............................................................ . Do ............................. ~ .............................. . August 4 .......................................................... . Do .............................•............................... August 15 ......................................................... . Do ................. ~-········ ................................. . Do ....................... · ..................................... . Do ............................................................ . Do ............................................................ . August 16 ......................................................... . Do ............................................................ . 

Feet. 

a -5.86 

-6.!!5 

-4.44 

-4.49 

-4.531 -4.75 

-5.18 

-.').451 -7.33 

-7.41 

-7.40 

-7.37 I 

--7.391 

-7.45 

-7.49 I 

a Elevations referred to Binghttmton City datum. 

Feet. 

a -4.74 

-5.88 

-3.16 

-3.16 

-3.26 

--3.42 

-3.91 

-4.20 

-6.35 

-6.43 

-6.43 

-6.42 

-6.46 

-6.55 

-6.62 

Feet. 1.12 

1.07 

1.28 

1.33 

1.27 

1.33 

1.27 

1.25 

.98 

.\)8 

.97 

.95 

.93 

.90 

.87 

Change.s in mean 1•elocity ·in t•e·1·tica1s with changes ·in ?'il•Pr stage, ttpper side E:rchange 

. 1'-.'treet B1·idgP, Binghamton, N. r: 

Distance of vertical from initial point. Date. Gage 

reading. 60 feet. 100 feet. 1125 feet. 170 feet. 245 feet.. 285 feet. 310 feet. 335 feet. 

------1--------1---------------------------

1901. Feet. T'Ily 10 -0.33 0.50 1.07 1.30 .............. ---------- 1. 70 ..................... ................... .July 30 - .87 .58 ............... ---------- .................. ---------- ---------- ................... 

1902. 

Aug. 16 + .04 1. 57 1.88 1. 31 2.05 2.10 1. 92 1.80 Aug. 15 + .21 . 93 1.66 2.03 1. 36 2.22 2.26 2.03 2.01 ··1Jy 14 + . 73 1. 29 2.00 2.50 1. 63 2.71 2.95 2.50 2.33 T'Ily 4 +1.85 1.89 3.00 3.46 2.26 .................. ................... ................... .. ................. T,Ily 2 +1. 97 1. 89 2. 76 3.42 2.37 3. 60 3.57 3. 21 3.02 Aug. 4 +2.54 :;!.40 3.35 4.17 3.09 4.41 3.31 2.88 Aug. 4 +2.46 2.35 3.32 4.09 3.09 3.88 3.38 2.94 Aug. 3 +3:23 2. 76 3.65 4.86 3.81 .................. ................... 3.98 3.23 

Changes ·in the ratio d: D in ·1•erticol.sfm· changes ·in r·i1•e·r .stage. 

Distanee of vertical from initial point. Gage 

reading. 60 feet. j100 feet. 125 feet. 170 feet /245 feet 285 feet 310 feet. 335 feet. 1------·j------

Feet. 

-0.33 

- .87 +.04 

+ .21 + .73 +1.85 

+1.97 

+2.54 

+2.46 

+3.23 

Means .. 

0.52 0.60 

. 58 

. 57 .54 .57 .58 .59 .61 .59 .50 .59 .62 .60 .61) .64 .63 .65 

.581 .598 

0.56 a0./55 

a .66 .............. .62 .51\ 0.69 .59 .58 .63 .62 .55 .63 .66 .64 .63 . 67 .59 .69 .65 .63 .71 .66 .63 .68 .61 .................. 

.634 .600 .670 

a At 175 feet from initial point. 

0.57 .................. .................... --------·· ................... ................... .65 0.57 0.54 . 61 .61 .57 .63 .60 .56 ................ ---------- ................... .57 .56 .66 .69 .64 .68 .68 .65 ................... .56 .61 

.620 .600 .600 
128 ACCURACY OF STREAM ME.ASUREMENTB. [No.95. 

Changes -in the ratio T~n : rs ·in 1!ert·icals for chnnge:~ ·in river stage. 

Gage I Distance of vertical from initial point. 

reading. f f I I f --

'~k;; 1 ~:~:·. 1oo0r;c 1~:;"_ ";,.~; :2~ •• ~'-: 2~;;"_ ::~I.~t.: :~::~'·. + . 04 

1

. _ _ _ _ _ _ _ _ _ . 85 . 86 . 80 o. 93 _ 91 0. 84 0. 87 

+ -~ .m -~ .M -~ .w -~ -~ -~ 

+ .rn .00 -~ .M .rn .W .00 -~ .M 

+1.8.5 .83 .91 .88 .75 ---------· ---------- -·-------- -------·--

tt~i !, :~~ J~ J~ :~~ :~~ ..... :~.- :~~ :~~ +2.46 I. .88 .85 .89 .78 .91 9·) .91 

+3.23 .83 .86 9'' .86 ---·------ --·------- .92 .90 

Means .. ~-. 861 ~~------:885 --------:803 ----:920 ~1------:8901 ~ 

a At 175 feet from initial point. 

The slope of the surface from Exchange Street Bridge to \\"' ashingtol! 

Street Bridge was obtained, for different river stages, by measuring 

0 

Fall of surface in feet. from points of known elevaO.Ii 1.o 1 .fi tion on these bridges. These 

data are given in the following table and plotted in fig. 53. 

It is seen -that the slope ina creases more and more slowly -a 1-------+------+-------l..__-i as the surface elevation in-

_.J 

-6 

~7 

creases. 

+ 3 The preceding table shows 

changes in mean velocity in 

1 '~-----+-----+---1-----1 l . d .d . h t' t 1e ratiO .D an In t e ra 10 

Cl) 

T:n: T: in verticals for change-s 

in river stage. The mean value 

t----+-------+--1-------i of ~_vades from 0._58 to 0.67, -4:: 

~ and increases slightly with the 

depth for a given river stage, 

and also increases somewhat 

r---t-----+f------1 as the stage increases. Fig. "1:j 

~~r 52c illustrates this change for ~ the vertical 100 feet fron1 ini0 

A 

tial point. The mean value of 

the ratio v:n : l~ varies from ~---+-----+-----1 0.86 to 0.92 (omitting that for <!> Fall in 1850 -Feet 

- I 

170 feet from initial point), 

and does not change much with 

change of stage. Fig. 52b il-

. lustrates this change for the 

FIG. 53.-Slope of Susquehanna River from Exchan5e • l 1 O f t F' . 5'-). 'l 

Street Bridge to Washington _Street Bridge, Bing- VertiCa 0 ee • Ig · .:Ja 1 -

hamton, N. Y. lustrates the change in mean 

velocity with change in river stage. The velocity is seen to increase 

very rapidly as the stage increases. 
li[URPHY.) OSWEGO RIVER :MEASUREMENTS. 129 

WORK O.N OSWEGO RIVER AT BATTLE ISLAND, NEW YORK. 

Oswego River is formed by Oneida and Seneca rivers in the northern 

part of Onondaga County, N. Y., and flows northwest into Lake 

Ontario. It drains several of the lakes of central New York~ and hence 

is not subject to the ex- Depth in feet. 

tt·eme changes of flow of o o oo 0> ~ t.:. e 

many streams without natural storage. On the other 

hand, there are several 

dams on it where the water :5 

is held back to some extent 

and the flow rendered irregular. The Oswego and 

Syracuse canal takes water 

from it and to a slight extent increases the irregularity of the flow. 

The gaging station is 

located 3 miles above Minetto, N. Y., and 8 n1iles ~ 

from the river's mouth, 

just below a bend of large ~ 

radius. Measurements ~ ~ 

are made from the car sus- ; 

pended from a cable (Pl. g 8 

VI, B). The river bed is ~ 

ro0k except near the ~ 

shores, where it is gravel. 

The cross section is shown 

in fig. 5±. The central 8 

part is triangular, and the 

station being at or just 1:5 

0 

below a bend this shape 

modifies to a marked de- ~ gree the vertical velocity o 

curve near the upper edge 

of the east side. The bed ~ 

rock is smooth, but is 

broken by irregular 

cracks, the edges of which ~ 

are rough. The gage is of 

( 

(( 

\ 

\ 

~ v/ / 

/ ...------

I//,.............. 

~ --

/ ------ .( 

', ': ,,f -

,/ 

/ / ( 

y 

IJ v--

/:/ ~ 

;/ 

---- V> 

c:: ....- ~ 0 

" 

fll 

- " ~ 

g-:.__ 

~ 

~ Q) 

~ 

C) 

C) 

ir 

..... 

-........... 

' 

~ 

the wire-weight type, and 8 . . . i~ on the west bank, 2,900 Fm. 54.-Cross sectwn of Oswego River at cable station. 

feet upstream from the station. A temporary gage was put in at 

the cable, which, with the aid of th{} elevation of a bench mark at the 

IRR 95-04-9 
130 ACCURACY OF STREAM MEASUREMENTS. [NO. 95. 

gage and one at the cable, enabled-fluctuations in the surface elevation 

and the slope of the surface from the gage to the cable to b(} Ineasured. 

Fifteen discharge m'easurements were made here by three methods. 

The results of these are given in the following table: 

Results of discharge measurements at Battle Island, Ne·w York, on Oswego River. 

Surface Mean Date. No. Method. elevatiou Area. Discharge. velocity. cable. 

1901. Feet. Square .feet. Cubic .feet. Feet. 

July 13 1 0.6 depth ••.••••........••••••.•...... 86.12 1,812 5,264 2.92 

Aug. 7 2 V. v. curves .......................... 85.04 1,344 3,224 2.40 Aug. 7 3 0.6 depth ............................. 85.06 1,358 3,235 2.39 

Aug. 27 4 ..... do ................................ 84.99 1,354 3,203 2.37 Aug. 27 5 ..... do ....................... -......... 84.90 1,322 2,938 2.22 Aug. 28 6 ..... do ................................ 85.02 1,363 3,169 2.32 Aug. 28 7 ..... do ...•.••.••.....•......•.•....... 84.96 1,344 3,066 2.28 

1902. 

Mar. 31 8 Harlacher's ..•...•..••.••••.•••...... 90.77 3,491 15,982 4.68 Apr. 1 9 V. v.curve>~ .......................... 90.63 3,440 15,653 4.55 July 8 10 Harlacher's .......................... 87.85 2,421 8,601 3.55 July 8 11 V. v. curve!!! .......................... 87.83 2,414 8,634 3.57 July 9 12 Harlacher's .......................... 87.88 2,431 9,019 3. 71 July 9 13 V. v. curves .............•............ 87.85 2,421 8,585 3.55 Aug. 19 14 Harlacher's ... .................................... 87.00 2,061 6,999 3.40 Aug. 19 15 V. v. curves .......................... 86.88 2,018 6,562 3.25 

Discharge in feet per second. 

3,000 4 5,000 6 7 8 10,000 11 12 13 14 15,000 16 11 92 

..., 91 Q) 

~ 

.E 90 <D 

:0 

0:! 

0 89 ..., 

0:! 

= 0 88 :;:3 

0:! 

.s 

.§ 87 

Q3 

<D 

0 so ~ .... 

::l 

00. 85 

84 

I 

I ~ ~ ~; 

I ----~ .......--

I 

--------

~/ 

- - I ?tJ' IZ ! I l/ 

I / 

_..AS,... I 

~p v / /Afean Velocity n eros~ sect1on 

74 IT J 0 0 v~~ity. :;t 4 

FIG. 55.-Station rating curve for Oswego River at Battle Island, New York. 

These discharges and the corresponding surface elevations are 

plotted in fig. 55. From this curve the following station-rating table 

has been prepared: 
llll'RPHY.] OSWEGO RIVER MEASUREMENTS. 131 

Station-mting table fo·r Oswego Ri-ver, Battle Isla·ml, New York. 

Surface I Surface Dlscha'l<•·l 

Surface 

elevation Discharge. elevation elevation Discharge. 

cable. cable. cable. 

Feet. Cnbiejeet. 

I 

Feet. Culricjeet. Feet. Gnbicjeet. 85.0 3,130 87.0 6,850 89.0 11,380 .1 3,300 .1 7,060 .1 11,620 .2 3,480 

I 

.2 7,270 .2 11,870 .3 3,660 .3 7,480 .3 12,120 .4 3,840 .4 7,690 .4 12,370 .5 4,020 .5 7,910 .5 12,620 .6 4,200 .6 8,130 .6 12,870 • 7 4,380 • 7 8,350 • 7 13,120 .8 4,560 .8 8,570 .8 13,370 .9 4, 740 .9 8, 790 .9 13,630 86.0 4,930 88.0 9,020 90.0 13,890 .1 5,120 .1 9,250 .1 14,150 .2 5,310 .2 9,480 .2 14,410' 

.3 5,500 

I 

.3 9, 710 .3 14,670 

.4 5,690 .4 9,940 .4 14,930 .5 5,880 .5 10,180 .5 15,200 .6 6,070 .6 10,420 .6 15,470 .7 6,260 .7 10,660 . 7 15,740 .8 6,450 .8 10,900 .8 16,010 .9 6,650 .9 11,140 .9 1(),280 

91.0 16,550 

Velocity in feet. 

0 1 2 3 4 5 2 3 4 5 

At 70 reef f"'rom /. P. 

~~ At 100 reef f)-om I. P. _§_i 

90 I I 

I I 

89 

88 

..... 

Cl) 

$ 87 

.s 

Cl) 

:;:; 

o:s 86 <:) 

..... 

o:s 

1=1 

~ 85 ~ Cl) 

Q) 

Q) 

0 

$ 84 ::::s 

U1 

83 

82 

81 

I I 

-- I I I 

I I I 

I I I 

I 

_:1_~ 

I rLf I I _}_ ,/ 

I 

II I I I 

f I I 

I 

I I I I 

I 1 / I I 

r.; I 

/ 

/ v J v /l I? /;; I I I vj VI, I // I 

v// ~ v /. / 

/ / 1/ vh v; I 

I 

/~ v/ v ;L_ 

80 

FIG. 56.-Vertical velocity curves for Oswego River at Battle Jsland, New York. 
132 ACCURACY OF STREAM MEASUREMENTS. [NO. 95. 

The following table prepared from the two preceding oPes shows 

the percentage difference between the measured discharge. and the 

mean discharge or that given by the station rating curve: 

Comparison of measttred and nuan dischm·ge, Os·wego River, Battle Island, New YO'i·k. 

Elevation, Discharge. 

Date. No. surface Discharge difference 

cable. By meas- By curve (M.-C.). 

ure (M.). (C.). 

1901. Feet. Cubic jed. Cubic feet. Cubicjeet. Per cent. July 13 ............................. 1 86.12 5,264 5,158 +106 +2.05 August 7 ........................... 2 85.04 3,224 3,198 + 26 + .80 Do ............................. 3 85.06 3,2.)5 3,232 + 3 + .01 August27 .......................... 4 84.99 3,203 3,113 + 90 +2.89 Do ....•........................ 5 84.90 2,938 3,070 - 32 -1.00 August28 .......................... 6 85.02 3,169 3,164 + 5 + .02 Do ............................. 7 84.96 3,066 3,062 + 4 + .01 

1902. March31. .......................... 8 90.77 16,368 15,929 +439 +2.80 April1 ............................. 9 90.63 15,653 15,551 +102 + .65 JulyS .............................. 10 87.85 8,610 8,680 - 70 - .80 Do ............................. 11 87.83 8,634 8,636 - 2 .00 July9 .............................. 12 87.88 9,019 8, 746 +273 +3.12 Do ....................... 13 87.85 8,585 8,680 - 95 -1.09 July 19 •....................... ~~~:: 14 87.00 6,999 6,8.50 +145 +2.17 Do ............................. 15 86.88 6,562 6,612 - 50 - . 76 

It is seen that the percentage difference, or variation of the measured from the mean discharge, 'i~ sn1all, the largest being ahout 3 per 

cent. The four by Harlacher~s method, Nos. 8, 10, 12, and 1±, are too 

_ large by 2 to 3 per cent, showing that i!or this river, at this particular 

place, the coefficient in the formula Q =c ':E YsF should be-0.83 instead 

of 0.85. It was seen op pages 116, 125 that the extreme variation of the 

measured discharges from the mean discharge is :from -8.3 to +5.1 per 

cent for the Chenango River station, fron1 -5.3 to +2.1 per cent :for the 

Susquehanna. It is from +2.89 to -'1.09 per cent :for Oswego River. 

The per cent variation being a measure of the accuracy, it is clear that 

the discharge measurements at the Oswego River station, where there 

are no obstructions, is more accurate hy several per cent than those at 

the Chenango and Susquehanna river stations. 

Nine sets of vertical velocity curves have been- obtx<tined in 12 verticals in substantially the same way as described on page 117. For the 

higher river stages the current was so swift in the deeper parts of the 

section that the meter was carried several feet downstream when 

the largest sinker that could be managed :from the car was used. The 

position of the meter was obtained :from the length of cable immersed, 

the angle it made with the· vertical, and the distance of the car above 

the water. 

The vertical velocity curves in each vertical are divided into five 

groups, and the mean of each group plotted in figs. 56, 57, and 58. 

Fron1 a study of these sets of vertical velocity curves, and those in fig. 

5±, it is seen that the greatest velocity is at or near the surface, and that 
MURPHY.] OSWEGO RIVER MEASUREMENTS. 133 

near the shore for shallow depths the vertical velocity curve is a nearly 

straight line. As the depth and velocity increase, this line becomes 

more curved and more inclined from the vertical, and the ratio ~ Velocity in feet. 

0 2 3 4 5 2 4 5 6 

-- At 140 reef from I. P .2.- At 180 Feel rrom I. P. _L 

I I 

I 

II I I 

I 

I v I / 2 I 

' -~ I I I/ I 

I 

I I I I I l! 1 I 

90 

89 

88 

87 

86 

I I I / 

I I ~7 

J I 

I I I 

I f I 

77 

7 I 1/ 

1£ I 

/; v I l 

f v IV/; J 

;/ I / v; v /}; v / / 

~I -

~ ! 

81 

80 

79 

78 

FIG. 57.-Vertical velocity curves :!lor Oswego River at Battle Island, New York. 

increases from 0. 55 to 0. 63. The effect of the bed and bend in the 

stream, is very noticeable in the curves at 220 feet from initial point 

in figs. 54 and 58. The stream lines striking the 8teep incline at this 
134 ACCURACY OF STREAM MEASUREMEliTS. (No. 95. 

point are thrown upward, causing '' boiling" of the water and a decrease 

of velocity. A~ the river rises thisphenomenon is less marked. The 

-effect of the bend is further seen in the table on page 136. The ratio f 

s 

is much larger on the concav_e than on the convex part ?f the stream. 

Velocity in feet. 

0 1 2 3 4 1 2 3 4 5 

Af 220 f'eer f'rom 1. P. At 300 reef f'rom I. P. -r-Lp / 90 I 

I 

89 

88 

I 

I 

I I 

I 

87 

-a:l 

~ 

.s 86 Q) 

:a 

o:l 

<:J 

.... 

o:l 

~ 85 0 

<3 

o:l 

I> 

$ 

Q) 84 Q) 

C) 

~ 

::I '"' 00. 

83 

82 

81 

80 

I~ ~~ 

1/ I 

I --71 -;-~ _/jl J / / 

/, 

I // II I ' / / / 

I / I .I 

J I I I// 

I I J 1/ f ~;; 

I I 

I // 

I l I 

FIG. 58.-Vertical velocity curves for Oswego River at Battle Island, New York. 

The shape of the bed has abo a marked effect on the curves for different river stages at 180 :feet. 

The :following table shows the change in mean velocity, the change 

in the ratio ~' and the change in the ratio ~ in verticals :for changes 

in river stage. The mean velocity is seen to increase very rapidly 

with the increase in stage. The ratio of the depth of the thread of 
MURPHY.] OSWEGO RIVER :MEASUREMENTS. 135 

mean velocity to the total depth increases in some verticals, in others 

it decreases; as a rule it increases slightly. The ratio of mean velocity 

Fall of surface in feet. 

0.1 0.2 0.3 0.4 0.5 . 0.6 0.7 0.8 0.9 1.0 

91 

90 

...., 

<l.l 89 .;!l 

.s 

<l.l 

:0 

CIS 88 <:.1 

.... 

CIS 

1=1 

0 

i --

I / 

V£ 

v v 

_V 

v ~ 87 1>-

$ 

<l.l 

Q) 

<:.1 

/ 

CIS v ~ 86 :::1 

00 

85 

84 

v 

:{ Fall in,2930 leet 

FIG. 59.-Slope of surface of Oswego River at Battle Island, New York. 

to velocity 1 foot below the surface increases with the increase in stage, 

and is greater on the concave than on the convex side. 

Data obtained on Oswego River at Battle Island, New York, showing change of mean 

velocity in ur.ticals U'ith change in ri'L·er stages. 

Surface Distances of verticals from initial point. 

Date. elevation 

at cable. 40. 70. 100. 120. 140. 160. 180. 200. 220. 240. 260. 300. 

----------------------- Feet Feet Feet Feet Feet Feet Feet Feet Feet Feet Feet Feet 

per per per per per per per per per per per per 

1901. Feet. sec. sec. sec. sec. sec. sec. sec. sec. sec. sec. sec. sec. 

Aug. 27 ......... 84.95 1.19 1. 79 2.10 2.12 2.43 2.58 2.92 3.01 1.63 1. 93 1.58 

Aug. 28 ......... 85.00 'i.'7i' 2.20 2.14 2.51 2.66 2.97 3.12 1. 70 ........... .. ........ "i.'67 Aug. 7 ......... 85.04 1.28 2.08 2.32 2.57 2. 74 3.01 3.34 1. 76 2.12 2.19 

July 13 ......... 86.07 1. 73 2.60 2.95 3.03 3.23 3.49 2.82 2.90 

1902. Aug. 19 ......... - 86.88 2.22 3.10 3.50 3.34 3.47 3. 70 3.84 3.30 3.91 3.57 3.31 

Aug. 19 ......... 86.95 3.37 3.29 3.30 3.55 3.65 3.92 3.22 .. ....... ........... .............. 

July 8 ......... 87.83 2.49 3.26 3.53 3.80 3.93 3.94 3.~77 4.00 3.90 3.65 

July 9 ......... 87.85 ............. '4.'59' '4.'73' .. ......... ........... ........... . ....... ........... ............ ............ 

Apr. 1. ........ 90.63 ............ .............. 5.07 ........... 4. 79 ............. ........... . ......... ............ .............. 

----------------- --------

Depths .......... 85.00 2.2 2.5 4.0 5.5 8.0 9.4 9.1 7. 7 5.2 2.0 1.9 2.0 
AcCURACY OF S'l'REAM M~ASURE\IENTS. [No. 95. 

Table sho·wing changes in the ratio d: D in tJerticals for changes in rit'er stages. 

Surface Distances of verticals from initial point. elevation ---,---,----;-----,--------,----.---,-----,.----7---------.---

at cable. ~ ~ ~ ~' 140. 160. ~ ~ 220. . 240. j 2t:O. • ~ 

Feet Feet Feet Feet Feet Feet Feet Feet Feet Feet Feet Feet 

per per pe-r per per· per· per per per pe1· per per Feet. sec. Sr~C. sec. sec. sec. sec. sec. sec. sec. sec. se.c. sec. 84.95 0.54 0. 5.'3 0.58 0.60 0.61 0.61 0.64 0.59 0.60 0.50 0.50 0.50 85.00 ................ ............... .52 .55 .60 .65 .64 .60 .61 .. .......... ................ ............... 85.04 .53 .60 . 60 .55 .61 .64 .60 .60 .60 .55 .53 .53 86.07 .55 .56 .63 .60 .64 .66 .60 .60 

86.88 .59 .60 .59 .61 .61 .62 .66 .55 .55 .ti-l .53 86.95 ............. ............. .62 .61 .67 .65 .67 .66 .51 .56 .54 87.83 . 70 .55 .65 .66 . 61 .62 ,55 .57 .63 87.85 ------- ............... .............. ............ ............. ------- .. ............ ------- .............. .66 90.63 .59 .59 ............... .63 .60 .60 .. ............ .58 .............. .58 ------------------------

Means. 58" .572 .59'2 .602 .620 .630 .631 .IHR .51i7 .5!i2 I .580 .554 

Table shmving changes in thP. rat·io Ym : T~ -in vertical.~ for cha·nges -in river stages. 

Surface Distances of verticals from initial point. 

elevationl------,---~------,------;---:--------,-----.-----7--......,-----.,----:---l 

at cable. 40. 70. 100. 120. 140. 160. 180. 200. 220. 240. 260. 300. 

Feet Feet Feet Feet Feet Feet Feet Feet Feet Fefl Fed Feet 

per· per per pa per· per per per per J>er Pf'l' per Feet. sec. sec. sec. sec. sec. sec. sec. sec. sec. sec. sec. sec. 84.95 0. 79 0. 77 0.79 0. 71 0.80 0.82 0.87 0.85 0.99 0.92 0.92 0. 93 85.00 ------- .............. . 76 . 70 .83 .82 .87 .87 ,96 ............. ............. ............ 85.04 .88 .75 .71 .71 .86 .81 ,85 .91 :98 . 9'2 9'' .93 86.07 .83 • 75 . 77 .RO .80 .85 .80 8'' 86.88 .85 .85 .83 . 77 .80 .77 .82 .84 .83 .93 .94 .86 86.95 --:85" ............. .8'2 . 77 . 79 .81 .83 .87 • 78 ............ .............. .. ............. 87.83 8'l .86 .84 8') .8:.! .81 .91 .94 .92 87.85 ............ .............. ............. ".'86" .............. ".'8i" .............. .. ............ ............... 90.63 .85 .82 .............. .............. .89 .............. .85 .. ........... .87 

------------------------

Means . . 840 . 798 • 799 . 753 . 820 . 807 . 840 . 872 . 879 . 906 • 908 . 902 

The surface slope data obtained at this station are given in the followhig table: 

Slope of surface of Oswego River at Battle Island, New York, in a distance of 2,930 

feet, for variation of river stage. 

