57TH CoNGREss, } HOUSE OF REPRESENTATIVES. j DocUMENT 

1st Session. 1 No. 484. 

DEPARTMENT OF THE INTERIOR 

WATER-SUPPLY 

AND 

IRRIGATION PAPERS 

OF THE 

UNrrED STATES GEOLOGICAL SURVEY 

No. 64 

ACCURACY OF STREAM MEASUREMENTS.-1\IURPHY 

WASHINGTON 

GOVERNMEN'l' PRINTING OFFICE 

1902 

UNITED STATES GEOLOGICAL SURVEY 

CHARLES D. WALCOTT, DIRECTOR 

ACCURACY 

OF 

STREAM MEASUREMENTS 

BY 

EDWARD CHARLES MURPHY 

WASHINGTON 

GOVERNMENT PRINTING OFFICE 

1902 

CONTENTS. 

Page. 

Letter of transmittal .. _ . ____ .. __ ....... _ . .. _____ ... __ . _ ............ __ •.....•.. -- . .. .. .. .. 9 

Factors controlling accuracy of stream measurements .... ___ .... _ ......... -- .. -.. 11 

Methods of measuring velocity ...... _. ___ ... _ .... __ ...................... _ ....... __ ..... -.... 13 

Direct methods _ ......... _ ..................... _ ............... _ .. _ ... ___ .... _ ......... _ _ 14 

Surface floats ..... ____ ----·-·---- ____ ----------- _______ ··-------- 14. 

Double floats ________ .. _. _ .. ___________ ........... _ .. _ .... _ _ _ .... _. __ ... _ _ _ _ _ _ 14 

Float rods __ .. ___ .. _ _ _ _ . _____ .. _ ... __ ...... _. __ .... _ .... _ ....... _. _____ ... __ .. _ _ 16 

Float frame _____ . _ .... __ . ___ .... ________ ........ ___ .. ______ .. _ _ __ .. _ _ _ _ _ _ 17 

Indirect methods ... __ ... _ . _ _ _ .. __ .. _______ .... _ .. _ . _______ .. _ ....... ____ -_ _ . _ 17 

Float wheeL ____ .. _____ .. ________ ..... _.. _. _. ___ .. __ . _ . __ .. ___ .. _. _ . _. 17 

Pressure plate . ______ .. _________ ...... _ . ____ .... ___ .. __ ..... ____ .. _ _ _ _ _ _ _ _ _ 17 

Box with hole in side _____ ..... __ .. _ _ _ _ _ _ ..... _ .. ___ .. __ .. _ ...... __ ..... __ .. _ . _ 17 

Hydromet-ric tube _