Date. 

1901. August 26 .............................................. . August 27 .............................................. . Do ................................................. . Do ................................................. . August 28 .••............................................ Do ................................................. . 

190'2. March 31 .............................................. .. Do ................................................. . 

tJI~~~:::::: ::::::::: ~ ~: ::::::: :::::~: :::::::::::.::::::: 

Do ................................................. . July 9 ............ .' .................................... .. Do • . .. . . . . . . .. . .. .. . . . . .. . .. ...................... . August 19 ..................... ~. ~ ..................... .. Do ................................................. . Do ................................................. . 

Elevation surface. 

At gage. At cable. 

Feet. 

q85.16 

84.98 

85.03 

85.03 

84.93 

85.08 

91.71 

91.68 

91.51 

88.44 

88.42 

88.41 

88.37 

87.45 

87.34 

87.35 

Feet. 

a84.87 

84.71 

84.77 

84.75 

84.66 

84.78 

90.77 

90.75 

90.62 

87.85 

87.83 

87.88 

87.85 

86.99 

86.88 

86.88 

Eg- Ec. Mean. 

Foot. Foot. 0.29 

/ 

.27 

.26 0.278 .28 

.27 

.30 

.94 } .93 .92 .89 

.59 ) .59 .557 .53 

.52 

.46 } .46 .463 .47 

a The elevations of bench m~rks at gage and cable were furnished by R. E. Horton. 
MURPHY.] LOW·W .ATER STRE~M MEASUREMENTS. 137 

These data have been combined as shown, giving the fall in the surface in 2,930 feet for four river stage~. These are plotted in fig. 59, 

giving the curve AB. This curve is seen to be concave to the horizontal axis, whereas the slope curves for Chenango and Susquehanna 

rivers, figs. 4:6 and 53, are convex to this axis. 

CONCLUSibNS.a 

In the following statements relative to methods and accuracy of 

current meter work done on a stream at a gaging station it is assumed 

that the. channel is approximately straight, regular in shape, with few 

obstructions, and the bed is such that there are few projections of 

more than 4 inches in height above its -general contour. It is also 

assumed that there is a permanent gage at the station that can be read 

to hundredths of a foot and that is frequently checked by measurement 

from a permanent bench mark. 

(1) The distance of the thread of mean velocity below the surface 

increases with the depth and with the ratio of depth to width. In 

general it varies from about 0.55 to 0.65 of the depth. 

(2) In a br~ad, shallow stream from 3 to 12 inches in depth, and 

having a sand or fine gravel bed, the thread of mean velocity is fron1 

0.50 to 0.55 depth below the surface. The mean velocity in a vertical 

is the half sum of the velocities found by holding the center of the 

meter 0.15 foot below the surface and then 0.15 foot above the bed. 

If the bed is coarse gravel (particles 1 to 2~ inches in diameter) the 

center of the meter should be held 0.15 foot below the surface and 

then from 0.3 to 0.4 foot above the bed. 

(3) In broad streams from 1 to 3 feet in depth, and having gravelly 

beds, the thread of mean velocity it~ from 0.55 to 0.60 of the depth 

below the surface. The single-point1nethod of measuring the velocity, 

holding the center of the meter 0. 58 of the depth below the surface, 

will give good results. 

(4:) In ordinary streams where the depth varies from about 1 to 6 

feet, the thread of mean velocity is about 0. 6 below the surface. 

(5} In the smaller streams (creeks) having a width of from 20 to 40 

feet, the thread of mean velocity is farther below the surface than in 

a broader stream Qf the same depth. 

(H) When the velocity is more than 2 feet per second the center of 

the Price meter should not be held nearer to the surface than 1 foot. 

('7t The top a.nd bottom method (center of meter half a foot below 

the surface and then half a foot above the bed of the stream) gives 

velocity from 2 to 8 per cent or more greater than the mean velocity. 

This method should be used only where the bed is comparatively 

smooth and visible. 

a See also pp. 98, 150, 151, and HiO. 
138 ACCURACY OF STREAM ME.AS UREMENT8. [NO. 95. 

(8) The vertical integration method is rapid, and is a very good 

method to t~se as a check on the single-point method. It gives better 

results than the single-point method at a bendjn a stream, under ice, 

under logs, or where the conditions are poor. 

(9) The single-point method gives satisfactory results where the 

conditions are good, hut the hydrographer must use his judgment as 

to the depth of the thread of mean velocity below the surface, which 

may be from 0.55 to 0.65 of the depth. 

(10) The vertical-velocity-curve method of obtaining mean velocity is 

the most accurate, but requires the longest time to operate it. A few 

vertical velocity curves should be taken at each measurement at characteristic places in the cross section as a check on the results obtained 

by the other method. 

(11) At stations with fairly permanent bed and without obstructions, 

the individual discharge measurements when plotted should not vary 

from the station rating curve by more than 3 to 5 per cent for ordinary river stages. For very low stages it may be 10 per cent, and for 

high water, where the banks overflow, the variation from the mean 

rating curve may be 20 per cent. 

(12) At stations with permanent bed and channel obstructions the 

variation of a plotted discharge from the station rating curve may be 

8 per cent of the discharge for ordinary stages. 

(13) A discharge measurement should never be considered complete 

until some test has been applied to see if it satisfies some criterion of 

accuracy, as those in (11) or (12) or some other, and.if it does not 

satisfy the proper criterion the reason should be sought in the change 

in channel, in gage, or in mistakes. ,· 

(14) For flood measurements and in cases where th~ velocity is so 

great that the meter can not be kept at about 0. 6 depth, the velocity 1 

foot below tbe surface should be obtained and the discharge computed 

from the formula Q= 0 ( V' 8 F'+ V" 8-F"+ .... ) where V'8 , V" 8 , 

. . . . are the velocities 1 foot below the surface; F', F'1

, • • • • are 

the component areas; and 0 a coefficient whose value varies from 0.95 

for deep streams to 0.85 for streams of somewhat less than moderate 

size and depth. An easily recognized mark on· the meter cable will 

facilitate the keeping of the_ meter 1 foot below the surface. 

(15) Discharge should not be measured with a current meter in a 

section where the mean velocity is less than half a foot per second in 

more than 15 per cent of it. usually during low water a section can 

be found within a reasonable distance of the station with· a velocity of 

1 foot or more and with a comparatively smooth bed, to which access 

can be had by wading. 
:M:"EASURlJMENTS iN' TilE SOUTH. 139 

VERTICAL-VELOCITY -CURVE MEASUREMENTS .. 

ON SOUTHERN RIVERS. 

During 1903 a series of 301 vertical-velocity"'curve measurements 

were made on a number of rivers inVirginia, North Carolina, South 

Carolina, and Tennessee, by E. W. Myers and BrentS. Drane, of the 

Survey. In the 1najority of instances these observations were made 

after a gaging of the stream by the six-tenths depth method, the object 

being to get, for that gaging, the coefficient for reducing the velocities 

observed at six-tenths depth to mean velocity. At times, however, 

the entire gaging would be made by taking the vertical velocity 

curved at regular intervals of five or ten feet, across the section. 

In these instances the velocity at six-tenths depth was usually not 

observed. 

The top-and-bottom method was not used. The velocities tabulated 

as observed at surface were really observed at a depth of 0.5 foot 

below the surface, Mr. E. C. Murphy having found in his Cornell 

experiments that the small Price meter does not register. the true 

velocity when run just beneath the surface,· if the velocity is greater 

than about 2 feet per second. Similarly, no readings were taken 

closer than 0. 5 foot from the bottom, this being the distance of the 

center of the meter wheel above the botton1 of the weight. 

With only two exceptions the measurements were made from 

bridges. ~roperly, the meter should be lowered from the downstream 

side of the bridge, and have an additional cable attached to it, running 

down to if from the upstream side of the bridge, thus insuring its 

being lowered vertically in the section. This practice was followed 

at only one- station, at Judson, N. C., on Little Tennessee River. At 

all other stations the meter was swung downstream more or less·by 

the current, and the ~Telocities were not strictly in the vertical plane 

of the section; the slant was so slight, however, a.s not to be of 

material consequence. 

In measuring, the meter was carefully lowered until the middle of 

the meter wheel was just on the water surface. It was then lowered 

0.5 foot and run for fifty seconds. This reading having been recorded, 

it was lowered 0.5 foot, placing it 1 foot below the surface. The meter 

was run here, and in like manner downward in succession, at intervals 

of an amount dependent on the depth and on the time at the disposal 

of the hydrographer, the last reading being taken with the meter weight 

resting on the stream bottom. The meter was then raised until the 

bottom of the weight just touched the water surface, and the distance 

through which it had been raised was carefully measured. This _was 

the slant depth, and was recorded in such a manner as to avoid confusion with the vertical sounding previously made to develop the section. 
140 .ACCURACY OF STREAM MEASUREMENTS. (NO. 95 . 

The field notes of a typical curve are a<:~ follows: 

[Gaging made January 23, 1904, by B.S. Drane, meter No. 349, on Dan River, at Madison, State of 

North Carolina. Gage height: beginning 2.10 feet, ending 2.26 feet, mean 2.18 feet. River rising.) 

Soundings. Observations. 

Total Revolu- Velocity Per cent Distance number 

from Depth of Time in of revo- tions per per of (slant) 

initial Depth. observa- seconds. lutions. second. second. depth. 

point. tions. 

------------------------

{ 

0.5 50 60 1.20 2.&! 17 1.0 50 58 1.16 2. 78 33 460 a3.0 1.5 50 54 1.08 2.59 50 

2.0 50 47 .94 2.27 67 2.5 50 38 • 76 1.83 83 

a Equal slant. 

In computing results, the first step was to express the depths at 

which velocities were observed, as decimal parts of the slant depth. 

This operation was very quickly performed by the help of a slide rule, 

and the decimal fractions entered in the field notebook, each immediately after its 'Telocity. This is indicated as having been done in the 

field notes above. 

The observations were then plotted on cross-section paper, record 

book 9-209 being very convenient for the purpose. Depths were 

plotted as ordinates and velocities as abscissas. A convenient scale is 

4 inches to the total (slant) depth, this being considered as unity, and 

1 inch for each foot per second of velocity. 

A smooth curve was next drawn through the points thus plotted, 

care being taken to give them, as nearly as possible, equal weight, if 

all did not fall on a smooth curve. The abscis~as were read off from 

the drawing, at the surface at each tenth of the distance from top 

to bottom and at the bottom, and set down in order. Thus, from the 

above curve were set down: I 

.s-2.90 

.1-2.90 

.2-2.87 

.3-2.81 

.4-2. 71 

.5-2.58 

.6-2.40 

.7-2.19 

.8-1.93 

.9-1. 64 

b-1. 31 

The mean abscissa, or mean velocity, was then computed from these 

by an expanded form of the prismoidal formula for eleven abscissas, 

as follows: 

· V m=s1u[4(V. 1+ V. 3+ V. 5+ V. 7+ y. 9)+2(V. 2+ V.,+ V. 6+ V.s)+ Vs+ Vb] 
MURPHY.] MEASUREMENTS OF SOUTHERN RIVERS. 141 

Combining the above abscissas according to this formula, gave-

.1-2.90 .2- 2.87 

.3-2.81 .4- 2. 71 

.5- 2.58 .6- 2.40 

.7-2.19 .8- 1. 93 

.9- 1. 64 ---- ---- 12. 12 9.91 

4 2 ----

48.48 

19.82 19.82 

8-2.90 

b- 1. 31 ----

30) 72.51 

2.417=Vw 

The mean velocity for this curve was thus 2.417 feet per second, a 

velocity found to lie on the curve at 0. 59 of the depth from the surface; 

this was marked on the curve in the eross-section book. The velocities 

Vo.6n, V Top, and t (V Top+ V Bottom) were read off from the curve, and the 

:ffi . Vm, Vm, d Vm d COe Clents -V y- an y compute . 0.6 D Top :!1) (T-t-B) 

A notebook was kept for these con1putations in which all data were 

preserved. Above eaeh set of curves was entered the rivei· and :.;tation, 

the date, and the gage height, with the number of the eurrcnt-me~er 

nolebook in which the field notes were to be foutid, and the page of 

thecross-t~13ction book on which the curves were drawn. Similar cross 

referenceE! were entered in the original field notes and in the crosssection bqok, thus making it easy to collect quickly all the information 

and compp.tation of any particular curve. 

In the following tables the general character of the botton1 at eaeh 

point of observation is indicated, as follows: M, mud or soft bottmu; 

S, hard sand bottom; G, gravel bottom; R, smooth rock bottom~ B, 

rough bottom of bowlders. 
142 ACCURACY OF STREAM MEASUREMENTS. [No.95. 

Verticalcelocity meaSU'rements ·in 1903 on rive1·s ·in Jcirginia, North Carol·ina, South Carolina, and Tennessee . 

.ArfOMAI lOX ltiVER,a MATTOAX, VA. 

...... 

al Depth of Coefficient for re- :0 Velocity in feet per second by fol- ducing to mean thread i :§ lowing methods: of mean velocity. velocity. 

a . c-;:1 d> <0 a A· P. a A. P. '0 .0 

Date. ~ ~-s p. 0 0 E@ E 2 .sa E 0 

·~ 00 ""' -;:;. A 'O.ci ...... ...... 'O.s a> ""' a}~ ,.qa> '0+> '0 ,.qa> '0 Q,l,.q C) a>+> ~ 

a~ <l.lo Q,l ~t t2 <ll ,.q ~ ~~ ~ P.A i::;.o t p. ....; C) <:,..)·~ <ll al a> ...... o ""'Q) a> ::I b(J ~ A +>o 

~ ...... ~'0 ~<:) ~'g Q) '00 ~'g <ll ""' ~ ~:~ ""' 1l 1l al a: E a> .0 <D 

~al <D 

~al .:: .:: ,.q C!l A ~ ,:;, 0 0 0 0 H H 0 

------------------------------------ July 25 1.50 100 3.3 2.215 2.260 2.220 2.490 2. 720 1.00 0.89 0.81 2.01 61.0 8. 110 3.3 2.295 2.190 2.290 2.040 2.390 1.00 1.12 .96 1. 97 59.6 s. 115 3.2 2.214 2.190 2.250 2.160 2.330 .98 1.02 .95 2.06 64.5 s. May 21 2.33 90 2.5 .920 .810 .820 .950 1.690 1.12 .97 . 54 1. 32 53.0 s . 100 4.1 2.020 2.070 2.070 1. 980 2.340 .98 1.02 .86 2.58 63.0 s. 110 4.5 2.150 2.370 2.320 1. 920 2.610 .93 1.12 .82 3.15 70.0 s. 130 4.1 1. 760 1. 760 1. 760 1. 380 2.640 1.00 1.27 .67 2.46 60.0 s. Aug. 29 4.62 90 4.9 2.238 2.330 2.260 1.500 2.590 .99 1.49 .86 2.99 61.0 s. ------------------------------- Mean. .......... .......... ------ .. ............. ............... .............. .............. ............... 1.00 1.11 0.81 ------ 61.5 

JAMES RIVER,b CARTERSVILLE, VA. 

May 22 2.42 90 4.4 1. 880 ............. 1.840 1. 760 2.130 1.02 1. 07 0.88 2.53 57.6 s. 200 3.0 2.200 ............. 2.220 1.660 2.470 1.00 1.32 .89 1.83 61.0 s. 350 3.8 2.270 2.370 2.300 2.200 2.580 .99 1. 03 .88 2.36 62.0 8. 500 4.0 1. 960 2.200 1. 930 1. 900 2.370 1.02 1. 03 .83 2.32 58.0 s. 640 3.8 2.370 .............. 2.355 2.340 2.580 1. 01 1.01 .92 2.18 57.5 s. 760 4.0 2.340 2.300 2.350 2.240 2.580 1.00 1.04 .91 2.46 61.5 s. --

~~~ ------ ---------------- M~anl ..... -----·- 1.01 1.08 .88 59.6 

ROANOKE RIVER,c ROANOKE, VA. 

July 20 1. 03 95 3.31 O.R7l 0.810 0.880 0.800 0.840 0.99 1. 09 0. 93 2.05 62.0 s.-

Mny 13 1.40 25 2.4 1.485 1. 530 1.570 1. 660 2.030 .95 .89 . 73 1. 49 62.0 s. 40 2. 9 1. 730 1. 570 1. 730 1.300 2.030 .89 1.33 .85 1. 87 64.5 s. 50 2. 9 1. 346 1. 500 1.275 1.560 2.030 1.06 .86 .66 1. 62 56.0 s. 55 1.8 1. 960 1.820 1.990 2.020 2.130 .98 .97 .92 1.16 64.5 s. 60 3.0- 1.500 1.410 1.450 1.460 2.000 1.03 1.03 .75 1.74 58.0 s. 90 2.5 1. 720 1.860 1.760 1. 700 1.830 .98 1. 01 .99 1.60 64.0 R. 95 1.8 1. 310 1.120 1.270 1.510 1. 930 1.03 .87 .68 1.01 56.0 R. 

-------------------------------

Menu. ------ ------ ............ ........... ............ . ............ .............. .............. .99 1.01 .81 ......... 60.9 

STAUNTON RIVER,d RANDOLPH, VA. 

I 

Aug. 28 3. 61 ::!00 4.2 2.394 2.300 2.450 2. lJlO ,2. "" 0.98 1.12 1.03 2.67 63.5 s. 230 2.8 2. 726 2.990 2.800 2.590 3. 050 .97 1.05 . 89 1. 76 63.0 s . 260 2.0 2.810 2.9'20 '2. &10 2. 770 3. 090 .99 1.01 .91 1.22 61.0 s. 330 2.3 ]. 350 1.600 1.300 1. 430 11. 800 1.04 .94 . 75 1.25 54.5 s . 360 3. 7 2.417 2.630 2.460 2. 290 2.520 .98 1.06 .96 2.29 62.0 G. 390 2.0 2.920 2.920 2.980 2.850 2.850 .98 1.02 1.0'..! 1.34 67.0 G. 

a This station is on the steel deck bridge of the Southern Railway, 27 miles south of Richmond, Va., at Mnttoax station. The right bank is high and steep, but the left bnnk is low, and overflowed by floods. The bottom is firm, of sand nnd gravel. The current is steady at low water and ordinary 

stages, but very irregular in flood stages. bThe station here is on the wooden wagon bridge between Cartersville post-office and Pemberton 

station, on the James River branch of the Chesapeake and Ohio Railroad. There are 6 spans, with n total width of 790 feet at low water. The bottom is remarkably uniform, of sand, gravel, nnd small 

rocks, and the current very regular. · c The old station, where these curves were made, is at the Walnut Street Bridge, on the edge of the 

city of Ronnokt>. The bottom is of rock and sand, very uneven, and the current irregular and shifting. dThis station is on the steel bridge of the Richmond and Danville branch of the Southern Railway, nenr Randolph, Va. At ordinary stages the stream flows under two spans. Floods spread (IUt under 

nll four spans and overflow the left bank; there are two flood channels through the long embank- ment on which the track approaches the bridge, on left bank. The bottom is soft, of silt and fine 

sand along left bank; but becomes firmer toward right bank, of sand and gravel. The current is 

steady and of fairly good velocity at all stages. 
MURPH~.] MEASUREMENTS OF SOUTHERN RrVERS. 143 

Vertical ·velocity measurements -in 1903 on rivers ·in Yirginia, etc.-Continued. 

STAUNTON RIVER, RANDOLPH, VA.-Continued. 

~ - Coeffielentfone-~ Depth of 

Velocity in feet per second by fol- I ducing to mean thread Ei :§ lowing methods: . velocity. of mean 

I 

0 velocity. :g s~ ..... .0 

Date. ~ .§~ dJ <0 s §'s• ~ ~ P.· 

~ 0 'S I> 0 8 E E~ 1:i- -~ p. ..; 

~.9 ~~ .... 0 of::· "" ~ (I) <O+> 'd .St 'd .... 'd ~..c:l 

~ ~ 

]~ t2 ~ e2 ~ <:,>+> 

..c:l c., 

~ I::; A §'~ t t .... ~§' <:,) 

l=l P.:;j ~ ~ 

~ 

~ .... o ~~ 'de, ~'g (I) .@<:.> ~'g ~ .a:: p.'d bll p. "" ""- 15 15 ~ 

~ ~ ~ .0 <0 <0 ..c:l iS 0 i3~ i3~ 1=1 .:1 c.? A p. 0 0 0 0 ~ 0 

--------------------------------- Aug. 8 4.60 200 4.8 2.504 2.390 2.540 2.260 2.330 .99 1.11 1. 07 3.10 64.5 s. 220 4.3 2.849 2.990 2.870 2.660 2. 920 .99 1.07 .98 2.64 61.5 s. 240 3. 7 3.111 3.120 3.210 2. 730 3. 3'20 .97 1.14 • 94 2.48 67.0 s . 340 4. 7 2.802 3.380 2.920 2.250 2.990 .~6 1. 25 • 94 3.08 65.5 s . 370 3.5 1.952 1. 730 2.060 1. 700 1. 930 .95 1.15 1. 01 2.31 66.0 G. 

390 3.8 2. 778 3.290 2.900 1.870 2.990 .96 1.49 . 93 2.47 65.0 G • 

420 4.4 2.103 2.560 2.250 1.830 1. 930 .93 1.15 1.09 3.43 78.0 G. 

June 24 5.28 200 5.2 2.290 2.660 2.370 2.210 2.520 .97 1.04 .91 3.38 65.0 s. 220 5.2 2. 758 2.660 2.810 2.510 2.890 .98 -:..:iO .95 3.35 64.5 s. 240 4.5 2. 725 3.3'20 2.920 2.350 3.320 .93 1.16 .82 2.99 66.5 s. 260 4.1 2.900 3.110 1110 2.610 3.370 .93 1.11 .86 2. 75 67.0 s. 340 6.0 2.822 3.230 070 2.270 2.890 .92 1. 24 . 98 4.44 74.0 s . 380 5.0 2. 750 2.990 .970 2.410 2.680 .93 1.14 1.03 3.55 71.0 G. 

400 6.0 2.692 2.990 2.860 2.460 3.110 .94 1.09 .87 4.05 67.5 G. 

------------------------------- Mean. .......... ............ ------ .............. .............. ............... ............ .. ............. .96 1.12 .95 ............. 65.7 

DAN RIVER,a MADISON, N.C. 

Oct. 1 0.86 510 1.9 0. 734 0. 783 0. 730 0. 751 O.l-180 1.00 0.98 0.83 1.14 -60.0 M. 520 3.8 1.638 1.570 1.620 1.640 1.880 1.01 1.00 .87 2.20 58.0 M. 

560 1.7 1. 777 1.830 1. 730 1. 780 2.220 1.04 1.00 .80 .99 58.0 M. 

uly 18 1.14 455 2. 7 2. 791 .............. 2.880 2.670 2.820 .97 1.05 .99 1.71 63.5 G. 

460 2. 7 2.641 2. 790 2.690 2.400 2. 790 . 98 1.10 .95 1. 67 62.0 G . J 

500 3.0 2.133 2.130 2.120 2.100 2.430 1. 01 !.02 .88 1. 77 59.0 M. 550 2.3 2.312 .............. 2.540 1.510 2.660 .91 1. 53 .87 1.53 66.5 M. J une 18 2.05 450 2.5 2.308 ........... 2.450 2.240 2.940 .94 1.03 . 79 1.60 64.0 -G. 

455 2. 7 2.680 ------- 3.000 2. 770 3.180 .89 .97 .1:14 1.86 69.0 G. 

460 3. 2 2. 741 ............ 2.810 2.630 3.130 .98 1. 04 .88 2.08 65.0 G. 

465 '3.5 2.948 ............ 3.050 2.800 3.080 .97 1.05 .96 2.33 66.5 G. 

470 :,,3.4 2.987 ............ 3.010 2.890 3.300 .99 1.03 .91 2.07 61.0 G. 

475 :'3.5 2.996 .............. 3.000 2.900 3.470 1.00 1.03 .86 2.10 60.0 G. 

480 '3.1 2.881 ............ 2.970 2.800 3.320 .97 1.03 .87 1. 97 63.5 G. 

485 . 2.8 2.645 ............. 2.680 2.630 3.080 .99 1.01 .86 1.71 61.0 G. 

490 3.1 2.664 ............... 2.680 2.610 3.080 .99 1.02 .86 1.89 61.0 G. 

495 3.3 2.642 .............. 2.650 2.620 2. 990 1.00 1.01 .88 2.00 60.5 s. 500 '3.3 2.59'2 ........... 2.570 2.560 2. 940 1.01 1.01 .88 1. 95 59.0 M. 505 I 3.1 2.528 .............. 2.6.')() 2.470 2.990 .95 1.02 .85 2.05 66.0 M. 510 3.2 2.556 ............. 2.680 2.400 3.130 . !15 1.06 .82 2.08 65.0 M . 515 3. 2 2.440 ............. 2.440 2.440 3.030 1.00 1.00 .81 1. 9'2 60.0 M. 520 3. 7 1. 720 ............... 1. 570 2.210 2.560 1.10 • 78 .67 1.96 53.0 M. 545 2.8 1.480 .............. 1.420 1.820 2.180 1.04 .81 .68 1.62 58.0 M. 550 2.5 2.019 ............. 2.000 2.070 2.370 1.01 .98 .85 1.47 59.0 M. 555 1.8 2.100 .............. 2.100 2.190 2.370 1.00 .96 .89 1.08 60.0 M. 

560 1.4 2.086 .............. 2.120 2.180 2.280 .98 .97 .91 .98 64.0 M. 565 1.7 1.806 .............. 1.840 1.900 2.130 .98 .95 .85 1.05 61.5 M. 570 1.6 1. 933 ............. 1. 960 2.020 2. 230 .99 .96 .87 .98 61.5 M. 575 1.8 1.490 1.450 1.570 2.040 1.03 .95 . 73 1.05 58.5 M. 580 1.3 1.2901::::::: 1. 390 1.540 1.570 .93 .84 .82 .86 66.5 M. 585 1. 4 1.600 ....... 1. 750 1.590 1.470 .91 1.01 1.09 .98 70.0 M. ec. 21 2. 0.5 515 3.2 1.859 ....... 1.700 2.000 2.590 1.09 .93 7') 1.68 52.5 s. 55-5 :l.O 2.314 ....... 2.420 2.140 2. 710 .96 1.08 .85 1. 90 6.~. 5 M. 565 2.6 2.5H ....... 2.500 2.610 2.810 1.02 .97 .90 1.38 53.0 M. 575 2.6 2.479 ....... 2.510 2.430 2. 780 .99 1.02 .89 1.61 62.0 M. 

D 

M ay 14 2.07 450 2.4 2.180 ............ 2.180 2.140 2.610 1.00 1.02 .84 1.44 60.0 G. 

460 3.1 2.540 .............. 2.620 2.430 2.900 . 97 1.05 .88 2.00 64.4 G . 

470 3.1 2.800 ............. 2.830 2.830 3.090 .99 .99 .91 1:92 62.0 G. 

490 2. 7 2.750 ............ 2. 780 2.680 3.0'20 .99 1.03 .91 1.69 62.5 G. 

510 3. 7 2.800 ............. 2.830 2.670 .2.880 .99 1.05 .97 2.36 63.7 s. 550 3.0 2.600 ............. 2.610 2.630 2.950 .99 .99 .88 1.86 62.0 M. - 570 2.4 2.466 .............. 2.470 2.460 2. 730 1.00 1.00 .83 1. 44 60.0 M. 

-------------~ ------------

Mean. ........... ............ ........... .............. ------- .............. .............. ............ .99 1.01 .86 ............ 61.6 

-

a This station is on the covered wooden bridge of the Southern Railway, about one-half mile from 1\fadison. At all ordinary stages the river flows under only two spans. The banks are. of loose sand, and the bottom to right of central pier is of coarse, loose sand, subject to change. Under the span to the left of central pier the bottom is hard sand, except for a short section close to the pier. The current is uniform and fairly swift. 
144 AOOURAOY OF STREAM MEASUREMENTS. [NO. 95. 

ratical ·velocity measurements ·in 1903 on r·ivers in Virginia., etc.-Continued. 

DAN RIVER,a SOUTH BOSTON, VA. 

] Coefficient for re- Depth of 

] Velocity in feet per second by fol- ducing to mean thread 

lowing methods: of mean velocity. velocity. 

S..3 '0 t. s P. ..... Date. ~ 8.S <{, 0 A.. P. A.. 0 

""'0 l> ss s 0 .ss B -~ A 00 'd..t:i '0.8 .!::!- '0.8 ~- Q) 

al'"~ o:S~ '!j 

o:S~ '!j Q)~ Q) <:; Q) ..... tE <!) Q) ..... Q) <:.>...., 

~ ~ ..t:l <:;'""' e;g. g.~ e; g.~ t2 l> ~ ~g. ~8 ~ <ll $ bD 0. ~- ~'!j 'de.> ~'g Q) 'de.> <ll'!j ~- ~ o.,'d 

<Z ;S OJ <ll .0 '0 ~d $ '0 .f:l~ ..a ~ .:: (!) A :> 0 0 0 0 o.z 0 H H 

------------------------------

Aug. 27 1. 40 160 5.6 1. 508 1.570 1.600 1.390 1. 670 0. 94 1.08 0.90 3. 75 67.0 

180 5.5 1. 953 1. 930 1.940 1.880 2.260 1.01 1.04 .86 3.25 59.0 280 4. 7 1. 968 1. 910 1.970 1. 900 2.130 1.00 1. 04 g·~ 2.87 61.0 

323 3.5 .952 ........... .960 . 910 1.010 .99 1.05 .94 2.17 62.0 Aug. 8 2.62 275 6.1 2.399 ............. 2.440 2.170 2.520 .98 1.11 .95 3.81 62.5 

300 5. 7 2.021 2.330 2.060 1. 900 2.330 .98 1. 06 . 87 3.59 63.0 520 5.3 1.883 1. 800 1.970 1.640 1.800 .96 1.15 1.05 ,3. 76 71.8 Jun<) 23 3. 71 130 9.0 .900 . 660 .900 • 780 1.140 1.00 1.15 . 79 5.40 60.0 150 8.8 2.065 2.250 2.260 1.850 2.280 .91 1.12 .91 5.85 69.0 180 7.9 2.295 2.420 2.360 2.070 2.660 .97 1.11 .86 5.02 63.5 260 8.1 2.413 2. 710 2.500 2.070 2.850 .97 1.11 .85 5.31 65.5 300 6. 7 2.215 2.280 2.250 2.040 2.610 . 98 1. 09 .85 4.19 62.5 330 5.1 1.510 1.640 1.520 1. 380 1. 590 .99 1. 09 .95 3.09 60.5 ----------

~~~ ------------

Mean. .98 1.09 .90 63.6 

REDDIE RIVER,b NORTH WILKESBORO, N.C. 

July 17 c24.67 45 1.7 1.620 1.600 1.570 1.730 2.060 1.03 0. 94 0. 79 0. 96 56. 5 55 2. 1 2. 010 .. - .. .. 2. 000 2. 040 2. 300 1. uo . 99 . 87 1. 24 59. 0 70 2. 5 1. 640 1. 530 1. 610 1. 670 2. 000 1. 02 . 98 . 82 1. 44 57.5 

Mean. ~ ~ ~-~~~-~-r~~~~ ~ ~ ~ .. . .... 1. o2 -.-97- --_-83- -__ -_-.. -. _5_7 __ 1-

YADKIN RIVER,d NORTH WILKESBORO, N. C. 

0 ct. 3 0.3.~ 8:} 3.511.203 1.160 1.200 1. 210 1.310 1.00 0.99 0. 9212.10 60.0 

90 4.1 1. 372 1. 3.50 1.370 1. 330 1.550 1.00 1. 03 .89 2.46 60.0 

llO 3.4 2.092 2.070 2.070 1. 960 2.360 1. 01 1. 07 .89 2. 01 59.0 

120 3.0 2.242 2.640 2.250 2.120 2.640 1.00 1. 06 .85 11.82 60.5 

130 2.7 2.648 2.190 2.690 2.280 2.190 .98 1.16 1,21 I 1. 7o 63.0 

140 3.0 2.583 2. 740 2.560 2.460 3.880 1.01 1.0.'l .90 1.77 59.0 N ov. 6 0. 71 80 3.8 2.397 2.570 2 . .')50 2.220 2.310 .97 1.08 1.04 2. 77 73.0 

100 .'l.2 2.556 2. 760 2. 700 2.370 2.460 .9.'l 1.08 1.04 3.85 74.0 

130 3.2 2.063 2.220 2.100 1. 930 2.070 .98 1.07 1.00 2.02 63.0 

J uly 16 1.1o 70 4.2 1.514 1.860 1.500 1.160 1. 970 1.01 1. 31 .. 77 2.48 59.0 

80 4.5 2.390 2.540 2.400 2.250 3.320 1.00 1.06 . 72 2. 72 60.5 

90 f•.3 2.680 ------· 2.850 2.320 2. 790 .94 1.16 .96 3.55 67.0 

100 5.4 2.967 3.050 3.0fi0 2.860 3.050 .97 1.04 .97 4.05 75.0 

110 5.3 2.800 3.050 3.040 2.070 2.990 .92 1.35 .94 3.60 68.0 

120 4.3 2.960 2.920 2.990 2. 760 3.180 .99 1. 07 .93 2.62 61.0 

130 3.3 2.530 3.050 2. 780 2.330 2.920 .90 1.09 .87 2.21 67.0 

J une 17 1. 46 70 4.3 1. 787 .............. 1. 710 1.810 2.420 1.04 .99 . 74 2.45 57.0 

75 4.4 2.845 .............. 3.0.."0 2.590 3.180 .93 1.10· .89 3.01 68.5 

8.5 5.5 2.821 .............. 3. 0.50 2.450 3.080 .92 1.15 .92 4.18 76.0 

95 6.0 2. 909 ------- 3.040 2.630 3.180 .96 1.11 .91 4.50 75.0 

105 6.3 2.927 ----·-- 3.050 2.300 2. 750 .93 1. 27 1.06 4.91 78.0 

I 115 6.3 3.162 3.320 3.310 2.880 2.990 .!16 1.10 1.06 4.95 78.5 

125 4.5 3.120 3.230 3.240 3.250 3.230 .96 .96 .97 3.37 75.0 1S.'i- 3.8 2.R76 2. 760 2.810 2.940 3.270 1.02 :98 .8!! 2.00 52.5 

145 4.2 2. 737 3.13() 3.070 2.260 3.370 .89 1. 21 .81 2.90 69.0 

s 

:§ 

0 

.0 

..... 

0 

~ 

2 

<:.> 

<Z 

~ 

<Z 

~ 

0 

s. 

s. 

s. 

s. 

s. 

s . 

s. 

M . R. 

s. 

s. 

s. 

s. 

s. 

s. 

s . 

M. 

M. 

M. 

s. 

s. 

s. 

M. 

M. 

s. 

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M. 

M. 

M. 

s. 

s. 

s. 

M. 

M. 

M. 

M. 

s. 

s. 

s. 

s. 

s. 

a This station is on the steel bridge of the Norfolk and Western Railway. At ordinary stages there is 

only one obstruction in the section-the tubular steel central pier. Floods do not spre~d far on left 

bank, but overflow a wide flood plain on right bank. A portion of a dam washed down from above, 

stranded near left bank about 200 feet above the bridge, makes the current uneven for about .50 feet 

from left bank. The bottom in lee of this obstruction is of soft mud. Elsewhere it is hard, clayey sand. 

bThere is no regular station on this stream, which is a tributary of Yadkin River. The bottom is 

smooth and hard, of sand. c Below bench mark. 

dThis station IS on the lower wagon bridge, crossing the river about 1 mile from Wilkesboro railroad station. At ordinary stageA there is no obstruction in the section, but floods overflow the nght 

bank around a stone J!ier and trestle beats. The current makes a slight a11glt with the bridge, and 

~1~1lt!n\~lsation in it. The bottom is somewhat shifting, of coarse sand, wit some bowlders close 
MURPHY.] MEASUREMENTS OF SOUTHERN RIVERS. 145 

Vertical velocily measttrement.~ in 190.'5 on rivers in r:irginia, etc.-Continued. 

Date. 

I~ I·S 

YADKIN RIVER, NORTH WILKESBORO, N. C.-Continued. 

Velocitv in feet per second by fol- Coefficient for re- " ducing to mean lowing methods: velocity. 

Depth of 

thre.ad 

of mean velocity. 

I E:J...; . o ~ • <0 a A • ...:. d p. • • .... .... ......... ~ 0 0 os .... ~ Od p. 0 I .... ~ ""'8. 00 • .:::. .....0 .s .::: .... E5 .s -;::. ~ .Cil <l) ...... ~ a;~ ~ ~ a;~ a; ~ ~ a;~ a; Q)~ I ~ 

~ ~ ~ .@-13 t ~ ~~ t;2 t ~~ ~:;..8 t t ~ ~ ' ~ 

al ..... <l) Q) ,Q 0:0 .Q~ ,Q 0:0 ,Q~ ,Q ~ ~ ~ ~ ~ ~ t:.S: ~'0 ~ <:;> ~'0 ~ ~ <:;> ~'0 :i: ~ ~'0 I ~ 

---~~~ A :--- o o oal o o oal o ~ ~~ 

June 16 1. 56 70 4. 4 2. 150 . . . . . . . 2. 030 1. 870 2. 930 1. 05 1. 15 o. 73 2. 46 56. 0 M. 80 5. 2 3. 026 3. 320 3. 160 2. 780 3. 230 • 96 1. 09 . 9Jl 3. 69 71. 0 M. 90 6.0 2.767 ....... 3.040 2.190 3.3.20 .91 1.26 .~ 4.41 73.5 M. 100 6. 4 3. 070 .. .. .. . 3. 330 2. 680 3. 270 • 92 1. 15 . 94 4. 58 71. 5 M. 

110 5.9 3.026 ....... 3.350 2.300 3.490 .90 1.32 .87 4.19 71.0 s. 120 5. 8 2. 648 .. • .. .. 2. 700 2. 570 3. 180 . 98 1. 03 • 83 3. 62 62. 5 s. 130 4.5 2. 335 ....... 2.580 1. 900 2.850 . 90 1. 23 .82 3.06 68.0 s. 140 4. 3 2. 990 . .. . . .. 3. 080 2. 870 3. 270 . 97 1. 04 . 91 2. 75 64. 0 s. 

Mean ............. 

1 

....................................... .. .96 1.12 .91 ...... 66.5 

YADKIN RIVER,a SALISBURY, N.C. 

Dec. 17 1.80 120 4.0 0. 780 0.690 0. 760 o.no 1. 020 1.03 1.08 0. 76 2.a2 58.0 s. 140 3. 7 .958 .950 .900 .960 1.090 1.01 1.00 .88 2.18 59.0 s. 160 6.1 1.063 1.190 1.060 1.020 1.350 1.01 1.04 . 79 3.66 60.0 s. June 20 2.57 80 3.1 1. 970 2.000 2.090 1.920 2.180 . 94 1.03 .90 2.05 66.0 s . 110 3.2 1. 700 1.230 1.630 1. 700 2.280 1.04 1.00 .75 1. 78 57.5 s. 200 3.1 2.540 2.800 2.610 2.470 2.760 .97 1.03 .92 2.02 65.0 s. 260 4.3 1.990 1.850 1.830 1. 870 2.890 1.09 1.06 .69 2.37 55.0 s. 360 5.4 2.950 2.850 2.970 2.370 3.320 .99 1.24 .89 3.32 e1.5 s. 380 11.3 3.230 4.180 2.980 3.040 4.650 1.08 1.06 .69 6.10 54.0 s. 420 3.9 2.980 3.130 2.880 2.900 3.660 1.03 1.03 .81 2.16 55.5 s. --------------------------- Mean. ........ .......... ·----- .............. ............ ............ .. ............ .. ............. 1.02 1.06 .81 ------ 59.2 

CATAWBA RIVER,b MORGANTON, N. C. 

- Oct. 28 1.16 50 1.9 1.072 1.040 1.050 1.150 1.310 1.02 0.92 0."82 1.10 58.0 s. 70 3.0 1.029 .980 .970 1.100 1.470 1.06 .94 . 70 1.68 56.0 s. 90 3.5 1.367 1.260 1.330 1.300 1.690 1.03 1.05 .81 2.03 58.0 s. 110 3.2 1.420 1.300 1.390 1.330 1. 740 1.02 1. 07 .82 1.86 58.0· s. 130 2.8 1.636 1.720 1.600 1.600 1. 980 1.02 1.02 .83 1.61 57.5 G. 150 3-.5 1.190 1.130 1.180 1.160 1.450 1. 01 1.03 .82 2.08 59.5 G. 170 3.5 .825 .830 .825 .800 .970 1.00 1.03 .85 2.10 60.0 G. 

Dec. 11 1.20 50 1.8 .851 .690 .810 .910 1.190 1.05 .94 . 72 1.03 57.5 R. 60 2.8 .858 .990 .900 . 830 1.070 .95 1.03 .80 1.85 66.0 R . 70 3.0 1.002 .870 1.040 . 980 1.310 .96 1.02 .76 1.89 63.0 R . 

80 3.3 1.105 1.190 1.100 1.100 1.450 1.00 1.00 . 76 1. 98 60.0 R. 90 3.3 1.293 1.280 1.290 1.220 1.690 1.00 1.06 . 77 1. 98 60.0 R. 100 3.2 1. 351 1.430 1.330 1.360 1. 790 1.02 .99 ". 75 1.86 58.0 s. 110 3.2 1.370 1.160 1.310 1.370 1.930 1.05 1.00 . 71 1. 79 56.0 s. 120 3.0 1.685 1.620 1. 730 1.600 1. 980 .97 1.05 .85 1.89 63.0 s. - 130 3.3 1.651 1.690 1.680 1. 570 1. 930 1:~ 1.05 .86 2.06 62.5 s. 140 3.2 1.489 1.350 1.430 1.450 1.830 1.03 .81 1. 74 54.5 s. 140 3.2 1.394 1.470 1.400 1.360 1.640 1.00 1.02 .85 1.92 60.0 s. .150 3.1 1.193 1.140 1.190 1.190 1.350 1.00 1.00 .88 1.86 60.0 s. 160 3.4 . 786 .830 .830 1. 740 1. 0'20 .95 1.06 . 77 2.23 65.5 s. 160 3.5 . 799 .870 .820 . 770 1.070 .97 1.04 . 75 2.17 62.Q s . 170 3.6 . 742 .790 .770 .740 .920 .96 1.00 .81 2.27 63.0 s. - 180 3.1 • 799 .740 . 760 !140 .830 .98 1.08 .96 1. 9'2 62.0 s. 

a All of :the following curves were made at the Piedmont Fall Bridge, several hun!lred yards above 

the raili:td bridge, wbere the g~e is placed, about 6 miles from Salisbury, N. C. The railroad 

bridge is referab1e for gagings in t1me ot highest floods, which cut around the end of the tall bridge on left nk, but the bottom is rocky and rough, and the current is whirled in all directions by ragged rock ledges just above. For thil'l reason the toll bridge is to be preferred for gaging all 

ordinary stages. At the toll bridge the current is regular at all stages. Tl:ie bottom is sand, except under first span from left bank, where it is rock. 

bThis station is on the Lenoir wagon bridge, 1 mile frorri Morgapton, a one-s~n steel bridge, with wood trestle approach on right bank. The Jeft·bank is a high rock cliff; the nght bank is sand, 

sloping gradually up above flood height. Along the left bank the bottom is rock for a short distance, 

then of coarse sand and gravel, which changes very little. The current is very even and. well distribut~·d across. 

IRR 95--04----10 
146 ACCURACY OF STREAM MEASUREMENTS. [NO, 95, 

Vertical 1.1elocity mea8'tt":ements in 1903 on ri-vers in Virg·inia, etc.-Continued. 

CATAWBA RIVER, MORGANTON, N. C.-Continued. 

~ Coefficient for re- Depth of 

Velocity in .feet per second by fol- ducing to mean tliread 

~ lowing methods: of mean .s velocity. velocity. 

s . 0 

<0 s s .0 

~ 0~ <h A· ci. A. ci. ~ Date. .t·o ~ 0 0 .s~ ~ .s .§. ss 00 I'< 

-o.S .s ~· I'< 

-~ QlA ~·~ -o.d ~~ '0"" '0 ..Q<li '0 Q;>..cl Q) <li..., 2 e2 Q) 

"A~ Q;>"'"" Q) 

..Q ;:;"A <:,) 

.d -~~ ~A A~ ~ ~0 ~ ~ <:,) ~- 1'-<<li I'< Q)::l 1'<.0 I'< Q)<ll d Q) 

~ "A -+->0 Q;>rc;j ~<:,) gs'g Q) -o<:.J gs'g $ ~ A'O I'< 

~ ~'-~- 15 15 d 

;s Q) Q) <0 ~d <C ;3d .!:! .s ..Q 

C!:l A :;;;. 0 0 0 0 0 0 

------------------------------- Aug. 21 1. 76 70 3.8 1. 716 1.440 1. 740 1.460 2.460 0.99 1.18 0. 70 2.34 61.5 R. 120 4.3 2.432 2.390 2.440 2.230 2.520 1.00 1.09 .93 2.64 61.5 s. 170 3.5 1.874 2.160 1. 900 1. 780 2.060 . 99 1. 05 .91 2 17 62.0 s . June 25 1.96 70 4.0 1.861 1. 950 1.870 1.540 2.080 1.00 1.21 .89 2.42 60.5 R. 80 3.9 2.233 1.930 2.220 2.160 2.800 1. 01 1.03 .80 2.32 59.5 R. 100 4.2 2.845 2.950 2.860 2.830 3.130 .99 1.01 .91 2.62 62.5 s. 135 5.0 2.120 2.400 2.160 1.830 2.610 .98 1.16 .81 3.10 62.0 s. 160 4.0 2.048 1.950 2.070 1.900 2.230 .99 1.08 9') 2.50 62.5 s. 180 3.5 1.861 1.830 1. 940 1. 730 2.040 . 96 1.08 .91 2.31 66.0 s . May 5 2.00 50 3.0 2.043 2.410 2.000 2.000 2.510 1. 02 1.02 .81 1. 72 57.5 R. 60 3.8 2.223 2.470 2.a:LO 1.860 2.440 .96 1. 20 .91 2.41 63.5 R. 70 5.0 1.636 1. 960 1. 520 1.690 2.370 1.08 .97 .69 2. 70 54.0 R. 80 3. 7 2.465 1.~30 2.460 2.440 3.120 1.00 1. 01 . 79 2.20 59.5 R. 90 3.9 2.605 2.580 2.620 2.820 3.050 .99 .92 .85 2.36 60.5 R. 125 5.0 2.623 2. 710 2. 760 2.440 2.980 .95 1.08 .88 3.45 69.0 s. 150 5.0 2.601 2. 780 2.620 2.490 2.810 .99 1.04 .93 3.02 60.5 s. ------

~~~ ---------------- Mean. ------~------ -------~------- 1.00 1.04 .82 60.6 

CATAWBA RIVER, MOUNT HOLLY, N. C. (MISCELLANEOUS); BOTTOM MUDDY; CURRENT. 

SLUGGISH. 

Nov. 13 (a) 80 6.3 0.494 0.450 0.470 0.480 0.610 1.05 1.03 0.81 3.34 53.0 M. (a) 180 7.0 .743 .720 .770 .660 .780 .96 1.13 .95 4.48 64.0 M. 

Mean .................................................•.•.. 1.00 1.08 .88 ...... 58.5 

CATAWBA RIVER, BELMONT, N. C. (MISCELLANEOUS); BOTTOM HARD SAND. 

D:~.: .[.(a}.[ .. '::.[ .. ':~. '-~['·em 1.520 1.460 1. .ro 11. 01 ['· ~; 0.80 2.06 59.0 s. ----

......................... -- ---- - 1. 01 1. 05 .80 59.0 

WATEREE (CATAWBA) RIVER,b CAMDEN, S.C. ON TOLL BRIDGE, 3 MILES FROM CAMDEN. 

May 26 8.35 180 12.3 1.430 1.330 1.440 1.340 1.620 1.00 1.07 0.88 7.38 60.0 280 14.2 1.330 1.370 1.270 1.090 1.500 1.04 1.22 .89 7.53 53.0 June 23 10.80 180 1&.4 1. 780 1.830 1. 770 1.590 1.970 1.01 1.12 .90 9.51 58.0 280 17.7 1.835 1.830 1.850 1.670 1.930 .99 1.10 .95 11.06 62.5 

------------------------~-

Mean. .......... .......... ........... .. ...... ......... ............ ........ ......... 1.01 1.13 .90 .. ........ 58.4 

BROAD RIVER,o ALSTON, S. C. 

June 24 6.30 70 6. 1 2. 786 2. 850 2. 830 2. 630 12. 990 ~-0. 98 1. 06 0. 93 3. 87 63. 5 200 6. 2 4. 000 ------- 4. 210 2. 920 4. 500 • 95 1. 37 . 89 4.15 67.0 350 8. 9 3. 479 ------- 3. 630 2. 670 4. 310 • 96 1. 30 . 81 5. 61 63. 0 480 5. 0 3. 929 ------- 4.190 3. 440 4. 240 • 94 1.14 . 93 3. 40 68. 0 

Mean.=~=~~~~~:~~ 1.22 -.--;-= 65.4 

a No gage. 

M. 

M. 

M. 

M. 

M. 

s. 

s. 

s. 

b The section is deep, with mud bottom, and the current very sluggish. c This station is on the bridge of the Southern Railw~ty, at Alston, S. C. The current is steady; the 

!>ottom of fine sand, occasionallr muddr, and sub,ect to slig-ht change. 
-MURPHY.) MEASUREMENTS OF SOUTHERN RIVERS. 

},..ertical·velocity measurements -in 1903 on ?~it,ers in l'"irginia., etc.-Continued. 

Date. 

Sept. 5 1.25 Nov. 26 1.26 

July 3 1. 61 

-- Mean. ............ 

Sept. 4 0.11 July 2 .40 

May 9 1.50 

--

Mean. ............ 

Oct. 15 0.00 

July 1 0.61 

SALUDA RIVER,a WATERLOO, S. C. 

Velocity in feet per second by fol- Coefficientforrelowing methods: ducing to mean velocity. 

WATAUGA RIVER,b ELIZABETHTON, TENN. 

55 4.1 1.012 ~ ........... 1.010 1.020 1.160 1.00 0.99 0.87 30 3.2 .344 0.384 .380 .322 .384 .90 1.07 .90 40 3.3 .422 .480 .470 .380 .500 .90 1.11 .84 65 5.3 .461 .465 .450 .440 .600 1.02 1. 05 . 77 40 3. 7 .266 ............. .290 .210 .280 .92 1. 27 .95 45 3.5 .439 .............. .420 .420 .650 1.05 1.05 .68 55 4.3 .401 .............. .390 .410 .610 1. 03 . 98 .66 155 3.0 .692 ............ .660 .730 .870 1.05 .95 .80 195 3.0 . 702 .............. . 740 .690 . 780 .95 1. 02 .90 210 2.6 .643 .............. .650 . 530 . 790 .99 1. :.!1 .81 ---------------------- ............ ............. .............. ............... .............. .............. ............. .98 1. 07 .82 

SOUTH FORK, HOLSTON RIVER, BLUFF CITY, TENN. 

210 3.1 1.084 ............... 1.080 1.090 1.260 1.00 0.99 0.86 200 1.9 2.628 ............. 2.540 2.920 3.910 1. 35 .90 .67 205 2.4 5.066 .............. 5.010 5.010 6.230 1. 01 1. 01 .81 215 3.6 2.695 .............. 2.880 2.530 2.590 .94 1. 07 1.04 250 2.8 3.366 ............. 3.360 3.150 3.840 1.00 1. 07 .88 255 2.3 2.346 .............. 2.500 1.880 2.520 .94 1. 25 .93 115 2. 7 6. 770 0.890 .770 . 740 1.220 1.00 1.04 .63 120 2.2 1.540 ............. 1.600 1.560 1. 760 .96 . 99 .88 130 2.8 1.650 ............. 1.680 1.630 2.200 .98 1. 01 . 75 140 3. 7 1. 770 ........... 1.830 1. 590 2.340 .97 1.11 . 76 210 3.9 4.860 .............. 4.520 4.980 6.800 1.08 .98 . 70 240 4.1 2.290 ........... 2.220 2.020 3.600 1.03 1.13 .64 250 4.1 4.210 .............. 4.310 4.020 5.090 .98 1.05 .83 

--- ------------------

............. .......... .............. .............. ............... ------- -------11.02 1.05 .80 

NOLICHUCKY RIVER,c GREENEVILLE, TENN. 

100 1.6 0.935 0.870 0.900 1.010 1.210 1.04 0.93 0. 77 120 1.6 . 775 . 720 . 730 .840 1.160 1.06 .82 .67 140 1.8 .903 . 970 .900 .900 1.020 1.00 1.00 .39 170 2.3 .487 .450 .480 .540 .690 1.02 .90 .71 230 3.8 .627 .610 .640 .610 . 760 1.00 1.03 .82 260 3. 7 . 743 . 770 . 750 .710 .970 .99 1.05 . 71 100 2.2 1.663 ........ 1.650 1.640 2.000 1.01 1.01 .83 120 2.4 1.536 1.400 1.510 1.540 2.000 1.02 1.00 . 77 140 2.5 1.416 1.340 1.400 1.400 1. 730 1.00 1. 01 .82 

Depth of thread 

of mean velocity. 

2.46 60.0 2.18 68.0 2.24 68.0 3.05 57.5 2.40 65.0 2.40 57.0 2.54 59.0 1. 57 52.5 2.01 67.0 1.56 60.0 

----

.. .......... 61.4 

1.86 60.0 1.10 58.0 1.39 58.0 2. 77 77.0 1. 68 60.0 1.52 66.0 1.62 60.0 1.43 65.0 1.71 61.0 4.60 63.0 2.07 53.0 2.38 58.0 2.54 62.0 

----

.. .......... 61.6 

0.90 56.0 .90 57.0 1.08 60.0 1.06 59.0 2.36 62.0 2.28 61.5 1.30 59.0 1.42 59.0 1.46 58.5 

147 

R. 

s. 

s. 

8 

B • 

s . 

s . 

s . 

s . 

G . 

R . 

B . 

B . 

B . 

B . 

B . 

B. 

B . 

B. 

B. 

B. 

B. 

B. 

B. 

B. 

B . 

B. 

B. 

B. 

B. 

B . 

B. 

a'!lhis station is on the bridge of the Charleston and Western Carolina Railroad, 10 miles north of Greenwood, S.C., and is best reached by driving from Greenwood. The current is regular; the bottom sandy and somewhat shifting. bThis station is on the bridge of the Virginia and Southwestern Railway, at Siam station, 3 miles from Elizabethton, Tenn. The bottom ~s of fine sand and gravel, with a shoal of small rocks in mid stream. The current is Rmall at low water. cThis station is at Jones's Bridge, a two-span steel wagon bridge, 6 miles from Greeneville. The banks are steep and high: the left bank is never overflowed, and the right only by the highest floods. The current is even ttnd fairly swift, The bottom is of smooth rock and small rounded stones. 
148 ACCURACY OF STREAM MEASUREMENTS. [NO. 95. 

Vert·ica.l1'elocity measurements in 1903 on rivers ·in ri·rginia, etc.-Continued. 

NOLICHUCKY RIVER, GREENEVILLE, TENN.-Continued. 

~ Coefficient for re- Depth of 

Velocity in feet per second by fol- ducingto mean thread a .::! lowing methods: of mean velocity. velocity. ~ a . 0 

0~ <h <0 a A. ci. @ P.. ci. ..... .0 

Date. .:E ~-o ~ 0 0 .sa .£ .sa .8 0 '0 "" "" ~- -~ A l1l <C.ci ~a) 0 ..... 'C.£ '0 Q) "" ~E 'C ... '0 .d<l) Q) <:) .., .... .... t ~.s ~ 

~.8 Q)- ~t Q)b Q) ..; .d t ~p, 1>- t.o ~ ~e <:) >=l ~$ ""Q) A~ "" Q)::l "" .., o:! Q) 

~ ~'0 ~C) ~'0 Q) '0<:,) ~'8 ~ $ p,'C "" 0/) 2.l o:! o:! iS Q) .., .0 <0 .o>=l <0 

bo:! .0 .:1 .:1 .d C."l A >- 0 0 oo:S 0 0 0 0 -------------------------------

July 1 0.61 160 2.5 2.143 1.070 1.110 1.160 1. 370 1.17 1.12 0.82 1. 45 58.0 B. 220 4.4 1.826 ............ .850 .670 1. 200 .98 1. 24 .69 2. 73 62.0 B. 250 4.3 1.138 ........... 1.240 .970 1.400 9') 1.17 . 81 2. 92 6~.0 B. May 7 1.48 80 2.9 1. 620 ......... 1. 610 1.610 1. 790 1. 01 1. 01 9'' 1.71 59.0 B. 100 3.1 2.680 2.640 2. 720 2.640 3.150 .98 1.02 .85 1.89 61.0 B. 120 3.2 2.690 2.510 2. 720 2. 770 3.190 .99 . 97 .84 1. 95 61.0 B . 140 3.3 2.550 2.640 2.640 2.57(}1 2.850 .97 .99 .89 2.18 66.0 B. 160 3.4 2.160 2.100 2.100 2.100 2.580 1. 03 1.03 .8-l 1. 94 57.0 B. 180 4.5 1. 650 ................. 1.520 1.670 2.240 1.09 .99 . 74 2.43 54.0 B. 220 4. 7 1. 700 .............. 1. 520 1. 770 2.370 1.11 .96 . 72 2.35 50.0 B . 240 5.1 ,2. 200 ....... 2.110 2.100 2.640 1.04 1.05 .83 2.86 56.0 B. 270 4.6 2. 460 ....... 2.460 2.170 2.8110 1.00 1.13 .86 2. 76 60.0 B. 290 --=-=-- 2.070 ...... 11970 2.000 2. 7il0 1.05 1.04 . 74 2. 74 56.0 B . 

Mean.=t= 

-------------- --

----.. 1------- ........................... 1.02 1. 0'2 .80 ------ 59.1 

FRENCH BROAD RIVER,a OLDTOWN (NEWPORT). TENN. 

Oct. 14 1. 31 270 7.3 0.894 ................... 0.890 0.900 1.110 1. {)() I 0. "'I 0. 81 4.34 59,.5 s. 300 5.3 . 787 ·------ . 780 . 760 .950 1. 01 1. 04 . 83 3.13 59.0 s. 410 5.4 . 742 ............... .750 .690 .860 .99 1.08 .86 3.27 60.5 s. 440 4.2 .527 0.550 .520 .570 .690 1. 01 . 92 . 76 2.110 59.5 s. June 30 2.29 40 5.3 1.233 1. 340 1. 240 1.110 1.340 .99 1.11 .92 3.19 60.2 s. 140 5.3 2.116 2.260 2.190 1. 9'20 2.360 . 97 1.10 .90 3.52 66.5 s. 205 6.2 2.178 ............. 2.170 2.060 2.590 1.00 1. 06 .8-1 3.!19 59.5 s. 280 8.0 1. 933 ------- 2.000 1.570 1. 930 .97 1.23 1.00 5.20 65.0 s. 420 6.0 1.842 ------- 1.880 1. 740 2.130 .98 1.06 .86 3.87 64.5 s. --------------------------

Mean. ------ ............ ........... ------- -----·- .................... ------- ------- .99 1.07 .86 .............. 61.6 

PIGEON RIVER,b NEWPORT, TENN. 

Nov. 20 1.10 90 4.4 0.827 0.810 0.820 0.800 0.950 1.01 1.03 0.87 2. 77 63.0 s. June 30 1.51 30 6.9 .823 .860 . 730 .860 .96 1.13 .96 4.31 62.5 M. 40 11.6 .847 . 780 .850 .650 .910 1.00 1.30 .93 7.02 60.5 M. 60 10.1 1.142 .940 1.130 .990 1.320 1.01 1.15 . 87 5. 96 59.0 M . 

Mean ....... ----------------------------------------------- .99 1.15 .91 -----· 61.2 

TUCKASEGEE RIVER,c BRYSON, N.C. 

Oct. 9 1.16 30 5. 7 0.496 -----·- 0.510 0.560 o. 740 0.97 0.89 0.67. 3.53 62.0 M. 40 5.6 .547 ............. .600 .520 .500 .91 1.05 1.09 3.92 70.0 M. 60 4.6 .833 .830 .830 1.020 1.00 1.00 • 82 2. 76 60.0 M . June 26 }1. 70 { 20 3.5 .673 0.690 .690 .670 .870 .98 1.00 . 77 2.20 63.0 M. June 27 2.') 5.1 . 763 ............. . 770 .810 1.000 .99 .94 . 76 3.22 62.0 M. 30 6.0 1. 093 1.230 1.190 .990 1.100 .92 1.10 .99 4.32 72.0 M. 35 6. 3 1. 231 ............... 1.270 1.170 1. 350 . 97 1.05 . 91 4.47 71.0 M . 40 6.0 1.211 1. 230 1.300 1.050 1.050 .93 1.15 1.15 4.53 75.5 M. 45 6.1 1.039 .............. 1.150 .850 .900 .90 1.22 1.09 4.58 75.0 M. 50 6.3 1.010 ............. 1.020 .960 1.100 .99 1.05 . 92 3.94 62.5 .M . 55 6.4 1.198 .............. 1.186 1.170 1.330 1.00 1.02 .90 4.00 62.5 M. 

a This station is on the Oldtown_steel wagon bridge, 3 miles from Newport, Tenn. The banks are high and not overflowed. The current is regular. The bottom is of fine sand and shifts slightly. 

bThis station is on the wagon bridge, 1 mile east of Newport. The section is bad, being deep, with 

shallow water above and below. The bottom is mud, changing constantly. The current is sluggish. cThis station is on the highway bridge in the town oi' Bryson. The bottom is soft, and changes 

slightly. But for one old pier, tb,e section is very smooth. The current is of fair velocity, except near right bank, where it is quite sluggish at low water. There is a decided pulse in current. 
MURPHY.) MEASUREMENTS OF SOUTHERN RIVERS. 149 

Vertical1'elocity mea8urements in 1903 on rivers in Virginia, etc.-Continued. 

TUCKASEGEE RIVER, BRYSON, N. C.-Continued. 

"; Coefficient for re- Depth of 

:§ Velocity in feet per second by fol- ducing to mean thread 

lowing methods: velocity. velocity. 

of mean ~ ~ 

S...; 0 

<0 J. A. s A. ..0 

Date. 01=! d> A· A· ~ ..... :c; ........ 0 .8@ ..... 0 ~ .8-S .8 ~' .8 "E· 0 

.~ A rii -o.d -r;;.S ... Q) ~·~ ..c:<l> '0"'"' '0 .Q<l.i '0 Q>..C: Q) ~ '-' Q)-l-' ....,~ ~<:) Q) At t2 Q) '-' .... .Q .d ., .... ~A A ... t ~ ...., fil~ '-' 1=1 '-''"" ... <1.> Q)~ ... .o Cll::l ... C1l "' C1l 

~ A t$ ~'0 -r;;<:.> %'g ~ '00 <l.i'!j $ $ A'O ... 0() 8§ "' "' iS Q) Q) ..0 <0 ;§"' ..0 <0 1=1 1=1 .Q (;!l A :>- 0 0 0 0 0 1-1 1-1 0 --------------------------------~ 

J une 27 60 5.8 1.591 1.710 1. 720 1.380 1.660 0.92 1.15 0.96 4.20 72.5 M. 65 5.6 1.611 1. 710 1. 710 1.430 1. 760 .94 1.13 .92 3.95 70.5 M. 70 5.3 1. 6R4 ............. 1. 666 1.620 2.040 1.01 1.04 .83 3.07 58.0 M. 75 4.9 1.836 .............. 1.820 1. 770 2.080 1.01 1.04 .88 2.82 57.5 M. 80 4.3 1. 902 1.880 1.940 1. 750 2.020 .98 1.09 .94 2.80 65.0 M. 85 4.0 1.670 1.520 1.650 1.690 2.040 1.01 .99 .82 2.34 58.5 M. 90 4.0 1.828 1.810 1.830 1. 780 2.130 1.00 1.03 .86 2.40 60.0 M. 95 4.6 1.645 ............ , .. 1.640 1.660 1.850 1.00 .99 .89 2.40 60.0 M. 100 4.5 1.873 .............. 1.890 1. 780 2.320 -.99 1.05 .81 2. 79 62.0 M. 105 4.6 1.850 .............. 1.850 1. 910 2.000 1.00 I . 97 .92 2. 76 60.0 M. 110 4.9 2.044 .............. 2.040 1. 970 2.280 1.00 1. 04 .90 2.94 60.0 M. 115 5.5 1. 743 2.000 1.810 l.il90 1. 950 . 96 1.10 .89 3.58 65.0 M. 120 5.0 1.826 .............. 1.860 1.570 2.080 . 98 1.16 .88 3.12 .62.5 M . 130 5.5 1. 678 .............. 1.640 1.570 2.230 1.02 1.07 . 75 3.14 57.0 M. 

pr. 25 2. 70 30 6.8 2.040 2.020 2.100 1. 750 1. 970 .97 1.17 1.01 e.iO 25.0 } M. 4.28 63.0 40 6.9 1. 970 ............... 1. 970 1. 790 1.970 1.00 1.10 1.00 4.14 60.0 M. 

A 

50 7.1 1. 730 .............. 1.840 1.420 1.630 .94 1.22 1.06 4.34 67.0 M. 

60 7.1 2.210 2.460 1.800 1. 760 .90 1.23 1.26 r 17.0 .............. }M. 5.25 74.0 

70 7.4 2.910 3.220 2.200 2.640 .90 1.32 1.1Q .30 4.0 ............... } M. 5.18 70.0 80 7.8 3.390 3.430 3.450 3.070 3.600 .98 1.10 .94 4.88 62.5 M. 100 8.5 3.200 3.220 3.240 2.830 3.460 .99 1.13 .92 5.27 62.0 M. 110 7.9 3.010 .............. 3.080 2.640 2.980 .98 1.14 1.01 5.06 64.0 M. 130 6.4 3.140 .............. 3.120 2.810 3.490 1.00 1.12 .90 3. 71 58.0 M. 150 6.3 2.830 .............. 2.880 2.480 2. 780 .98 1.14 1.02 3.97 63.0 M. 170 6.4 1.430 .............. 1.500 1.180 1.420 .95 1. 21 1.01 4.16 65.0 M. ------------------

1.09~1= -- Mean. ....................... .97 64.2 

LITTLE TENNESSEE RIVER,ct JUDSON, N.C. 

Apr. 27 4.25 580 4.2 5.380 5.640 5. 700 4. 950 6. 770 ··"I'"' 0. 78 2.81 67.0 B. 595 3.6 6.120 ............. 5. 950 6.200 7.330 1.03 .99 .83 1.98 55.0 B. 615 4.0 7.450 7.080 7.500 7.210 8. 210 .99 1.03 .91 2.48 62.0 B. 637 5.0 7.280 7.800 7.900 6.480 8. 270 . 92 1.12 .88 3.35 67.0 B. 645 6.0 6.010 4.340 4.500 4.690 8.470 1.34 1.28 . 71 3.18 53.0 B . 

June 28 3.56 520 2. 7 3.840 ........... 3.700 3. 760 5.000 1.04 1.02 . 77 1.55 57.5 B . 530 3.8 5. 235 ------- 5.150 5.180 5. 790 ............. 1.01 .90 2.13 56.0 B. 580 3.4 4. 913 ·------ 4.800 4.810 5.630 1.02 1.02 . 87 ]. 92 56.5 B . 

595 3.3 5.430 ------- 5.260 5.460 6.280 1.03 .99 .86 1. 75 53.0 B. 605 3. 9 5.520 ------- 2.530 5.360 6.070 1. 00 1.03 .91 2.36 60.5 R 645 I 3. 7 5.040 ............... 4.900 4.660 6. 720 1.03 1.08 . 75 2.15 58.0 B. 

=:= -----------------~ --

Mean. ------ 1.03 1.06 .83 58.7 

a This station is on the wooden bridge of the Southern Railway, about one-third of a mile*om 

Welch (flag station) or Judson P. 0., N. C. The current is steady and swift; the bottom is of b wlders, from 3 inches to about 18 inches in diameter, and does not change. High floods overfio the 

thickly wooded left bank, but probably a very small part of the c'Urrent passes through. The right bank is steep and high. · 
150 ACCURACY OF STREAM MEASUREMENTS. (NO. 95, 

Vertical ~'elocity measurements in 1903 on T'ivers in Virg{nia, etc.-Continued. 

SUMMARY. 

Coefficient for reducing to mean Per cent velocity the velocities observed of depth 

Num.- at following points: at which 

River and station. berof thread of curves. Six-tenths Top and mean 

depth. bottom Top. velocity is 

(mean of). found. 

Appomattox, Mattoax, Va ................... 8 1.00 1.11 0.81' 61.5 James, Cartersville, Va ....................... 6 1.01 1.08 .88 59.6 Roanoke, Roanoke, Va ....................... 8 .99 1.01 .81 60.9 Staunton, Randolph, Va ....................• 20 .96 1.12 .95 65.7 Dan, Madison, N.C .......................... 42 .99 1. 01 .86 61.6 Dan, South Boston, Va ....................... 13 .98 1.09 .90 63.6 Reddie, North Wilkesboro, N.C .............. 3 1.02 .97 .83 57.7 Yadkin, North Wilkesboro, N. C .............. 33 .96 1.12 .91 66.5 Yadkin, Salisbury, N. C ...................... 10 1.02 1.06 .81 59.2 Catawba, Morganton, N. C ................... 39 1.00 1.04 .82 60.6 Catawba, Mount Holly, N.C ..... ~ ............ 2 1.00 1.08 .88 58.5 Catawba, Belmont, N. C, ..................... 1 1.01 1.05 .80 59.0 Wateree, Camden, S. C ....................... 4 1. 01 1.13 .90 58.4 Broad, Alston, S. C ...........••.............. 4 .96 1.22 .89 65.4 Saluda, Waterloo, S. C ....................... 3 .97 1.03 .82 62.2 Watauga, Elizabethton, Tenn ................ 10 .98 1.07 .82 61.4 South Fork Holston, Bluff City, Term •....... 13 1.02 1.05 .80 61.6 Nolichucky, Greeneville, Tenn .............. 22 1.02 1.02 .80 59.1 French Broad, Oldtown, Tenn ............... 9 .99 1.07 .86 61.6 Pigeon, Newport, Tenn ...................... 4 .99 1.15 .91 61.2 T~ckasegee, Bryson City, N.C ............... 36 .97 1.09 .93 64.2 

Little Tennessee, Judson, N.C ............... 11 1.03 1.06 .83 58.7 

For all the above curves ............... 301 1.00 1.07 .86 61.3 

MEASUREMENTS ON STREAMS IN THE CATSKILL MOUNTAINS. 

The results in the following tables were deduced from 378 measurements, taken in the Catskill Mountains in 1902-3·, ct at the time of regular gagings of the rivers, and with the same degree of accuracy with 

which the current-meter measurements were made. A small Price 

current meter was used, being held so that velocities were obtained 

at various points in regular order vertically, usuall.v at intervals of 

from one-half to 1 foot. The meter in 1nost cases hung freely in the 

water, but where the current was swift and tended to swing it out of 

the vertical, it was lowered from the downstrean1 side of the briuge 

and stayed by means of a wire from the upstream side, being thus 

kept in the vertieal plane. 

The meter was held fifty seeonds at each point to determine the 

veloeity, and in eaeh case the fir!';t reading was checked by a second. 

The re~mlts were plotted upon cross-seetion paper, the depth:; as ordinateH and the veloeities as ab:;eissas, and a smooth curve drawn through 

the points. The mean veloeity was then obtained by taking 10 velocities from the curve at distances of one-tenth the total depth apart and 

dividing their sum by ten. The velocities were taken at points 0.05, 

0.15, 0.25, etc.-0.95 of the total depth on the curve. 

A study of the tables for each river will explain itself. The first 

colnnin gives the date on whieh the observations were made; the second, 

a Results previous to this time are found in Water Sup. and Irr, Paper No. 76, U.S. Geol. Survey, 1903. 
MURPHY.) MEASUREMENTS IN THE OA.TSKILLS. 151 

the gage height at time of gaging; the third, the distance from the 

initial point (this bei~g pe~·manently marked on the bridge); the fourth, 

the depth of water at the ~neasuring point; the fifth, the mean velocity 

in feet per second as obtained from the vertical velocity curves as 

previously shown; the sixth, the velocities at lo depth ~s scaled from 

the velocity curves; the seventh, the velocities at about 0.5 foot below 

the surface; the eighth and the ninth, the coefficients to be applied to 

the velocity columns marked "Six-tenths." and "Top,'' respectively, 

to reduce them to mean velocity; the tenth, the depth of thread of 

mean velocity in per cent of total depth as measured from the surface 

of the water; the last, the character of the bed of the stream at the 

point of observation. 

The summary explains itself. It shows that the mean velocity of 

378 determinations is found practically at a depth of 0. 60 of the total 

depth, and that the velocity at this depth is well within a permissible 

error, whether obtained from the curve or from actual observation. 

It appears from a study of these vertical velocity curves (1) that a 

rough hed causes a drag at the lower end of the vertical velocity curve 

and tends to raise the point of mean velocity in the secti~n, so that a 

measurement at 0.6 depth would be too small; (2) that, vice versa, a 

smooth bed tends to make the measurement at 0.60 depth too large; (3) 

that the depth of a river has·a marked effect on the point of mean 

velocity, this point in a shallow river approaching 0.55 depth, and in 

a deeper one approaching 0.65 depth; (4) that in general the error 

in using the 0.60-depth 1nethod is well within the limit of accuracy 

in stream-gaging ~ork. 

In the following tables G "indicates gravel; S, sand or silt; R, smooth 

rock; B, bowlders; *that the actual l 0 -measured velocity coincides 

with that taken from the curve. 

Vertical ·velocity mea8'ltrements on ri·vers in the Catskill Mountains. 

CATSKILL CREEK, SOUTH CAIRO, N.Y. 

Velocity in feet per I Coefficients for Depth second by following reducing to of Dis- Depth methods: mean velocity: thread CharacGage tance at of mean ter of Date. from me as- veloci- height. initial uring Verti- ty (in bed of Six- Six- stream. point. point. calve- tenths. Top. tenths. '.fop. percent 

locity. of depth). ------------------

Feet. Feet. Feet. Feet. 

September 5, 1902 ..•. 2. 79 50.0 2.1 0.27 0.26 0.32 1.04 0.84 55.0 G. August 27, 1902 ....... 2. 74 31.5 2.2 *.56 *.56 .62 1.00 .90 60.0 R. 

September 5, 1902 .... 2. 79 31.5 2.3 .63 .62 .72 1. 0'2 .87 55.0 R. 

August 27, 190~ ...•... 2. 74 29.0 2.5 .45 *.40 .62 1.12 . 73 48.0 B. 

September 5, 1!J02 .... 2. 79 29.0 2.5 .53 .52 .69 1.02 . 77 60.0 B . Do ............... 2. 79 25.0 2.6 .34 .31 .43 1.09 . 79 55.0 B. 

August 27, 1902 ....... 2. 74 25.0 2. 7 .30 *.30 .37 1.00 .81 60.0 B. 

September 22, 1902 ... 3.32 50.0 2. 7 . 72 .65 .94 1.11 . 77 50.0 G . August 13, 1902 ....... 3.49 50.0 2.9 .80 *· 75 1.0'..! 1.07 .78 52.0 G. Do ............... 3.49 30.0 2.9 .99 1.00 1.17 .99 .85 60.0 Small B. August 12, 1903 ....... 2.99 50.0 3.0 . 77 . 75 .92 1.03 .84 57.0 R. 

August 27, 1902 ....... 2. 74 45.0 3.2 .40 .40 .41 1.00 .97 60.0 R. 

September 22, 1902 .•• 3.32 25.0 3.2 .83 .83 .88 1.00 .94 60.0 Small B. 
152 .A00URAOY 0~, STREAM MEASUREMENTS. [NO. 95 . 

Vertical11elocity measurements on rivers in the Catsl.:ill Mountains-Continued. 

CATSKILL CREEK, SOUTH C.<\.IRO, N. Y.-Continued. 

Date. 

Velocity in feet per second by following 

Dis- Depth methods~ 

Gage \~: m:!sheight. initial uring Verti- · Sixpoint. point. cal ve- tenths. Top. locity. 

Coefficients for Depth 

reducing to of mean velocity: thread 

ofmean Charac- veloci- ter of 

Six- ty (in bed of tenths. Tpp. pergfnt stream. 

_ depth). 

--------1----------------------------

August 13, 1902 ...... . September 5, 1902 ... . October 10, 1902 ..... . August27, 190'.! ...... . September 5, 1902 ... . September 12, 1903 .. . Do ............•.. October 10, l!.l02 ..... . August 27, 1902 ...... . October 10, 1902 ..... . Aprilll, 1902 ........ . Mayl0,1902 ........•. August 13, 1902 ....••• September 22, 1902 ... October 10, 1902 •...•. Do ............. .. September 9, 1902 ... . July 9, 1902 .......... . August 13, 1902 ...... . September 5, 1902 ... . September 22, 1902 ..• August 12, 1903 ...... . April 11, 1902., ...... . May 10, 1902 ......... . October 10, 1902 ..... . September 22, 190'.2 .. . April 22, 1902 ........ . August 13, 1902 ...... . October 10, 1902 ..... . August 2, 1902 ....... . October 10, 1902 ..... . August 2, 1902 ....... . Aprilll, 190'2 .•....... Do ............. .. 

Feet. 

3.49 

2. 79 3.96 

2. 74 2. 79 2.99 

2.99 

3.96 

2.U 

3.96 

6.S6 

3.47 

3.d9 

3.32 

3.96 

3.96 

3.31 

3.36 

3.49 

2. 79 3.32 

2.99 

6.86 

3.47 

3.96 

3.32 

4.06 

3.49 

3.96 

5.36 

3.96 

5.36 

6.86 

6.86 

Feet. 

25,0 

45.0 

30.0 

40.0 

40.0 

45.0 

40.0 

60.0 

35.0 

5.'>. 0 90.0 

45.0 

45.0 

45.0 

25.0 

50.0 

40.0 

40.0 

40.0 

35.0 

40.0 

35.0 

70.0 

35.0 

45.0 

35.0 

40.0 

35.0 

40.0 

30.0 

35.0 

40.0 

30.0 

50.0 

Feet. 

3.3 

3.3 

3.4 

3.5 

3.6 

3.6 

3. 7 3.8 

3.9 

3.9 

4.0 

4.0 

4.0 

4.0 

4.0 

4.1 

4.1 

4.2 

4.2 

4.2 

4.2 

4.2 

4.6 

4.6 

4.6 

4. 7 4.8 

4.9 

4.9 

fi.2 

5.4 

6.1 

6.6 

7.0 

0.83 

. 51 1.08 

.6.'> 

. 72 

.81 

. 78 1. 08 

.43 

1.12 

3. 91 

.95 

1.00 

.93 

,83 

1.18 

1.00 

1.09 

1.17 

.53 

1.14 

.45 

3. 76 

.93 

1.19 

.9'2 

1. 79 

.99 

1.14 

2.49 

.98 

3.09 

3.08 

3.56 

0.84 

.50 

1.10 

.65 

.70 

.80 

. 77 1.08 

*.43 

1.08 

3. 90 

.93 

.93 

.85 

*.80 

1.17 

.98 

1.09 

1.14 

.53 

1.12 

.42 

3.87 

.90 

1.17 

.90 

1. 74 1.00 

1.14 

2.45 

.98 

*3.20 

2.98 

3.65 

1.03 

• 54 1.25 

. 72 

.81 

. 97 

.85 

l. 42 

.63 

1. 46 4.47 

1.22 

1.26 

1.15 

1.08 

1.42 

1.16 

1. 23 1.32 

. 72 1.29 

.66 

4.42 

1. 27 1.41 

1.15 

2.07 

1. 27 1.34 

3.00 

1. 21 3.24 

3.64 

4.12 

0.99 

1.02 

.98 

1.00 

1.03 

1. 01 1.01 

1.00 

1.00 

1.03 

1.00 

1. 0'2 1.08 

1.10 

1.03 

1.01 

1.02 

1.00 

1.02 

1.00 

1.02 

1. 07 

.97 

1.03 

1. 02 1.02 

1.03 

.99 

1.00 

1. 02 1.00 

.96 

1.03 

.97 

0.81 

.94 

.86 

.90 

.89 

.83 

. 9'2 

.76 

.68 

• 77 

.87 

. 78 

• 79 

.81 

. 77 

.83 

.86 

.89 

.89 

. 74 

.88 

.68 

.85 

. 73 

.84 

.80 

.86 

.78 

.85 

.83 

.81 

.95 

. 85 

.86 

Feet. 

60. 0 Small B. 60.0 R . 61.0 R. 60.0 R . 55.0 R. 59.0 R . 58.0 G. 60.0 G. 60.0 R. 57.0 G. 60.0 G. 58.0 R. 50.0 R. 50.0 R. 55.0 B. 59.0 G. 59.0 G. 60.0 R. 52.0 R. 60.0 R. 55.0 R. 55.0 G. 63.0 G. 59.0 R. 57.0 R. 59.0 R. 58.0 R. 60.0 R. 60.0 R. 57.0 R. 60.0 R. 67.0 R. 55.0 G . 64.0 R. 

Mean .......... --------~------- ....................... 1 ....... . 1.02 .83 . 57.7 

DELAWARE RIVER (EAST BRANCH), HANCOCK, N.Y. 

May 29, 1903 ........ .. Do ............. . Do ............. .. September 1, 1903 ... . Do .............. . Do .............. . 

2. 72 

2. 72 2. 72 4.96 

4.96 

4.96 

320 

230 

240 

90 

320 

240 

2.1 

2.4 

2.5 

3.0 

4.4 

4.8 

0.92 

. 75 1.05 

3.23 

3.65 

4.12 

0.91 

. 70 1.04 

3.14 

3.58 

4.13 

1.20 

1.02 

1.22 

4.04 

4.51 

4.46 

1.01 

1.07 

1.01 

1.03 

1.02 

1.00 

Mean........................................................ 1.()9..3 

0. 77 

.74 

.86 

.80 

.81 

.92 

.816 

DELAWARE RIVER (WEST BRANCH), HANCOCK, N.Y. 

July 21, 1903 .......... 3.10 140 1. 7 1.67 1.60 2.051 1.04 0.82 Do ............... 3.10 160 1.9 2.06 2.00 2.45 l.O::S .84 Do ............... 3.10 170 2.0 1.93 2.00 2.25 .96 .86 Do ............... 3.10 180 2.2 2.40 2.30 3.07 1.04 . 78 Do ............... 3.10 190 2.5 2. 78 2. 74 2.90 1.01 .95 August 31, 1903 ....... 5.35 220 3.1 3.10 3.00 3.90 1.03 .80 Do ............... 5.35 60 3.2 3.07 3.05 . 3. 78 1. 01 I .81 Do ............... 5.35 80 3.9 3.80 3.65 4. 74 1.04 .80 Do ............... 5.35 130 3.9 4.26 4.25 5.17 1.00 .82 Do ............... 5.35 210 3.9 3.82 3.68 4. 70 1.04 .81 Do ............... 5.35 150 4.1 4.67 4.60 5.40 1.01 .86 Do ............... 5.35 200 4.2 4.45 4.40 5.32 1.01 .83 

--------------------·-- Mean .......... ............... ............. .............. .. .. .. .. .. .. . ~ ................. .. ................ 1.018 .831 I 

I 

~I 60 

58 

59 

60 

59 

58 

62 

59 

58 

!).') 

60 

56 

60 

5.5 

!).') 

59 ---

58 

B. 

G. 

B. 

G. 

B. 

B. 

G. 

G. 

G. 

G . 

G. 

G. 

G. 

G. 

G. 

G. 

G. 

G. 
MURPHY.] MEASUREMENTS IN THE CATSKILLS. 

rertical veloc·ity measurements on rive1·s in the Catskill Mountains-Continued. 

ESOPUS CREEK, KINGSTON, N. Y .. 

Velocity in feet per Coefficients for Depth I second by following reducing to of Dis- Depth methods: mean velocity: thread CharacGage tance at - of mean terof Date. from meas- veloci- height. initial uring Verti- ty (in bed of Six- Six- stream. point. point. calve- tenths. Top. tenths. Top. percent 

locity. of depth). 

-------------------------

Feet. Feet. Feet. Feet: 

August 21, 1902. _ .•.• ·1 4.94 40 '1.9 0. 74 *0.72 0.82 \ 1.03 0.90 

I 

54.0 B. July 2'2, 1903 ......... 5.17 35 2.1 .96 .95 1.18 1.00 .82 60.0 B. 

May 24, 1902 .......... 5.02 40 2.2 • 79 *· 76 1.03 1.04 .77 58.0 B. Do ............... 5.02 70 2.4 1.06 1.06 1.32 1.00 .80 60.0 B. 

July 22, 1903 ......... 5.17 40 2.6 1.04 1.01 1.16 1.03 .90 57.0 B. Do ............... 5.17 70 2.6 1.33 1.33 1. 51 1.00 .88 60.0 B. September 23, 1902 ... 5.87 60 2.9 1.59 1. 52 2.03 1.05 • 78 . 55.0 B. 

July 9, 1902 .......... 5.81 40 3.0 1.29 1. 29 1.50 1.00 • 86 60.0 B • August 24, 1903 ....... 5. 72 40 3.0 1. 37 1.34 1.58 1.02 .87 ~g B. September 23, 1902 ... 5.87 40 3.1 1.19 1.19 1.45 1.00 8·~ B. 3. 2 ................ ................ ............... .............. ................ ............... 3.4 ............... .............. "'"i.'i8' .. ............ .............. ······o:· August 21, 1902 ....... 4.94 75 3. 5 . 99 *1.02 . 97 .84 60.0 B. June 6, 1902 .......... 4.48 75 3.6 .65 . 64 .86 1.00 . 76 60.0 B . 

August 12, 1902 ....... 6.28 40 3.6 1.48 *1.42 1. 77 1.04 .84 55.0 B. September 4, 1902 _ ... 4.49 75 3. 7 .66 *.60 . 91 1,10 . 73 53.0 B. 

July 16, 1902 .......... 5.13 75 4.1 1.12 1.11 1.41 1.00 .80 60.0 B. 

July22, 1903 .......... 5.17 75 4.1 1.16 1.15 1.42 1.00 8·~ 60.0 B. May24, 1902 .......... 5.02 100 4.4 . 73 *· 78 .86 . 93 .85 66.0 s. July 22, 1903 .......... 5.17 100 4.6 1. 21 1. 20 1.34 1.00 .90 60.0 s. July 30, 1902 .......... 7.65 60 4.8 2.37 *2.36 2.98 1~00 .80 60.0 B. September 4, 1903 .... 7.66 40 4.9 2.63 2. 74 2.99 .96 .88 65.0 B. May 14, 1902 .......... 5.83 100 5.0 1.19 1.24 1. 29 .96 .92 67.0 s. August 12, 1902 ....... 6.28 75 5.0 1. 67 1.64 2.15 1.02 . 78 59.0 B. June 26, 1902 ......... 4.98 80 5.2 1.69 1.08 1.22 1.00 .90 60.0 B. July 24, 1902 .......... 8.11 60 5.2 2. 71 *2. 71 3.07 1.00 .89 60.0 B. 

August 21, 1902 ....... 4.94 85 5.2 .96 . 97 1.03 .99 .93 61.0 s . May 24, 1902 .......... 5.02 80 5.4 1. 01 *1.00 1.16 1.00 .87 60.0 B. September 4, 1902 .... 4.49 85 5.4 . 74 *· 74 .84 1.00 .88 60.0 s. July22, 1903 .......... 5.17 80 5.4 1. 24 1. 23 1.44 1.00 .86 60.0 B. August 24,1903 ....... 5. 72 80 5.4 1.47 1.47 1. 72 1.00 .85 60.0 B. July 22,1903 .......... 5.17 85 5.5 1.17 1.18 1. 30 .99 .90 61.0 B. Se~tember23, 190'2 .... 5.87 80 5.6 1.56 *1.55 1. 74 1.00 .90 60.0 B. Ju y 22,1903 .......... 5.17 95 5. 7 1.16 1.13 1.37 1.03 .85 58.0 s. June 16, 1902 .•....... 4.48 90 5.8 .70 . 69 .80 1.00 .87 60.0 s . May 14,1902 .......... 5.83 80 6.0 1.38 *1.40 1.59 .99 .87 62.0 s. October 4, 1902 ....... 9.32 60 6.1 2.83 2.85 3.02 .99 .94 61.0 B. 

August 21,1902 •...... 4.94 90 6.2 .89 .87 1.06 1.02 .84 59.0 s. July 22,1903 .......... 5.17 90 6 ., 1.12 1.05 1. 44 1.07 . 78 55.0 s. July 16,1902 .......... 5.13 90 6.3 1. 07 *1. 0'2 1.23 1.05 .87 58.0 s. August 12, 1902 ....... 6.28 85 6.3 1. 71 *1. 71 1.71 1.00 1.00 60.0 s. October 4, 1902 ....... 9.32 40 6.3 3.12 3.23 3.16 .97 .99 66.0 B. Ml!-Y 24, 1902 .......... 5.02 90 6.4 .90 *.89 1.10 1.00 .82 60.0 s. April10, 1902 ...•..... 13.37 15 6.8 5.04 *5.12 5.16 .98 .97 70.0 B. May 14,1902 .......... 5.83 90 7.2 1.22 *1. 22 1.38 1.00 .88 60.0 s. July 9,1902 ........... 5.81 90 7.2 1.30 *1.28 1.50 1.00 .86 60.0 s. September 4,1903 ..... 7.66 90 7.6 2.28 2.23 2.67 1.02 .83 59.0 8. April10, 1902 •........ 13.37 20 7.8 4.89 5.07 5.12 .97 .95 74.0 B. 8. 7 .............. ............ ........... .. ........... ............. .......... 8.8 October 4, 1902 •....•. 9.32 80 9.0 2. 75 ···2:77" 2.80 .98 .98 65.0 B. 

April10, 1902 ......... 13.37 30 9.6 4.94 5.11 5.18 .97 .95 75.0 B. 9.6 ............... ............... ............ ............... ................ ................ AprillO, 1902 ......... 13.37 50 10.2 4.56 4. 75 4.83 .96 .94 70.0 B. Do ............... 13.37 60 10.5 4.48 4. 71 4.66 .95 .96 75.0 B. Do ............... 13.37 40 11.0 4. 70 4.90 4.-'97 .96 .94 70.0 B. Do ............... 13.37 70 11.0 4.34 4.55 4.40 . 96 .98 75.0 B . Do •.............. 13.37 100 13.0 ............... ............... .. ........... ................ ................ ............... Do .............•. 13.37 80 14.0 4.09 4.25 4.12 .96 .99 69.0 B.,s. 

~~~ ~~~ ~~~ ----:9991~ --- Mean .......... 61.7 
154 ACCURACY OF STREAM MEASUREMENTS. (NO. 95. 

Ye1·tical11elocity measurements on ri·vers in the Catskill llfountcdns-Continued. 

ESOPUS CREEK, OLIVEBRIDGE, N. Y. 

I I Velocity In feet !><" Coefficients for Depth 

second by fotlowing reducing to of 

Dis- Depth methods: mean velocity: thread 

Charac- tance at of mean 

Date. Gage from me as- veloci- ter of 

height. initial uring Verti- ty (in bed of 

Six- 'Six- stream. point. point. calve- tenths. Top. tenths. Top. percent 

locity. of I depth). 

------------------------- Feet. Feet. Feet. Feet. 

August 11, 1903 •.•.... 1. 70 25 0.9· 1.59 1.60 1.54 0.99 1.04 61.0 R. Do ............... 1. 70 30 1.0 1.74 1. 77 1.84 .98 .95 62.0 R. 

July 9, 1903 ........... 1.60 160 1.2 .50 .48 . 61 1. 04 .82 57.0 R. Do ............... 1.60 90 1.3 1. 01 1.00 1. 09 1.01 .92 60.0 R. 

August 11, 1903 ....... 1. 70 160 1.3 .51 .51 .54 1.00 .94 60.0 R. 

September 8, 1903 .... 1.81 70 1.3 2.59 2.53 2.86 1.02 .91 54.0 R. Do ............... 1. 81 8'o 1.3 3.18 3.15 3.33 1. 01 .96 55.0 R. June 2, 1903 ........•. 1.10 40 1.4 1. 36 1.34 1.58 1.01 .86 57.0 G. July 9, 19~3 ........... 1. 60 130 1.4 . 72 . 72 . 78 1.00 .81 60.0 R . 

July 2, 1903 ........... 2.14 160 1.5 .98 .94 1.13 1.04 .87 55.0 R. Do ............... 2.14 70 1.6 2. 70 2. 74 2.86 .99 .94 60.0 R. Do ............... 2.14 165 1.6 .99 .96 1.11 1. 03 .90 55.0 R. 

July 4, 1903 ......•.... 1. 92 130 1.6 1.49 1.42 1.68 1.05 .90 57.0, R. 

July 9, 1903 ........... 1.60 35 1.6 1. 62 1.60 1. 75 1. 01 .93 59.0 G. August 11, 1903 ....... 1. 70 130 1.6 1.17 1.15 1. 22 1.02 .95 59.0 R. 

August 14, 1903 ....... 1.62 35 1.6 1.41 1.35 1.66 1.04 .85 55.0 G. July 2, 1903 ........... 2.14 80 1. 7 3.02 3.04 3.09 .99 .97 61.0 R. 

July 9,1903 ........... 1.60 50 1. 7 1.69 1. 70 1. 79 .99 .95 60.0 R. Do ............... 1.60 60 1. 7 1.34 1.25 1.62 1. 07 .82 56.0 R. Do ............... 1.60 120 1.8 .53 . 52 .75 1.02 . 70 59.0 R . Do ............... 1.60 150 1.8 .42 .41 .54 1.03 . 78 60.0 R. 

August 11, 1903 ....... 1. 70 35 1.8 1.65 1.65 1.89 1.00 .87 60.0 G. Do ............... 1. 70 60 1.8 1. 76 1. 74 1.91 1.01 .93 57.0 R. Do ............... 1. 70 90 1.8 1.63 1.60 1.81 1.02 .90 59.0 R. 

September 8, 1903 .... 1.81 55 1.8 1.86 1.83 2.13 1.02 .87 58.0 R. 

July 2,1903 ........... 2.14 130 1.9 1. 98 1.96 2.13 1.01 .93 55.0 R. Augu~t 11, 1903 ....... 1. 70 50 1.9 1. 73 1. 75 1.93 • 99 .90 60.0 R . 

September 8, 1903 .... 1. 81 35 1.9 1.61 1.65 2.08 .9$ . 78 61.0 G. July 9, 1903 ........... 1.60 40 2.0 1.46 1.45 1.56 1.01 .94 60.0 G. Do ............... 1.60 140 2.0 .48 .50 .51 .96 .94 61.0 R. August 11, 1903 ....... 1. 70 150 2.0 .68 .69 .71 .98 .96 61.0 R. 

August 14, 1903 ....... 1.62 40 2.0 1.47 1.45 1.63 1.01 .90 59.0 G. September 2, 1\:103 .... 2. 74 30 2.0 3.53 3.53 3.61 1.00 .97 60.o R. 

July 2, 1903 ........... 2.14 35 2.1 2.32 2.25 2.67 1.03 .87 55.0 G. July 9, 1903 ........... 1. 60 45 2.1 1.62 1.57 1.86 1.03 .87 57.0 R. 

AuguHt 11, 1903 ...... " 1. 70 140 2.1 .90 .86 1.11 1.05 .82 53.0 R. 

August 14, 1903 .....•. 1.62 140 2.1 .65 .63 .80 1.03 .81 57.0 R. 

September 2, 1903 .... 2. 74 80 2.1 4.47 4.44 4. 79 1. 01 .94 57.0 R. ~eptember8, 1903 .... 1.81 50 2.1 1.91 1.92 2.17 1.00 .90 60.0 R. 

August 11, 1903 ....... 1. 70 40 2.2 1.61 1.57 1. 79 1.02 .90 55.0 G. August 14, 1903 ....... 1.62 45 2.2 1.60 1.55 1.84 1.03 .87 55.0 R. 

September 8, 1903 .... 1.81 40 2.2 1.27 1.30 1.63 . 98 .80 62.0 G . July 2, 1903 ........... ,2.14 60 2.3 2. 73 2.62 3.09 1.04 .88 56.0 R. Do ............... 2.14 120 2.3 1.30 1.27 1. 61 1.02 .80 56.0 R. Do ............... 2.14 150 2.3 1.35 1.33 1.49 1.01 .91 56.0 R. 

July 4, 1903 ........... 1. 92 140 2.3 1.15 1.10 1.32 1.04 .88 52.0 R. 

September 8, 1903 .... 1. 81 140 2.3 1.13 1.10 1. 32 1. 03 ·185 54.0 R. 

July 2, 1903 ........... 2.14 40 2.4 2.09 2.05 2.52 1. 0'2 .83 57.0 G. July 4, 1903 ........... 1. 92 50 2.4 2.05 2.00 2.27 1. 0'2 .90 57.0 R. 

August 11, 1903 ....... 1. 70 45 2.4 1.63 1.62 1. 72 1.00 .94 60.0 R. 

September .S, 1903 .... 1. 81 45 2.4 1. 85 1.85 2.05 1.00 .90 60.0 R. 

July 2, 1903 ........... 2.14 140 2.5 1.58 1.53 1.86 1.03 .86 52.0 R. Do ............... 2.14 50 2.6 2.50 2. 46 2.74 1.02 .91 58.0 R. 

September 2, 1903 .... 2. 74 90 2.6 4.09 4.10 4.41 1.00 .93 60.0 R. Do ............... 2. 74 130 2.6 2. 77 2. 76 3.04 1.00 .91 59.0 R. 

July 2, 1903 .......... 2.14 100 2.9 2.00 1.98 2.08 1.01 .96 55.0 R. 

September 2, 1903 .... 2. 74 150 2.9 3.02 3.03 3.31 1.00 .91 60.0 R. June 17, 1903 ......... 2.67 50 3.0 4.16 4.13 4.46 1.01 .93 55.0 R. 

September 2, 1903 .... 2. 74 35 3.0 3.91 3.89 4.39 1. 01 .89 59.0 G. Do ............... 2. 74 50 3.0 4.25 4.22 4.41 1.01 .97 55.0 R. Do ............... 2. 74 140 3.1 2. 71 2.59 3.61 1.05 . 75 54.0 R. Do ............... 2. 74 40 3.2 3. 74 3.69 4.27 1.02 .88 57.0 G. June 13, 1903 ......... 3.08 150 3.3 4.06 4.02 4.37 1.01 .93 56.0 R. 

October 11, 1903 ....•. 4.05 30 3.4 4.39 4.30 4.92 1.0~ .89 54.0 R. Do ............... 4.05 100 4.8 4.68 4.65 5.10 1.01 .91 57.0 R. 

October 10, 1903 ....•. 5.80 30 5.1 5.86 5.95 5.96 .98 .98 65.0 R. Do ............... 5.05 35 5.1 6.16 6.12 7.05 1.01 .87 59.0 G. 

Do ••••••••• ······1 5.80 1165 5.21 7.62 7.67 7. 971 .99 . 95 _OA"-1 R. ----- Mean ......................... .......................... ........ 1.012 .894 57.7 
MURPHY.] MEASUREMENTS IN THE CATSKiLLS. 155 

Vertical velocity measurements on ri-ve·rs in the Catskill Mo·untains-Continued. 

FISHKILL CREEK, GLENHAM, N.Y. 

Velocity in feet per Coefficients for Depth second by following reducing to of 

Dis- Depth methods: mean velocity: thread CharacGage tance at of mean terof Date. from meas- - veloci- height. initial uring Verti- ty (in bed of 

Six- Six- stream. point. point. calve- tenths. Top. tenths. Top. percent 

locity. of depth). 

-------------------------

Feet. Feet. Feet. Feet. 

August 26, 1902 ••..... 3.04 80 2.1 0.26 0.26 0.30 1.00 0.87 60.0 G. 

Do .•...•......... 3.04 65 2.2 .37 .33 .52 1.12 .71 55.0 G. 

Do •..••••........ 3.04 75 2.2 .27 .25 .39 1.08 .69 54.0 G. 

July28,1902 ••........ 3.90 90 2.3 .96 1. 03 . 1.08 .89 .89 66.0 G . 

August 26, 1902 •....•. 3.04 70 2.5 .37 .35 .49 1.06 .76 55.0 G. 

llo ............... 3.04 40 2. 6 .29 .29 .32 1.00 .91 60.0 G. 

August 11, 1902 •...... 3.51 80 2. 7 .61 .55 .85 1.10 .72 50.0 G. 

Do ............... 3. 51 65 2.8 . 74 . 76 .97 . 97 .76 62.0 G . 

August 26, 1902 •...... 3.04 60 2.9 .46 .48 .56 .96 .82 65.0 G. 

Do ............... 3.04 55 3.0 .45 .44 .56 1.00 .so 56.0 G. 

July 28, 1902 ..•....... 3.90 65 3.1 .99 .99 1. 37 1.00 .72 60.0 G. 

August 26, 1902 ....... 3.04 45 3.3 .37 .37 .39 1.00 .95 60.0 G. 

July 28, 1903 ..•....... 3.55 40 3.3 .64 .63 .80 1.00 .80 60.0 G. 

Do ............... 3.55 60 3.4 . 77 . 77 .90 1.00 .86 60.0 G. 

August 26, 1902 ....... 3.04 50 3.5 .38 .38 .49 1.00 . 78 60.0 G. 

July 28,1903 .......... 3.55 . 50 3. 7 . 73 . 70 .97 1.04 .75 55.0 G. 

August 11, 1902 ....... 3.51 45 3.8 . 73 . 70 . 92 1.04 . 79 55.0 G. 

September 5,1903 .... 4.52 70 3.9 1.60 1.58 1.96 1.01 .82 60.0 G. 

August 11, 1902 ....... 3.51 50 4.0 . 77 . 79 .94 .98 .82 62.0 G . 

July 28,1902 .......... 3.90 45 4.1 1.07 1.04 1.29 1. 03 .83 56.0 G. 

September 5, 190;3 .... 4.52 60 4.4 1.65 1. 67 1. 81 .99 .91 62.0 G. 

Do •••.•••.•...... 4.52 50 5.0 1. 75 1. 70 2.05 1.03 .85 57.0 G. ---------------------- --- Mean ..•....... .............. ............... .............. .............. ............. .............. 1. 036 . 79 58.7 .. ............... 

HOUSATONIC RIVER, GAYLORDSVILLE, CONN. 

August 5, 1902 ........ 4.28 130 2.1 1. 79 1. 79 2.27 1. 00 0. 79 60.0 G., B. 

July 24, 1903 ......... 5.20 180 2.1 .67 6'' . 99 1.08 .68 55.0 B. 

Do ............... 5.20 160 2.1 3.19 3.10 3. 73 1.03 . 85 58.0 B . 

Do ............... 5.20 150 2.2 3.42 3.30 .4.08 1.03 .84 54.0 B. 

August 5, 1902 ........ 4.28 120 2.5 1. 30 1.27 1.64 1.02 . 79 58.0 G., B. 

July 24, 1903 ......... 5.:W 170 2.5 2.37 2.35 2. 76 1.00 .86 60.0 B. 

August 20, 1902 ....... 3.95 100. 2. 7 2.04 1. 97 2.42 1. 03 .84 54.0 G., B. 

September 8, 1902 .... 3.45 90 2. 7 1. 67 1.58 2.10 1.05 . 80 56.0 G., B . 

June 23, 1902 ......... 4.46 110 2.8 2.22 2.19 2. 54 1.01 .87 57.0 G., B. 

September 8, 1902 .... 3.45 40 2.8 1. 65 1. 65 1. 95 1.00 .85 60.0 G. 

July 24, 1903 ......... 5.20 140 2. 8 3.41 3. 3R 3.90 1.01 ·.87 59.0 B. 

August 5, 1902 ........ 4.28 90 3.1 2.21 2. 25 2.83 .98 . 78 61.0 G., B. 

July 24, 1903 .......•. 5.20 130 3.1 2. 72 2.54 3.82 1.07 .71 58.0 G., B. 

June 23, 1902 ......... 4.~6 30 3.2 1. 96 1. 96 2.28 .99 .86 60.0 G. 

September 19, 1902 ... 3. 5 40 3.2 1.89 1.87 2.15 1.01 .88 59.0 G. 

August 20, 1902 ....... 3.95 40 3. 4 2.08 2.07 2.36 1.00 .88 59.0 G. 

July 24, 1903 ......... 5.20 120 ,3.6 2. 74 2. 76 3.61 .99 . 76 60.0 G., B. 

June 23, 1902 ......... 4.46 90 3. 7 2.59 2.59 3.07 1.00 .84 60.0 G., B. 

August 5, 1902 ........ 4.28 40 3. 7 2.11 2.03 2.54 1.04 .83 55.0 G. 

July 24, 1903 ......... 5.20 20 3.8 1. 79 1.77 2.11 1.00 .85 60.0 G. 

Do ............... 5.20 110 3.8 3.03 2.86 3.85 1. 06 . 79 55.0 G., B. 

June 23, 190'2 ......... 4.46 50 4.0 2.89 2. 91 3.18 .99 . 91 61.0 G. 

September 8, 1902 .... 3.45 70 4.0 2.07 2.00 2. 47 1.03 .84 55.0 G. 

July 24, 1903 •. : . ..... 5.20 100 4.3 3.36 3 •)•) 4.27 1.04 . 79 55.0 G., B. 

Do ............... 5.20 30 4.4 2.29 2. 37 2.36 .96 .97 63.0 G. 

September 15, 1903 ... 3.90 70 4.6 2.37 2.35 2.93 1.00 .81 60.0 G. 

Do .....•.....••.. 3.90 60 4. 7 2.27 2.26 2.84 1.00 .80 60.0 G. 

July24, 1903 ......... 5.:.w 90 4.8 3.05 2.R8 4.20 1.06 . 73 55.0 G., B. 

August 5, 1902 ......•. 4.28 70 4.~ 2.59 :.!.54 3.05 1.02 .85 57.0 G. 

Do ............... 4.28 60 I 4. 9 2.59 2.50 3.17 1.04 .82 52.0 G. 

June 23, 1902 ..•....•. 4.46 ~g I 5.0 2.83 2. 86 3. 26 .99 .87 63.0 G. 

July 24, 1903 ••.•..... 5.20 5.0 3.00 3.17 3.23 .95 .93 66.0 G. 

Do ...•........... 5.20 50 5.4 3.45 3.48 4.08 .99 .85 61.0 G. 

Do •.•..•.••..••.. 5.20 80 5.5 3.48 3.40 4.32 1. 0'2 .81 59.0 G. 

Do ••••••••....... 5. 20 60 6.2 3.66 3. 70 4.27 1.00 .86 60.0 G. 

Do •••••..••..•.•. 5.20 70 6.2 3.60 3.58 4.41 1.00 .82 60.0 G. 

-r---------------------------

Mean ...•...... ................... .............. ............... ... ............. ... ............... . .............. 1.01 .83 58.5 . ............. 
156 ACCURACY OF STREAM MEASUREMENTS. [No.95. 

Vertical velocity measurements on ri·vers in the Catskill .Llfountains-Continued. 

RONDOUT CREEK, ROSENDALE, N. Y. 

Velocity in feet per Coefficients for I Depth second by followmg reducing to of 

Dis- Depth methods: mean velocity: thread CharacGage tance at of mean ter of Date. from meas- veloci- height. initial uring Verti- ty (in bed of 

Six- Six- stream. point. point. calve- tenths. Top. tenths. Top. percent 

locity. of 

depth). ---- ~~-

------ ~~------- ~~-

Feet. Feet. Feet. Feet. August 7, 1902 ........ 7.39 35 4.4 1.26 1.30 1.45 0.97 0.87 65.0 B. July 29, 1902 ......... 7.40 35 4.5 1. 34 1. 40 1.49 . 96 .90 65.0 B. September 5, 1903 .... 7.24 40 5.1 1.68 1.67 1. 77 1.00 .95 60.0 B. August 21, 1902 ....... 6.33 75 5.3 . 39 .40 .49 1.00 .80 61.0 B . July 18,1902 ......... 6.33 75 5.5 .36 . 35 .44 1.00 .82 58.0 B . August 29, 1902 ....... 6.33 100 5.5 .35 .37 .39 .95 .90 67.0 B. Do ............... 6.33 75 5.6 . 42 .44 .51 .96 .82 62.0 B. 

August 21, 1902 ....... 6.33 85 5.9 .38 .38 .50 1.00 . 76 60.0 B. 

August 29, 1902 ....... 6.33 l:S5 5.9 .4t .44 .51 1.00 .86 60.0 B. July 18, 1902 ......... 6.33 90 6.0 .35 .33 .44 1.06 . 79 53.0 B. August 21, 1902 ....... 6.33 90 6.1 .39 .37 .49 1.06 .80 55.0 B. August 29, 1902 ....... 6.33 90 6.1 .41 .41 .48 1.00 .85 60.0 B. 

September 5, 1903 .... 7.24 100 6.3 1.17 1. 22 1.49 .96 . 79 63.0 B. March 21, 1902 ....... 8.07 40 6.4 2.42 2.46 2. 73 .98 .89 60.0 B. 

August 7, 190'2 ........ 7.39 75 6. 7 1.64 1.66 2.15 .99 . 77 61.0 B. July 29, 1902 .......... 7.40 75 6.8 1. 73 1. 75 2.1~ .99 . 79 61.0 B. September 5, 1903 .... 7.24 70 6.8 1.64 1.66 2.15 .99 . 76 61.0 B. Do ............... 7.24 60 7.2 1. 73 1.82 1.96 .95 .88 68.0 B. Do ............... 7.24 80 7.3 1.64 1. 70 1. 91 . 97 .86 65.0 B. Do ............... 7.24 90 7.3 1.36 1.41 1. 63 .97 .83 63.0 B. March 21, 1902 ....... 8.07 60 8.2 2.55 2.65 2.80 . 97 .91 61.0 B. 

Mean .......... ~~~~-=~~~~~6}A~ 

SCHOHARIE CREEK, PRATTSVILLE, N.Y. 

June 4, 1903 .......... 4. 72 12 1.1 1.421 1.42 1. 77 - 1.00 0.80 60.0 s. May 15, 1903 ......... 5.02 40 4.2 .52 .53 . 68 .98 . 77 60.0 s . Do ............... 5.02 3,0 4. 7 .64 .63 .83 1.02 . 77 60.0 s. August 26, 1903 ....... 6.29 60 4.8 1.59 1. 60 1. 78 .99 .89 60.0 s. June 30, 1903 ......... 5.98 50 5.0 1.66 1.66 2.03 1.00 .82 60.0 s. August 26, 1903 •...... 6.29 40. 5.2 2.07 2.06 2.55 1.01 .81 60.0 s. May 15, 1903 .......... 5.02 20 5.6 .56 .53 . 76 1.05 . 74 50.0 s. June 30, 1903 ......... 5.98 30 5. 7 1. 98 1.96 2.43 1.01 .81 59.0 s. August 26, 1903 ....... 6.29 30 5.8 2.28 2.22 2.76 1.02 .83 58.0 s. June 30,1903 ......... 5.98 20 6.3 1. 78 1. 72 2.31 1.03 . 77 57.0 s. August 30, 1903 ...... 7.62 40 6.6 3.20 3.05 4.22 1.05 . 76 57.0 s. ~~- ---- ~~- --- ~~- ~-- --------- Mean .......... ................ ............. ............... ............. .............. ................ 1.014 .797+ 58.3 .. ............. I 

TENMILE RIVER, DOVER PLAINS, N.Y. 

August 4, 1902 ........ 4.69 11 1.8 0.46 0.46' 0.67 1.00 0.69 60.0 B. Do ............... 4.69 35 2.2 1. 26 1.23 1.43 1.02 .88 53.0 R. Do ............... 4.69 40 2.4 1. 21 1.20 1. 45 1.00 .83 60.0 R. Do ............. :. 4.69 45 2.8 1. 24 1.24 1. 36 1.00 .91 60.0 R.,s. 

July :.!3,1903 .......... 6.18 10 3.0 L10 1.12 1.38 .98 .80 62.0 s. September 14, 1903 .... 4.81:1 55 3.0 1.10 1~08 1.30 1.02 .85 55.0 August 4, 1902 ........ 4.69 15 3.1 .66 . 72 .84 .92 . 79- 66.0 B. August 19,1902 ....... 4.28 50 3.4 . 64 .64 .66 1.00 .97 60.0 s . July 23,1903 .......... 6.18 35 3.4 1.98 1. 98 2.13 1.00 .93 60.0 s. Do ............... 6.18 40 3.5 1. 97 2.05 2.12 .96 .93 62.0 s. October 2,1902 ....... 5.80 40 3.6 1. 74 1.69 2.03 1.03 .86 55.0 R. September:.!, 1902 .•... 3.95 55 3. 7 . 24 .25 .24 .96 1.00 65.0 s . August 4, 1902 ........ 4.69 22 3.8 .88 .91 .99 .97 .89 65.0 B.,s. 

August 19, 1902 ....... 4.48 55 3.8 .51 .51 .51 1.00 1.00 60.0 s. August 4, 190'2 ........ 4.69 50 3.9 1.14 1.13 l. 27 1.00 .90 60.0 s. July 23,1903 .•........ 6.18 50 3.9 1.94 2.02 2.13 .96 .91 67.0 8. · Do ............... 6.18 45 4.0 1. 79 1.88 2.26 .95 . 79 63.0 s. 8eptem ber 2, 1902 .••.. 3.95 20 4.1 .60 . 60 • 74 1.00 .81 60.0 B . August 4, 190'2 ........ 4.69 55 4.2 .96 . 96 1.04 1.00 .92 60.0 s . 

August 19, 1902 •...... 4.2~ 20 4.2 .70 . 74 . 79 .95 .88 66.0 B . September 14,1903 •... 4.88 -25 4. 2 1.11 1.06 1.42 1.05 . 78 55.0 s. August 4, 190'2 .•...... 4.69 30 4.3 l. 07 1.05 1.33 1.02 .80 58.0 8. 

July 23, 1903 .......... 6.18 55 4.3 1. 94 l. 93 1.98 1.00 .98 60.0 s. Do ............... 6.18 15 4.4 };·53 l. 57 1. 75 .98 .87 61.0 s. 

August 4, 1902 .....•.• 4.69 20 4.7 s·> • 86 .88 .96 .93 70.0 B . 
MURPHY.] MEASUREMENTS IN 'l'HE CATSKILLS. 157 

Vertical 'oelocity rnea.<Jllrements on ·ri1'ers in the Catskill ]fowntains-Contimted. 

TENMILE RIVER, DOVER PLAINS, N. Y.-Continued. 

Date. 

Velocity in feet per Coefficientsfor Depth second by following reducing to of 

Dis- Depth methods: mean velocity: thread CharacG tance at ofme~~:n ter of b. ~~ from meas- vel~c1- bed of 

mg t. ini~iatl ur!ntg Velrti- Six- Top. Six- Top. pteyrc(Ienn-t stream. pom · pom · ca ve- tenths. tenths. locity. of 

depth). -------------------------

Feet. Feet: Feet. Feet. 

July 23,1903 ..•••....• 6.18 30 4.8 1. 81 1.80 1. 96 1.00 0.92 . 59.0 s. August 4,1902 ....•... 4.69 60 5.0 .67 .69 .69 .97 .97 65.0 s. 

October 2,1902 ....... 5.80 50 5.3 1. 75 1.73 1.93 1.03 .90 58.0 s. July 23,1903 .......... 6.18 20 5.3 1. 72 1. 72 1.98 1.00 .87 60.0 s. Do---········--·~. 6.18 25 5.3 1. 76 1. 70 2.08 1.04 .85 56.0 s. 

October 2,1902. _ ----. 5. 80 20 5. 9 1.36 1.37 1. 61 1.00 .84 60.0 B. 

Do---------·--··· 5.80 60 6.0 1.50 1.55 1.45 .97 1.03 67.0 s. July 21,1902 ....•.•.•. 7.18 25 7.3 2.15 2.18 2.44 .99 .88 63.0 s. ---------------------------- Mean---------- ................ .............. .............. .............. ............... ............... .992 .884 60.9 ............... 

WALLKILL RIVER, NEWPALTZ, N.Y. 

August 28, 19112 .. _ ... _ 5.86 40 3.3 0.32 0.32 0.34 1.00 0.91 .. .• I s. Do-----------·--· 5.86 45 3.3 .31 .32 . 33 .97 .94 65.0 s. September 18, 1902 ... 5.96 40 3.4 .39 .42 .43 .93 .91 66.0 s. Do·---·-···--···- 5.96 50 3.4 .41 .46 .41 .89 1.00 74.0 s. August 15, 1902 ....... 6. 72 30 3.6 .63 .62 . 76 1.01 .83 59.0 s. June 6, 1902 ..... _ .... 6.40 40 3.8 . 73 . 72 .84 1.01 . 87 55.0 s . May 13,1902 -----· .... 6.68 45 4.0 .96 .98 1. 09 .98 .88 65.0 s. August 15,1902. ______ 6. 72 40 4.0 .96 .97 1. 03 .99 . 85 65.0 s . August 6,1902 •. __ .... 7.98 30 5.2 1.19 1.15 1. 53 1.03 . 78 56.0 s . Do-··-·--···----- 7.98 40 5.6 1. 70 1. 70 1. 91 1.00 .89 60.0 s. August 28, 1902 ....... 5.86 75 5. 7 .37 .42 .40 .88 .92 74.0 s. May 1,1902 ........... 10.60 25 5.8 2.08 2.24 2.41 .93 .86 66.0 s. September 18,1902 ... 5.96 75 5.8 .46 .50 .51 .92 . 90 76.0 s. August 15, 1903 .. ___ .. 7.85 40 5.8 1. 70 1. 78 1. 70 .96 1.00 68.0 8. Do ............... 7.85 

~I 5.9 1.61 1.66 1. 68 .97 .96 68.0 s. September 18, 190'2 .... 5.96 6.2 .43 .43 .56 1.00 . 77 60.0 8. August 15,1902 •.... _. 6. 72 75 6.6 1.05 1. 05 1. 22 1.00 .86 60.0 8. May 1,1902.----- ..... 10.60 1~ 7.6 2.19 2.22 2.52 .99 . 87 62.0 8 . June 19, 1902 ......... 6.18 7.6 .57 .62 .63 .92 . 91 68.0 s . September 18, 1902 .... 5.96 110 7. 7 .53 .60 .46 .88 1.15 79.0 H. May 1, 190'2 ...... _ .... 10.52 40 7.8 2.81 2. 92 2. 78 .97 1. 01 72.0 8. Do ............... 10.52 45 8.0 2. 77 2. 79 2.86 .99 . 97 64.0 8 . Do ............... 10.46 50 8.0 2. 74 2. 76 2.88 .99 . 95 64.0 8 . Do ............... 10.46 55 8.0 2.40 2.48 2.95 .97 . 81 65.0 8 . Do ............... 10.46 60 8.2 1. 97· 2.02 2.98 . 98 .66 62.0 8 . May 13,1902 .......... 6.68 105 8.2 1.04 1.04 1.09 1.00 .95 60.0 8. Do: ... : .......... 6.68 ]...'>() 8.2 .37 .42 .38 .88 . 97 69.0 s, 

June 6,1902 .. __ ...... 6.40 no 8.2 .81 .80 .113 1. 01 . 87 60.0 8 . Do ............... 6.40 120 8.2 .18 .19 .19 .99 . 95 70.0 s . August 15,1903 ______ . 7.85 90 8.3 1. 78 1. 79 2.10 1.00 .85 60.0 8. August 15, 1902 ....... 6. 72 110 8.4 1.12 1.12 1.17 1. 00 0.96 60.0 8. June 6, 1902 ..... __ .•. 6.40 115 8.6 .55 .53 .69 . 1. 01 • 80 55.0 8 . May 1, 1902 •••... ____ . 10.38 65 9.4 2.00 1.83 3.02 1.09 .66 55.0 s. June 16, 1903 ......... 15.36 20 9. 7 3.07 3.05 3.11 1.01 .98 59.0 8. May 1, 1902 ••..... ___ . • 10.38 70 10.4 2.59 2.59 3.05 1. 00 • 85 60.0 8 . Do ............... 10.24 75 10.4 2.59 2.57 3.02 1.01 .86 59.0 8. Do ............... 10.24 90 10.6 2.61 2.60 2.98 1.00 . 87 60.0 s . Do ............... 10.24 80 10.8 2.60 2.70 3.02 .96 .86 67.0 8. Do ............... 10.2<1 85 10.8 2.68 2.69 3.10 1.00 . 87 60.0 s . Do·-------------- 10.24 95 11.0 2.68 2.68_ 3.05 1.00 .88 60.0 s. Do ............... 10.16 100 11.2 2. 74 2. 78 3.02 .98 .91 62.0 s. Do ............... 10.16 105 11.8 2.85 2.96 3.10 .96 .92 68.0 s. Do ............... 10.16 110 11.8 3.00 3.09 2.98 .97 1.01 75.0 B. 

June 16, 1903 ......... 15.36 60 11.8 4.15 4.17 4.37 .99 • 95 61.0 B . 

May 1, 1902 .•......••. 10.16 115 12.4 2.84 2.92 2.90 .97 .98 69.0 s. 

June 16, 1903 ......... 15.36 70 13.4 4.15 4.18 4.56 .99 .91 61.0 s. 

MR.rch 24,1903 •...... 14.95 80 15.0 4.05 4.08 4.20 .99 . 96 64.0 s . June 16, 1903 ......... 15.36 80 15.3 4.40 4.50 4.56 .98 .96 67.0 s. 

Do ............... 15.36 90 15.8 4.41 4.44 4.61 .99 . 95 61.0 8 . 

Do--------------- 15.36 100 16.3 4.54 4.55 4.84 1.00 .94 60.0 s. Do ............... 15.36 120 16.4 4.05 3.97 4.65 1.02 .87 57.0 s. Do ............... 15.36 110 17.3 4. 72 4.80 5.03 . 98 .94 62.0 s. ------------------------

Mean ......... ~ ...... -.... --...... -.... ............ ............... ................ -~ ......... -- .98 .846 63.7 I 
158 ACCURACY OF STREAM MEASUREMENTS. [No. 95. 

rertic(tl , ·elocity 1neasurements on ·rivers ·in the CatskW Mountains-Continued. 

WAPPINGER CREEK, WAPPINGER FALLS, N.Y. 

Velocity in feet per Coefficients for Depth second by following reducing to of 

Dis- Depth methods: mean velocity: thread Charac- Gage tance at of mean ter of Date. height. from meas- ~ veloci- bed of initial uring Verti- Six- Six- ty {in stream. point. point. calve- tenths. Top. tenthR; Top. percent 

locity. of depth). 

----------------------

Feet. Feet. Feet. Feet. 

July 7, 1903 ........... 1. 70-- 55 2.5 1.84 1. 82 2.03 1. 01 0.91 60.0 s. Do ............... 1. 70 15 2.8 .96 .93 1. 34 1.03 . 72 59.0 s . Do ............... 1. 70 20 2.8 1.24 1.19 1. 66 1. 04 . 75 58.0 s . Do ............... 1. 70 25 3.0 1. 39 1. 38 1.86 1.00 . 75 60.0 s . Do ......... : ..... 1. 70 10 3.2 .53 . 52 1.02 1.11 .57 52.0 s . Do ............... 1. 70 30 3.2 1.46 1.46 1.89. 1.00 . 77 60.0 s. Do ............... 1. 70 35 3.4 1. 69 ]. 67 2.05 1. 01 . 82 59.0 s . Do ............... 1. 70 40 3.4 1. 36 1.42 1. 42 .96 .96 65.0 s. September 3, 1903 .... 2.35 20 3.5 1. 76 1. 74 2.17 1.01 .81 59.0 s. July 7,1903 ........... 1. 70 70 3. 7 1.19 1. 08 1. 84 1.10 .65 M.o s. Do ............... 1. 70 .so 3. 7 1. 33 1. 2.5 1. 84 1.06 . 72 54.0 s . Do ............... 1. 70 60 3.8 1. 61 1. 58 1.96 1.01 . 82 58.0 s . 

September 3, 1903 .... 2.35 30 3.8 2.11 2.03 2.57 1.04 . 82 55.0 s . 

July 7, 1903 ........... 1. 70 75 4.0 1.52 1.52 1.81 1.00 . 84 60.0 s . 

September 3, 1903 .... 2.35 60 4.5 1. 97 1. 93 2.43 1.02 . 81 58.0 s . Do ............... 2.35 so 4.5 1. 67 1. 59 2.29 1. 05 . 73 55.0 s. 

July 7, 1903 ........... 1. 70 65 4. 7 1.24 1.11 1. 66 1.06 . 75 55.0 s. --------------------------

Mean ........... ............ ............. ............. ........... ............... ............. 1.03 . 777 57.8 

SUMMARY. 

[Legend: Sm=smooth, R=rough, M=medium, Sh=shallow, D=deep.] 

River. Location. Character 

of bed of river. 

------1--------------l----------------l---------------l----~--

Feel. 2-7 Catskill Creek.......... South Cairo, N.1f ..... .. 2-5 Del a ware River (east Hancock, N. Y ......... . branch). 1.5-4 Delaware River (west ..... do ................. . branch). 2-14 Esopus Creek .. . . .. . . .. Kingston, N.Y ........ .. 1-5 ..... do.................. Olivebridge, N.Y ..... .. 2-5 Fishkill Creek . . . . . . . . . Glenham, N. Y ......... . 2--6 Hoosatonic River...... Gaylordsville, Conn ... . 4-8 Rondout Creek ........ Rosendale,N.Y ....... .. 4-6 Schoharie Creek ....... Prattsville,N. Y ....... . 2-7 Tenmile River......... Dover Plains, N.Y ..... . 3-17 Wallkill River ......... Newpaltz, N.Y ....... .. 2-5 Wappinger Creek ...... Wappinger Falls,N. Y .. 

0.577 

.590 

.580 

.617 

.577 

.587 

.585 

.614 

.583 

.609 

I ,637 

.578 

1.020 

1.023 

1.018 

. 999 

1. 012 

1. 036 

1.010 

. 987 

1. 014 

• 992 

. 980 

1.030 

Mean . .. . .. . .. . . . . . .. .. . .. . . . .. .. . .. . . . . . .. . 595 1. 010 

a From the curve. 

0.830 

. 816 

.831 

.875 

.894 

• 790 

.830 

.840 

. 797 

.884 

.846 

. 777 

47 Sm. 6 R . 

12 R.-

53 M . 68 Sm. 22 M. 36 M. 21 R . 11 Sm. 33 M . 52 Sm . 17 Sm. 

.834 378 

b Meter held as near the surface as possible, and not affected by wind, etc . 

. MEASUREMENTS ON ICE-COVERED RIVERS. 

M. 

Sh. 

Sh. 

D. 

Sh. 

Sh . M. 

M. 

M. 

M. 

D. 

Sh. 

It was found necessary by T. H. Tillinghast and W. W. Schlecht, 

hydrograp:t,_ers, in computing the dischargeR of the rivers in the Catskill Mountains in the winteTs of 1901-2 and 1902-3, to study their 

velocities under ice and {1) to ascertain the effect of the ice c~overing 

upon the vertical distribution of velocities, especially upon the position 
MURPHY.] ICE-COVERED 14TREAMS. 159 

of the point of mean velocity, (2) to discover its effect upon the discharge of the stream, and (3) to learn how to adjust the gage heights 

and to compute the data obtained under iee, so as to obtain the most 

aecurate results. 

Only three of the streams under consideration remain frozen for 

any great length of time; these are the Wallkill, the Esopus, and the 

Rondout. The Wallkill is a deep river, with easy slopes and smooth 

·bed; the Rondout ia of medium depth, greater slope, and rough bed; 

while the Esopus is shallow, .with a bed partly smooth and partly 

rough. Of these three special studies were made. 

Observations were taken with a Price current meter, which was 

lowered through holes cut in the ice at regular distances across the 

stream. Velocities were obtained in'ten or more points in the vertical, 

and were plotted on cross-section paper, the depths as ordinates and 

the velocities as abscissas. The total depth at each station was measured from the under surface of the ice to the bed of the stream. The 

gage height was taken at the top of the ice, and the thickness of the 

ice in all cases recorded. 

After plotting the depths and velocities, a curve was drawn through 

the points and divided into ten equal parts. The center velocities of 

each part, taken from the curve, added and divided by 10, gave the 

mean velocity in that section. -

'Vhen the holes were cut the water rose nearly flush with the surface of the ice, showing that it was flowing under pressure. A study 

of the tables and curves showed that the flow of water under such 

conditions was somewhat similar to its flow in pipes and in closed 

flumes. The mean velocity occurred at two points in the vertical, the 

average of 83 curves being 0.11 depth and 0. 71 depth; the maximum 

velocity occurring at 0.36 depth. The curves dragged more for shallow depths and became more concave, and consequently the error of 

observation increased if the meter was not held at the proper point in 

the vertical depth. 

The reading of the gage is an important factor in computing the 

flow of rivers during the time they are frozen over. In these observations the gage was always read at the surface of the water as it 

stood in a hole cut in the ice, this being practically at the top of the 

ice in all cases. 

It was at first thought that by subtracting the thickness of the ice fron1 

the gage readings the regular open-channel discharge rating table might 

be used. It was found, however, that both the friction of the water 

on the ice and the head on the water itself, varied greatly, the former 

with the quantity of tilted, broken, and anchor ice, and the latter with 

the thickness of the ice and the. freezing and thawing of the upper 

stream, and thus so complicated the problem .as to render the error of 

this method far too great. It wa8 found to be more accurate and satisfactory to treat ice-closed rivers as a separate problem than to attempt 
160 ACCURACY OF 8TREAM 1\iEASUREM.EN'l'S. [NO. 95. 

to adjust the thickness of ice to the gage heights and apply them to the 

open-channel rating tables. Accordingly special tables were computed 

for use on the three streams in question when ice covered. 

Frmu the summary it appears that-

{1) The maximum velocity occurs at a point between 35 per cent and 

40 per cent of the total depth, as Ineasured fron1 the under surface of 

the ice; {2) the mean velocity occurs at two points in the .vertical, 

namely, from 0.08 to 0.13, and from 0.68 to 0.74 of the depth, measured from the under surface of the ice; (3) the depth of the stream 

has more effect on the point of mean velocity than the slope velocity, 

or the roughness of bed, this being probably due to the relation of 

wetted perimeter to cross seetion; {4) the vertical velocity curve 

becomes more concave as the river rises, this being due to the increased 

head; {5) in gaging streams under iee, Ineasurements Hhould be made 

by the vertical-velocity-curve method, or by the integTation method. 

Vertical velocity measurements on ice-covered streams in the Catskill Jfountains. 

Ga~ heig t, 

read Date. to top of ice. 

11.2 January 7, 1903 •.... Do .............. Do .............. Do .............. 10.9 February 10, 1903 ... Do .............. Do .............. Do .............. Do .............. 7.1 February 24, 1903 ... Do.: ............ Do ....•......... Do .............. 8.85 February 26, 1903 •.• Do ....•......... Do .....•........ Do .............. Do .....•........ Do ......•...••.. Do .............. 

Mean •.•..•... 

December 11, 1901. .. Do .............. Do .............. Do ............•. January 21, 1902 ..... Do .............. Do .............. Do._ ............. January 23, 1902 ..••. Do .............. Do .............. Do .............. Do .............. 

WALLKILL RIVER, NEWPALTZ, N.Y. 

[By F. H. Tillinghast.] 

Dis- Depth tance from Thick- Mean Depth of 

from under ness veloc- mean initial surface of ice. ity. vetocity. 

point. of ice. 

----

Feet. Feet. Inches. 60 6.8 9 2.31 0.04 0.59 80 10.3 9 2.57 .08 .68 90 10.8 9 2.40 .11 . 70 110 12.3 9 2.48 .15 .85 25 4.8 16 1. 29 • 0.5 .65 40 8.0 12 2.26 .25 .80 60 6.0 12 2.18 .09 .68 80 9.6 12 2.53 .09 .69 110 11.8 '12 2.60 .11 . 78 60 3.8 5 1.42 .08 .64 70 4.4 5 1.55 .0&. .71 85 6.8 5 1.60 .10 .68 

- 90 7.4 5 1.50 .13 . 77 25 4.0 14 .59 .10 .65 40 5.8 14 1.20 .07 . 72 60 4.2 12 1.11 .07 .67 80 7.8 12 1.43 .10 .72 100 9.2 12 1.41 .10 • 70 110 10.5 8 1.94 .30 • 77 120 7.9 7 .68 .20 . 78 

------------ .......... ......... ......... . ........... .12 .71 

[B-y W. W. Schlecht.] 

85 11.61 0. 7 2.61 0.150 0. 740 75 11.5 .7 2.64 .170 . 740 53 9.2 .7 2.48 .280 .860 40 9.0 ·.4 2.49 .140 . 750 50 3.4 1.2 .81 .090 .730 80 5.8 1.0 1.01 .130 .720 90 6.6 1.0 1.01 .120 .• 720 100 7.8 1.0 1.08 .120 .730 40 14.0 1.4 3.13 .170 .800 50 15.0 •.• I 3.63 .170 .840 60 14.0 .8 4.02 .130 .800 70 16.0 .8 4.02. .120 .820 80 17.0 . 7 3.96 .090 . 750 

I 

Maxi- Depth of mum maxiveloc- :.mum- ity. velocity. 

--

2. 78 0.35 2.95 .35 2. 71 .35 2.82 .35 1.45 .45 2.47 .45 2.63 .35 2.86 .35 3.02 .45 1.91 .35 1.96 .35 1.84 .45 1. 72 .45 . 76 .35 1.42 .25 1.54 .35 1. 70 .35 1.68 .35 "2.10 .55 .81 .45 

---- . ........... .38 

3.13 0.350 3.22 .350 2. 75 .550 2.89 .4."i0 .95 .350 1.20 .350 1.25 .350 1.27 .350 3.61 .450 4.00 .450 4.29 .350 4.37 .350 4.31 .450 

Coefficient 

to reduce 

maximum to mean. 

--

0.8 3 

7 

9 

.8 

.8 

88 

.8 9 

.91 

83 

88 

86 

:7 

• 7 

.8 

.8 

.7 

5 

9 

7 

7 

8 

85 

:7 3 

84 

84 

92 

84 

--

85 

0.830 

. 8:!0 

.900 

.860 

.850 

.840 

.810 

.850 

.R70 

.900 

.930 

.920 

.920 
MURPHY.) ICE-COVERED STREAMS. 161 

Vertical velocity measurements on ·ice-covered streams ·in the Catskill Jfountains-Cont'd. 

Gage 

height, 

r~ad 

to top of ice. 

-· 

6.60 

6.90 

7.1 

WALLKILL RIVER, NEWPALTZ, N. Y.-Continued. 

Date. 

January 23, 1902 ••... Do .............. Do .............. January 31, 190'2 ..... Do .............. Do .............. Do .............. Do .............. February 10, 1902 .... Do ........ ·: ..... February 24, 1902 .... Do .............. Do .............. 

Mean .............. 

December 11, 1902 ... Do .............. Do .............. Do .............. Do .............. Do .............. Do .............. January 14, 1903 ..... Do .............. Do .............. Do .............. February 24, 1903 .... Do .............. Do .............. no· .............. Do .............. 

Mean ......... 

Dis- Depth tance from Thick~ Mean Depth of from under ness veloc- m~an 

initial surface of ice. ity. velocity. point. of ice. 

------ Feet. Feet. I-nches. 

90 17.0 0, 7 3.93 0.070 0. 700 100 18.9 .8 3.89 .160 • 8.50 110 19.0 .8 3. 73 .160 . 760 40 5.8 1.0 1. 52 .150 . 740 70 7.8 1.0 2.08 :·~~ .680 80 7.8 1.0 2.14 . 720 90 9.0 1.0 2.09 .100 .690 100 10.3 1.2 2.24 .140 . 760 80 6.5 1.0 1.42 .150 .710 90 7.5 1.0 1.42 .090 .640 90 .6.0 2.0 .85 .080 .670 80 5.3 2.0 .84 .130 . 740 40 3.5 2.4 .51 .110 . 700 

----------------

............. ................ ................... .............. .131 . 744 

ESOPUS CREEK, KINGSTON, N. Y. 

[By F. H. Tillinghast.] 

25 2.2 1 0.57 0.11 0.68 30 3.0 1 .87 .07 . 73 40 4.0 1 1.13 .08 .65 50 3.2 1 1.21 .07 .65 60 3.8 1 1.24 .08 .65 80 7.0 1 1. 28 .07 . 73 100 6. 2 1 1.06 .07 .68 55 2. 9 7 1.08 .07 .60 70 3.6 7 1.08 .06 . 72 90 7.1 7 1.01 .05 .62 105 4.0 7 .90 .11 . 73 60 3.8 5 1.40 .08 .66 70 4.4 5 1.51 .08 . 70 85 6.8 5 1.60 .12 .67 / 

90 7.4 5 1.50 .12 . 72 100 6.1 5 1.40 .08 .66 ------------ .............. ............ ............. .08 .68 

[By W. W. Schlecht.l 

Maximum 

velocity. 

4.36 

4.20 

4.18 

1. 73 2.44 

2.44 

2.46 

2.48 

1. 65 1. 72 1.04 

1.00 

.62 

---

. .............. 

0.87 

1.10 

1.40 

1.64 

1.54 

1.5,1') 

1.28 

1. 32 1.32 

1.22 

1.17 

1. 91 

1.96 

1.84 

1. 72 1. 68 

---

.. ........... 

Depth Coe:ffi.-

of cient 

maxi- to 

mum reduce 

veloc- maxiity. mum to mean. 

------

0.350 0.900 .450 .920 .450 .890 .350 .880 .350 .850 .350 .870 .350 .850 .450 .900 .350 .860 .350 .820 .250 .820 .350 .840 .350 .820 

------

.385 .865 

0.45 0.66 .35 .79 .35 .81 .35 .74 .35 .80 

.25 .83 .35 .83 .25 .82 .25 .82 .25 .83 .55 • 77 .31\ .74 .35 . 77 .45 .87 ..15 .87 .45 .84 ------

.36 .So 

December 4, 1901 . . . . 90 6. 8 o. 05 0. 89 0. 200 0. 78 1.10 0. 550 0. 810 Do .. . .. . .. .. .. .. 100 5. 0 . 20 . 95 . 080 . 76 1. 08 . 450 . 880 January9,1902...... 80 6.6 .10 1.39 .150 .75 1.53 .350 .910 Do .. . .. .. .. .. . .. 90 8. 0 . 1 o 1. 15 . 080 . 69 1. 40 . 250 • 820 Do . .. .. .. . .. .. .. 100 6. 0 . 10 1. 20 . 160 . 80 1. 33 . 350 . 900 

February20,1902 .... 80 5.7 .10 .83 .110 .78 .95 .350 .870 Do .. . .. . . .. .. .. . 90 6.4 . 20 . 83 . 060 • . 63 1. 01 . 350 • 820 February 28, 1902 • . . . 40 1 6. 0 . 30 2. 58 • 080 • 65 3. 08 . 350 • 840 

, Mean.-........ ~~~~~~----:73~.~~ 

RONDOUT CREEK, ROSENDALE, N. Y. 

[By F. H. Tillinghast.] 

8. 50 February 23,1903.... 20 5. 0 8 1. 45 1....... 0. 68 1. 86 0. 35 0. 78 7. 90 February 25,1903.... 20 4.4 6 . 831 0.10 . 65 • 97 . 25 . 86 Do.............. 70 7.0 7 1.50 .05 .63 1.93 .25 .78 Do.............. 80 7.6 6 1.65 .06 .68 1.91 .45 .86 Do .. .. .. • .. .. • .. 90 7. 6 6 1. 46 . 11 . 74 1. 75 . 45 .,. . 83 

Mean ......... ~~ ... _ ..... :==~~~~~~ 

IRR 95-04-11 
162 ACCURACY OF STREAM MEASUREMENTS. (NO. 95. 

Verticalt,elocity measurements on ice-covered streams in the Catskill Mountains-Cont' d. 

Gage 

height, 

read 

to top 

of ice. 

RONDOUT CREEK, ROSENDALE, N. Y.-Continued. 

[By W. W. Schlecht.] 

Date. 

December 6, 1901 .... Do .............. January H, 1902 ..... Do .............. February 26, 1902 .... Do .............. Do .............. Do .............. 

Dis- Depth tance from Thick- . Mean from under ness velocinitial surface of ice. ity. 

point. of ice. 

Feet. Feet. Inches. 

80 6.1 0.1 0.66 

90 6.4 .2 .58 

80 6.3 .2 l. 24 

·90 6.8 .2 1.14 

92 6.2 1.5 l. 29 

92 6.6 1.4 1.64 

80 6.4 1.5 1. 51 

40 5.4 1.0 1. 51 

--.----------

Depth of mean 

velocity. 

0.13 0.690 

.11 .630 

.22 .810 

.16 . 720 

.13 .720 

.05 .670 

.09 . 700 

.15 . 750 

----

Maximum 

velocity. 

0. 76 

.68 

1.47 

1.27 

1.58 

2.02 

1.68 

1. 67 

---

Depth 93:~-

m~~i- to mum redu(/e 

veloc- maxlity. ~=n~ 

0.35 0.870 

.25 .850 .45 .840 

35 .900 

.35 .820 

.35 .820 

.35 .900 

.35 .900 

------

Mean . . . . . . . . . . . . . . . . . . . . . . . . . • • . . . . . . . . . . . . . . . 13 . 711 .....••• .35 .862 

SUMMARY. 

Stream. 

Num- Maxi- DeJfth 

~~J~r f:~~ ~!a~~ Depth of mean vmeu10mc- maxiface of ice. ure- velocity. mtim ments. ity. velocity. 

Coeffi- 0 cient • to ~ ~ redm;e .t:l 1:: 

maxi- a ::1 

mum to ::1 ~ 

mean. z -------------------------l----------1------ll------~----l----- ----------

Feet. 

Wallkilla ......................... 4 to 12 20 0.12 0. 71 0.38 0.85 20 Wallkillb ......................... 4 to19 26 .13 . 74 ·.38 .86 26 

Esopusa ........................... 2.2to7.4 16 .08 .68 .36 .so 16 

Esopusb ........................... 5to8 8 .11 . 73 .37 .85 8 

Rondouta .......................... 4 to 8 5 .08 .68 .35 .82 6 Rondoutb ......................... 5 to 7 8 .13 .71 .35· .86 8 1----------1----·-----------------

Mean ............................................. . .11 .71 ....... . .36 .84 

a By F. H. Tillinghast. bBy w. w. Schlecht. 
INDEX. 

Page. 

Abbot, H. L., Humphreys, A. A., and, cited 

on vertex of vertical velocity 

curves on Mississippi River . . . . 27-28 

observations by, on vertical velocity 

curves.......................... 26 

Alston, S.C., Broad River at, vertical velocity measurements on ......... 146, 150 

Appomattox River at Mattoax, Va., vertical 

velocity measurements on .... 142,150 

Bailey, J. C., ratings of Price meter by, 

quoted ................... ~....... 42 

Battle Island, N.Y., Oswego River at, cross 

section of. . . . . . . . . . . . . . . . . . . . . . . 129 

Oswego River at, discharge measurements of........................ 130 

gaging station on . . . . . . . . . . . . . . . . . . . 129 

gaging station on, view of, showing 

car and cable.. . . . . . . . . . . . . . . . . . 112 

measured and mean discharge of, 

comparison of.................. 132 

station-rating curve for . . . . . . . . . . . . 130 

station-rating table for............. 131 

surface slope of, diagram showing.. 135 

surface slope of, table showing..... U16 

velocity curves of . . . . . . . . . . . . 131, 133, 134 

velocity of, table showing change 

of, with change in river stages. 135, 136 

Baum, Adam, cited on variations of velocity 

of the Rhine. . . . . . . . . . . . . . . . . . . . 29 

Baumgarten, --, observations by, on 

vertical velocity curves . . . . . . . . 26 

Bazin, H., formula of, for determining 

discharge over weirs. . . . . . . . . . . 34 

Bazin, H., Darcy, H., and, cited on use of 

Pi tot tube . . . . . . . . . . . . . . . . . . . . . . Is 

observations by, on vertical velocity 

curves.......................... 26 

Pi tot tube ratings by, results of ........ 43,47 

Belmont, N.C., Catawba River at, vertical 

velocity measurements on .... 146,150 

Binghamton, N. Y., Chenango River at, 

discharge measurements on .. 113-122 

Chenango River at, gage used on...... 114 

station-rating curve of. ... -......... 115 

station-rating table of . . . . . . . . . . . . . . 116 

Susquehanna River at, comparison of 

mean and measured discharge 

of. .................. ~............ 125 

contours of bed of . . . . . . . . . . . . . . . . . . 122 

cross section of, diagram showing. . 123 

discharge measurements of . . . . . . . . 123 

station-rating curve of . . . . . . . . . . . . . 124 

station-rating table of.............. 124 

surface slope of, diagram showing.. 128 

surface slope of, table showing..... 127 

velocity curves of ................ 125,126 

Page. 

Binghamton, N.Y., Susquehanna River at, 

velocity of, changes in, with 

change in river stage, tables 

showing ...................... 127,128 

Susquehanna River at, velocity of, diagrams showing changes in, for 

changes in river stage.......... 126 

Bluff City, Tenn., South Fork Holston River 

at, vertical velocity measnrementson ...................... 147,150 

Boileau, Captain, method of measuring velocity used by . .. .. . .. .. .. .. .. .. 18 

observations by, on vertical velocity 

curves.......................... 26 

Boonville, N. Y., experiments at, with float 

rods and current meters ....... 52,53 

Borda and Dubuat, float wheel used by.... 17 

Bridges, accuracy of measurements taken 

from............................ 106 

Broad River at Alston, S. C., vertical velocity measurements on .......... 146, 150 

.Bryson, N.C., Tuckasegee River at, vertical 

velocity measurements on. 148--149,150 

Burlington, Iowa, velocity measurements 

at............................... 30 

Cabeo, --, float rods for measuring 

velocity first used by . .. . .. .. . .. 16 

Camden, S. C., Wateree (Catawba) River at, 

vertical velocity measurements 

on ............................ 146,150 

Cartersville, Va., James River at, vertical 

velocity measurements of .... 142, 150 

Cass, C. D., acknowledgments to........... 60 

Castelli, Benedetto, method of measuring 

velocity used by................ 18 

Catawba River at Belmont, N.C., vertical 

velocity measurementson .... 146,150 

at Morgantown, N.C., vertical velocity 

measurements on ......... 145-146,150 

at Mount Holly, N.C., vertical velocity 

measurements on ............ 146,150 

Catawba (Wateree) River at Camden, S.C., 

vertical velocity measurements 

on ............................ 146,150 

Catskill Creek at South Cairo, N.Y., vertical 

velocity measurements on. 151-152,158 

Catskill Mountains, streams in, vertical velocity measurements on ...... 150--158 

Chenango River at Binghamton, N. Y., 

comparison of measured and 

mean discharges of............. 116 

contour of bottom of, figure showing . . 113 

cross section of, figure showing . . . . . . . . 113 

discharge measurements on............ 115 

slope of, diagram showing change in, 

for change in river stage....... 121 

163 
164 INDEX. 

Page. 

Chenango River at Binghamton, N.Y., slope 

· of, from Court street to Ferry 

street brid~e, table showing.... 121 

station-rating curve of ... .. . .. ..•. ..... 115 

station-rating table of.................. 116 

velocity curves of .................... 117,-118 

velocity of, changes in, with change in 

river stage, diagram showing . . 120 

changes in, with change in river 

stage, tables showing ........ 118, 119 

workon .............................. 113-122 

Chittenango, N. Y., stream measurements 

at ............................. 106-108 

Chittenango Creek at Chittenango, N. Y., 

cross section of, figure showing. 107 

discharge measurements of, results of.. 108 

gaging station on .................... 106-107 

vertical velocity curves of . . . . . . . . . . . . . 107 

vertical velocity data of .. .. .. .. . . .. .. . 108 

Cippolettiweir, discharge measurements at, 

compared with current meter 

measurements . . . . . . . . . . . 103, 10!, 105 

Coefficient work, methods of ........... · .... 38-40 

Connecticut, rivers in, vertical velocity 

• measurements on ............ 155,158 

Connecticut River, discharge of, formulas 

used for computation of........ 46 

slope measurements of, discharge computations from ................• 23-24 

velocity measurements of, with double 

floats and current meters, comparison of...................... 48 

Cornell University Canal, experiments at, 

accuracy of results of. .......... 97-98 

experiments at, application of results 

of, to river gaging.......... .. .. 96-97 

conclusions drawn from .......... 98-100 

date of.............................. 59 

flume, penstock, and wheelhouse of, 

view of, plate showing......... 60 

plan and elevation of .. .. .. .. .. .. .. . .. . 61 

plan and sections of flume, figure ~howing ............................. 101 

surface velocity experiments at. ....... 89-92 

velocity ratios in, table showing . . . . . . . 80 

view of, pl3;te showing .. .. .. .. .. .. .. .. . 56 

view showing disturbed water surface 

during experiments............ 62 

Cornell University hydraulic laboratory, description of . . . . . . . . . . . . . . . . . . . . . 60-61 

experiments at, discussion of results 

of. .............................. 65-98 

methods used in .................... 63-64 

reduction of ................•....... 64-65 

scope of ............................. 62-63 

velocity curves derived from ....... 73-76 

with float-rod and weir measurements .......................... 5.5-58 

Cornell University standard weir, discharge 

measurements at, comparison of, 

with measurements by current 

meters .......................... 657 72 

Cunningham, Allan, cited on advantages 

of float rods..................... 17 

cited on pulsation of moving water . . . . 28 

quoted on pulsation of moving water.. 12 

Page. 

Cunningham, Allan, quoted on slope measurement.~ of Ganges Canal...... 24 

Current meters, accuracy of work with, conchisions in regard to .......... 137-138 

advantages of .......................... 21-22 

apparatus for moving, with uniform velocity ........................... 38,39 

coefficient work with................... 38-40 

disadvantages of....................... 22 

discharge measurements by, compared 

with double-float measurements .......................... 48-52 

compared with float-rod measurements .. .. . • . .. .. .. . .. . .. . 52-54, 90-92 

compared with Pitot tube measurements .......................... 96-97 

compared with weir measurements. 58-59, 

6S:.72, 103, 11)4, 105 

history of development of..... . . . . . . . . . 20 

low-velocity measurements with, compared with weir measurements. 93-95 

methods of holding in water, effect of.. 85-89 

methods of using. . . . . . . . . . . . . . . . . . . . . . . 34-38 

figures showing ..................... 35, 36 

comparison of results of .. .. .. .. .. .. 83-85 

rating of ................................ 40-44 

in still and in moving water........ 80-82 

rating tables of, in still and moving 

water........................... 81 

speed of, effect of....................... 84-85 

types of................................. 21 

use of, in obtaining vertical velocity 

curves.......................... '1!1 

vertical velocity measurements with, 

methods of making ........... 139-140 

view of, plate showing................. 102 

See also Price meters; Haskell meter; 

Fteley meter. 

Dan River at Madison, N.C., gaging of. .. UO, 150 

at Madison, N. C., vertical velocity 

measurements on ............. 143,150 

at South Boston, ·va., vertical velocity 

measurements on ..........•.. 144,150 

Darcy,H.,and Bazin, H.,citedon use of Pitot 

tube............................ 18 

observations by, 9n vertical velocity 

curves .. . . . . . . . .. . • . . . . . . . . . . .. . 26 

Pitot tube ratings by, resultsof ......... 43,47 

De Fontaine, Felice, observations by, on 

vertical velocity curves ......•. 

Delaware River (East and West Branches) 

26. 

at- Hancock, N. Y., vertical velocity measurements on •. . . . . 152, 158 

Depth, relation between velocity and ... 26,38-40 

Direct methods of measuring velocity, description of ..................... 14-17 

Discharge, formulas- for computation 

of ..................... ~ ••• 33-34, 44-47 

methods of measuring and computing . 32-47 

Discharge measurements, accuracy of, tests 

for.............................. 138 

Double floats, advantages of .•.....•.•...... 

disadvantages of ...................... . 

discharge measurements by, compared 

with current-meter measure15 

16 

ments ........................... 48-52 
INDEX. 165 

Page. 

Double floats, figure showing............... 15 

use of, in velocity mell.surements ....... 14-16 

Dover Plains, N.Y., Tenmile River at, vertical velocity measurements 

on ........................ 156-157,158 

Drane, :p, S., gaging by..................... 140 

vertical-velocity-curve measurements 

by.............................. 139 

Dubuat, Borda and, float wheel used by... 17 

Elizabethtown, Tenn., Watauga River at, 

vertical velocity measurements 

on ............................ 147,150 

Ellet, C., quoted on slope measurements of 

Mississippi River . . . . . . . . . . . . . . . 24 

Ellis, T. G., cited on method of computing 

discharge ........ ~.............. 46 

cited on slope formula computations ... 23-24 

experiments by, on measurement of 

velocity ........................ 48-49 

with double floats and current 

meters............... .. .. . . .. . .. 48-49 

float used by, in Connecticut River 

measurements, figure showing........................... 14 

Esopus Creek at Kingston, N. Y., vertical 

velocity measurements on ... 153, 158 

at Kingston, N. Y., vertical velocity 

measurements on, under ice .. 161, 162 

at Olivebridge, N.Y., vertical velocity 

measurements on............. 154, 158 

Farad flume, Cal., velocity curves in lower 

section of....................... 112 

velocity curves in upper section of..... 111 

Fishkill Creek at Glenham, N.Y., vertical 

velocity measurements on.... 155, 158 

Float frame, use of, for measurement of velocity........................... 11 

Float rods, advantages of.................. 17 

disadvantages of....................... 17 

discharge measurements by, compared 

with current-meter measurements .. .. .. . . . .. .. .. .. . . . 52-54, 90-9'2 

compared with weir measurements .......................... 54-58 

use of, in velocity measurements ...... 1{}-17 

Float wheel, use of, for velocity measurements.......................... 17 

Floats, use of, in measuring velocity ....... 14-16 

Floats, double. See Double floats. 

Floats, surface, discharge measurements 

by, compared with Pitot tube 

measurements... . . . . . . . • . . . . . . . 47 

Flood measurements, formula for computation of.......................... 138 

Fluctuations of surface, methods of measurement of ...... ~.......... . .. . 24-26 

Flumes, views of, plates showing ........ 102,112 

Formulas for computing discharge . . . . . . . . 44-47 

for weir discharge .................. 33-34,110 

Francis, J. B., cited on formula for measuring discharge ........... .-.. ~. 33 

cited on pulsation of moving water.... 28-29 

experiments and formula of . . . . . . . . . . . 32-33 

experiments by, on discharge measurements . .. .. . . .. .. . . . .. .. . . 32-'33, 54-55 

Page. 

Francis, J. B., experiments of, with float 

rod and weir measurements .... 54-55 

formula of, for weir-di~charge computations ......................... _.. 110 

quoted on pulsation of moving water .. 11-12 

French Broad River at Oldtown (Newport), 

Tenn., vertical velocity measurements of .. .. . .. .. .. .. . . .. . 148, 150 

Fteley and Steams, discharge measurements 

by .............................. 33-34 

experiments and formula of ............ 33-34 

experiments by, on measurement of discharge.......................... 58 

formula of, for computation of discharge.......................... 33 

Fteley cu rent meter, figure showing . . . . . . 22 

low-water measurements with, accuracy 

of. ............................ 102-105 

measurements with, accuracy of....... 69, 

81, 9'1, 93-94 

at Cornell University canal . . . . . . . . 62 

comparison of, with standard weir 

and other meter me.asurements . . . . . . . . . . . . . . . . . . . . . . . 65, 66, 69 

velocity curves derived from ....... 75,76 

rating tables for, in still and in moving 

water............................ 81 

ratings of . . . . . .. .. .. . .. . . . . .. . .. .. . .. .. . 94, 95 

speed of, relation between velocity of 

water and . . . . . . . . . . . . . . . . . . . . . . 84 

Fuertes, E. A., acknowledgments to........ 60 

Funk, --, observations by, on vertical 

velocity curves . .. .. . .. .. .. . . .. . 26 

-Gages, self-registering, description and figures of.................... . . . .. . 24-25 

Ganges Canal, slope measurements of...... 24 

velocity in, measurement of . . . . . . . . . . . 28 

Ganguillet, E., and Kutter, W. R., slope 

formula devised by............. 23 

Gaunthy, --, pressure plate invented 

by.............................. 18 

Gaylordsville, Conn., Housatonic River at, 

vertical velocity measurements . 

on ............................ 155,158 

Gleuha\n, N. Y., Fishkill Creek at, vertical · 

velocity measurements on .... 155,158 

Glens Falls, N.Y., experiments at, with float 

rods and current meters. . 52, 53-54, 55 

Gordon, Robert, experiments of, with double 

floats and current meters....... 52 

Grandi, Guido, box used by, for velocity 

measurements.................. 18 

Greeneville, Tenn., Nolichucky River at,. 

vertical velocity measurements 

on ........................ 147-148,150 

Hancock, N.Y., Delaware River {East and 

West branches) at, vertical velocity measri:rements on ...... 152,158 

Harlacher, A. R., cited on integration 

method of current-meter measurements....................... 'frl 

cited on methods of computing discharge ...... _ . .. .. .. . .. . .. . . .. .. 45, 46 

cited on variations of velocity of the 

Rhine.......................... 30 
166 INDEX. 

Page. 

Harlacher, A. R., method of, for computing 

flood discharge....... . . . . . . . . . . 40-47 

Harlacher's apparatus for moving current 

meter, figures showing. . . . . . . . . . 38, 39 

Haskell, E. E., vertical-velocity-curve observations by, on St. Clair River, 

description of............. . . . . . . 27 

Haskell current meter, experiments with, 

at Cornell University Canal . . . . 62-63 

figure showing .. .. .. . .. . .. .. .. .. . . . . .. . 22 

measurements with, accuracy of....... 69, 

72, 81, 83, 90, 91, 99 

comparison of, with standard weir 

and other meter measurements 68, 

velocity curves derived from ...... . 

vertical velocity curves derived 

69,71 

74 

from ............................ 77,90 

rating tables for, in still and in moving 

water .......................... . 81 

speed of, relation between velocity of 

water and . . .. . . . . . .. . . . . . . . . .. . 84 

Henry, D. F., cited on experiments with 

double floats..... . . . . . . . . . . . . . . . 50, 51 

experiments by, with double floats and 

current meters .................. 50-52 

observations by, on vertical velocity 

curves.......................... 26 

quoted on pulsation of moving water.. 12, 30 

quoted on use of double floats in measuring stream flow . . . . . . . . . . . . . . 16 

Hirn, --, float frame used by, in measuring velocity .. .. .. . . .. .. .. .. . . 17 

Holston River, South Fork of, at Bluff City, 

Tenn., vertical velocity measurements on .................. 147,150 

Hook gage, description of . . . . . . . . . . . . . . . . . . 25 

figure showing. . . . . . . . . . . . . . . . . . . . . . . . . . 26 

Horton, R. E., cited on weir discharge 

measurements.................. 110 

Housatonic River at Gaylordsville, Conn., 

vertical velocity measurements 

on ............................ 155,158 

Humphreys, A. A., and Abbot, H. L., cited 

on vertex of vertical velocity 

curves on Mississippi River .... 27-28 

observations by, on vertical velocity 

curves.......................... 26 

quoted on method of measuring stream 

flow by double floats ........... 15, 16 

Hydrometric pendulum, use of, for velocity 

measurements.................. 18 

Hydrometric tube, use of, for velocity measurements . .. . . . .. . .. . .. . . . .. .. . . 18 

Ice~covered rivers, vertical velocity measurements on .................. 158-162 

Indirect methods for measuring velocity, 

description of .................. 17-24 

Integration method, accuracy of measurements obtained by . . . . . . . . . . . . 99, 138 

description of .......................... 37-38 

variation of speed of meter in, table 

showing........................ 84 

James River at Cartersville·, Va., vertical 

velocity measurements on .... 142, 150 

Johnson, C. T., Mead, Elwood and, cited on 

weir discharge measurements.. 103 

Page. 

Judson, N. C., Little Tennessee River at, 

vertical velocity measurements 

on .............. , ............. 149,150 

Kingston, N. Y., Esopus Creek at, vertical 

velocity measurements on .... 153,158 

Esopus Creek at, vertical velocity measurements on, undl:'r ice . . . . . . 161, 162 

Kutter, W. R., Ganguillet, E. and, slope formula devised by............. .. . 23 

Little Tennessee River at Judson, N. C., 

method of using current meter 

at............................... 139 

vertical velocity measurements on ... 149, 150 

Lockport, N.Y., experiments at, with current meters and float rods ...... 52-53 

Low-water stream measurements, tests of. 100-105 

Lowell, Mass., velocity measurements iu 

wooden flume at ............... 28-:l9 

McKenzie, A., cited on current-meter observations......................... 30 

cited on employment of mid-depth 

point in current-meter measurements.......................... 37 

cited on employment of six-tenthsdepth point in current-meter 

measurements.................. 37 

cited on velocity measurements with 

double floats . . . . . . .. .. .. .. . .. .. 49 

Madison, N. C., Dan River at, vertical velocity measurements on ...... 143, 150 

Marr, G. A., experiments by, with double 

floats and current meters ....... 49-50 

observations by, on velocity of the Mississippi .. . . . .. . .. . .. .. . .. .. .. .. . 30 

Mattoax, Va., Appomattox River at, vertical velocity measurements on. 142,150 

Mead, Elwood, and Johnson, C. T., cited on 

weir discharge measurements.. 103 

Mississippi River, discharge of, formulas 

used for computation of........ 46 

methods of gaging. . . . . . . . .. . . . . .. . . . . . . 15-16 

slope measurements of . . . . . . . . . • . . . . . . . 24 

velocity in, variations of............... 30-31 

velocity measurements of, with double 

· floats and current meters, comparison of .. .. .. . .. .. .. .. .. .. . .. 49-50 

vertical velocity curve of . . . . . . . . . . . . . . 26 

vertical velocity curves on, table showing position of vertex of.... . . . . 28 

Moore, T.V., cited on method of computing discharge..... . . . . . . . . . . . . . . 46 

Moore current meter, figures showing...... 21 

Morgantown, N. C., Catawba River at, vertical velocity measurements o-n. 145-

146,150 

Mount Holly, N. C.,- Catawba River at, vertical velocity measurements on. 146, 

150 

Murphy, E. C., cited on ac:curacy of measurements with BIIUtll Price meter.............................. 139 

Myers, E. W., vertical velocity.curve measurements by.................... 139 

Neva River, vertical velocity curve of..... 26 

New York, streams in, ve.rtical velocity 

measurements on . . • . . . . . . . . . 150-158 
INDEX. 167 

.Page. 

New York State canal survey, discharge 

measurements by, with float 

rods and current meters........ 52-54 

Newell, F. H., acknowledgments to........ 60 

letter of transmittal by.. .. .. .. .. .. .. .. . 9 

Newpaltz, N. y:., Walkill River at, vertical 

velocity measurements on .... 157,158 

W alkill River at, vertical velocity measurements on, under ice ... 160-161, 162 

Newport, Tenn., Pigeon River at, vertical 

velocity measurements on .... 148,150 

Newport (Oldtown}, Tenn., French Broad 

River at, vertical velocity measurements on .................. 148,150 

Niagara River, discharge measurements 

of............................... 45 

Nolichucky River at Greeneville, Tenn., 

vertical velocity measurements 

on ........................ 147-148, 150 

North Carolina, rivers in, verticar velocity 

measurements on ............... _. 143, 

144-146,148-149,150 

North Wilkesboro, N.C., Reddie River at, 

vertic.al velocity measurements 

on ............................ 144,150 

Yadkin River at, vertical velocity measurements on .............. 144-145,150 

Oldtown (Newport), Tenn., French Broad 

River at, vertical velocity measurements on .................. 148,150 

Olivebridge, N.Y., Esopus Creek at, vertical velocity measurements 

on ................... ::... . . . .. 154, 158 

Oswego River at Battle Island, N.Y., cross 

section of. . . . . . . . . . . . . . . . . .. . .. . 129 

discharge measurements of . . . . . . . . . . . . 130 

gaging station on....................... 129 

view showing car and cable of...... 112 

measured and mean discharge of, comparison of..... . . .. . . .. . . .. . .. .. . 132 

station-rating curve for . . . . . . . . . . . . . . . . 130 

station-rating table for . . . . . . . . . . . . . . . . . 131 

surface slope of, diagram showing...... 135 

table showing...................... 136 

velocity curves of ................ 131, 133, 134 

velocity of, table showing change of, 

with change in river stages .. 135,136 

Paul, E. G., meter ratings by............... 86 

Pigeon River at Newport, Tenn., vertical 

velocity measurements on .... 148,150 

Pitot, --, tube invented by, for measuring velocity .. .. .. .. .. .. .. .. .. .. 18 

Pitot tube, discharge measurements with, 

compared with current-meter 

measurements .................. 96-97 

discharge measurements with, compared with rectangular orifice 

measurements .................. 47-48 

compared with surfll-Ce-floot measurements....................... 47 

featuresof .............................. 18-20 

ratings of, results of . . • . • • .. • . • . . . . . . . . . 43 

views of .. .. .. .. . .. . .. .. .. .. . . .. .. .. .. .. 19 

Point method, accuracy of results by use 

of............................... 138 

description of ......... ~ .............. _.. 37 

Page . 

Prattsville, N. Y., Schoharie Creek at, vertical velocity measurements 

on ..... :. . .. . . . . . . . . . .. . . . . . .. . 156, 158 

Pressure plate, use of, for velocity measurements.............................. 18 

Price, W. G., cited on integration method 

ofcurrent-metermea.Surements. 37 

Price meters, experiments with, at Cornell 

University canal ............... 62, 63 

low-watermeasurementswith, accuracy 

of ............................. 10'.2-105 

measurements with, accuracy of....... 69, 

70, 72, 82, 83, 90, 91, 93, 94, 96, 98, 139 

comparison of, with standard weir 

and other meter measurements. 65, 

66, 67' 68, 69, 70, 71, 72 

velocity curve~ derived from....... 73, 

74, 75, 76, 77,90 

method of holding..................... 137 

effect of ....................... 86, 87, 88,89 

rating of, observations and computations of ......................... 87,88 

rating tables for, in still and in moving 

water........................... 81 

ratings of. .............................. 42,43 

speed of, relation between velocity of 

water and...................... 84 

vertical velocity measurements with, 

under ice....... .. . . . . . .. . . . . . .. 159 

view of, plate showing . . . . . . . . . . . . . . . . . 20 

Pulsation of moving water, discussion of .. 28-32 

Racourt, --,observations by, on vertical 

velocity curves................. 26 

Rafter, George W., experiments by, on 

methods of measuring discharge, reference to............ 32 

Randolph, Va., Staunton River at, vertical 

velocity measurements on. 142-143, 150 

Rating of current meters, in still and in 

moving water . . . . . . . . . . . . . . . . . . 80-82 

methods of ............................. 40-44 

Rating tables, construction of, methods of. 41-44 

Rectangular orifices, discharge measurements by, compared with Pitot 

tube measurements ............ 47-48 

Reddie River at North Wilkesboro, N.C., 

vertical velocity measurements 

on ............................ 144,150 

Rhine River, velocity in, variations of ..•• 29, 30 

vertical velocity curveof.... ........... 26 

River gaging, application of Cornell experments to. . .. .. . . . . .. . .. .. . .. . . .. 96-97 

Roanoke River at Roanoke, Va., vertical 

velocity measurements of .... 142, 150 

Rochester, experiments at, with float rods 

and current meters ............. 52,53 

Rondout Creek at Rosendale, N.Y., vertical velocity measurements OI?-. 156-158 

vertical velocity measurements on, 

under ice . . . . . . . . . . . . . . . . . . . . . 161, 162 

Rosendale, N. Y., Rondout Creek at, vertical velocity measurements on. 156,158 

Rondout Creek at, vertical· velocity 

measurements on, under ice. 161-1b'2 

Sabin, L. C., velocity experiments by, on 

St. Clair River. . • . . . . . .. .. . . .. .. 31 
168 INDEX. 

Page. 

St. Clair River, velocity in, variations of... 31 

velocity measurements of, with double 

floats and current.meters, comparison of....................... 51 

vertical-velocity-curve work on, methods used in. . . . . . .. . . . . . . . . . . . . . 27 

Salisbury N. C., Yadkin River at, vertical 

-velocity measurements of .... 145,150 

Saluda River at Waterloo, S. C., vertical 

velocity measurements on .... 147,150 

Schlecht, W. W., vertical velocity measure· 

ments by, in ice-covered 

streams . . . . . . . . . . . . . . . 158, 150, 161, 162 

Schoharie Creek at Prattsville, N.Y., vertical velocity measurements on. 156, 158 

Skaneateles Lake outlet, di<;charge measurements-on .................. 108-111 

Slope formula for computation of velocity, 

applicability of................. 23 

disadvantages of . . . . . . . . . . . . . . . . . . . . . . . 23 

Smith, Hamilton, quoted on 'Francis's formula for computing discharge.. 33 

South Boston, Va., Dan River at, vertical 

velocity measurements on ... 144,150 

South Cairo, N. Y., Catskill Creek at, vertical velocity measurements on.. 151-

152,158 

South Carolina, rivers in, vertical velocity 

measurements on ........ 146-147,150 

Southern rivers, vertical velocity curve 

measurements on ... : . ....... 139-150 

Staunton River at Randolph, Va., vertical 

velocity measurements of. 142-143,150 

Stearns, Fteley and, discharge measurements by ....................... 33-34 

experiments and formula of. . . . . . . . . . . . 33-34 

experiments by, on measurement of 

discharge....................... 58 

formula of, for. computation of discharge.......................... 33 

Stream flow, formulas for computation of.. 33-34, 

44-47 

methods of measuring and computing ............................. 32-47 

Surface floats, discharge measurements by, 

compared with Pi tot tube measurements....................... 47 

use of, in measuring velocity........... 14 

Surface fluctuations, measurements of, 

methods of . . . . . . . . . . . . . . . . . . . . . 24--26 

Susquehanna River at Binghamton, N.Y., 

contours of bed of. . . . . . . . . . . . . . 122 

cross section of, diagram showing...... 123 

discharge measurements of . . . . . . • . . . . . 123 

mean and measured di~harge of, com- -

parison of . . . . . . . . . . . . . . . . . . . . . . 125 

station-rating curve of................. 124 

station-rating table of.............. . . . . 124 

surface slope of, diagram showing...... 128 

table showing...................... 127 

velocity curves of . . . . . . . . . . . . . . . . . . . . 125, 126 

velocity of·, diagrams showing changes 

in, for changes in river stage . . 126 

tables showing changes in, with 

change in river stage ......... 127,128 

·page. 

Syracuse, N. Y .• water supply of.. . . . . . . . . . 109 

Tenmile River at Dover Plains, N.Y., vertical velocity measurements 

on ........................ 156-157,158 

Tennessee, rivers in, vertical velocity meas-

. urements on .............. 147-148, 150 

Thames River, velocity in, variations of, 

table showing.................. 29 

Thermometer, use of, for measuring veloc* 

ity. -- ..... -... . . . . . . . . . . . . . . . . . . 18 

Tillinghast, T. H., vertical velocity measurements by, in ice-covered 

streams ................... 158,160,161 

Torrance, C. E., acknowledgments to...... 60 

Tuckasegee River at Bryson, N.C., vertical 

velocity measurements o-:t ... 148-149, 

150 

Truckee River, discharge measurements 

on .............•..•..•........ 111-112 

Truckee River flume, view of, plate show· 

ing ...... ...•................... 112 

United States Lake Survey gage, description and figure of. . . . . . . . . . . . . . . 24-25 

record of . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 

Unwin, W. C., cited on variations in velocity of the Thames........... 29 

Velocities, vertical distribution of, in icecovered streams .............. 158-162 

Velocity, methods of measuring ............ 13-24 

relation between depth and ......... 26, 38-40 

slope formula for computation of . . . . . . 23 

variations in, discussion of..... . . . . . . . . 28-32 

Velocity, mean. position of .... · ............ 99,137 

ratio of bottom velocity to . . . . . . . . . . . . . 99 

ratio of mid-depth velocity to . . . . . . . . . . 99 

relation between maximum and, table 

showing . . . . . . . . . . . . . . . . . . . . . . . . 78, 79 

Velocity, mean and average, of surface and 

bottom, relation between . . . . . . 82-83 

Velocity, mid-depth, ratio between mean 

and............................. 49 

Velocity, surface, experiments on, with float 

rods and current meters........ 90-92 

relation betwee~ bottom velocity 

and............................. 99 

Velocity curves, conditions affecting ...... 26-27 

diagrams showing ...... -.......... 73, 74, 75,76 

methods of obtaining . . . . . • . . . . . . . . . . . . 27 

vertex of, position of.... . . . . . . . . . . . . . . . 27-28 

&e also River names. 

Vertex of vertical velocity curves, position 

of............................... 28 

Vertical velocity measurements on Southern rivers, record of .......... 139-150 

field notes of ......................... 140-141 

Vertical-velocity-curve method, accuracy 

of results with.................. 138 

Virginia, rivers in, vertical velocity measurements on .......... 142-143,144, 150 

Walkill River at Newpaltz, N. Y., vertical 

velocity measurements of, under ice .. ~ ............... 160-161,162 

vertical velocity measurements on ... 157,158 

Waltman,-----, observations by, on vertical velocity curves • . . . . . . . . • •• • 26 
INDEX. 169. 

Pag_e. 

Wappinger Creek at Wappingers Falls, 

N.Y., vertical velocity measurements on . . . . . .. . .. . . . . .. . . . . . . . 158 

Watauga River at Elizabethtown, Tenn., 

vertical velocity measurements 

on ............................ 147,150 

Wateree (Catawba) River at Camden, 8. C., 

vertical velocity measurements 

on ............................ 146,158 

Waterloo, 8. C., Saluda River at, vertical 

velocitymeasurementson .... 147,150 

Weeks, E. F., elevations furnished by, at 

Binghamton, N.Y.............. 121 

Weir, sharp-crested, figure-showing. . . . . . . . 33 

Weirs, discharge measurements by, compared with float rod measurements .......................... 54-58 

discharge measurements by means 

of. .............................. 32-34 

() 

Page 

Weirs, discharge measurements by means 

of, compared with currentmeter measurements ..... 58-59, 65-7:.! 

discharge measurements by means of, 

compared withlow-velocitycurrent-meter measurements ...... 93-95 

experiments with ..... -. :: •.... - 62, 63, 64 

formulas for determining discharge 

over . .. . . . .. . . .. . .. .. . . .. . . . 32-34, llO 

view of, plate showing . .. .. .. .. .. .. .. .. 102 

Weser River, vertical velocity curve of..... 26 

Williams, Gardiner S.,acknowledgments to 60 

Willowglen weir, plan of; figure showing.. 109 

vertical velocity curves of.............. 110 

Yadkin River at North Wilkesboro, N.C., 

vertical velocity measurements 

on ........................ 144-145,150 

Yadkin River at Salisbury, N. C., vertical 

velocity measurements of. ... 145, 150 

LIBRARY CATALOGUE SLIPS. 

[Mount each slip upon a separate card, placing the subject at the top of the 

second slip. The name of the series should not be repeated on the series 

card, but the additional numbers should be added, as rece~ved, to the first 

entry.] 

Murphy, Edward Charles. 

. . . Accuracy of stream measurements, 2d enl. ed., 

~ by Edward Charles Murphy. Washington, Gov't print. 

!l off., r9o4. 

169 p., 11. illus., 6 pl., diagrs. 23lcm, (U.S. ~~ica.hmrvey. Watersupply and irrigation paper no. 95.) 

Subject series: M, General hydrographic investigations, 10. 

"Revision and enlargement of paper no. 64." 1902. 

Murphy, Edward Charles . 

. . . Accuracy of stream measurements, 2d enl. ed., 

~ by Edward Charles Murphy. Washington, Gov't print. 'S 

fl. of!., 1904. 

169 p., 11. illus., 6 pl., diagrs. 23lcm, (U.S. Geological survey. Watersupply and irrigation paper no. 95.) 

Subject series: M, General hydrographic investigations, 10. 

" Revision and enlargement of paper no. 64." 1902. 

U. S. Geological survey. 

! Water-supply and irrigation papers. ~ 

oo no. 95· Murphy, E. C., Accuracy of 'stream measurements, 2d enl. ed. r 904. 

U. S. Dept. of the Interior. 

see also 

U. S. Geological suryey.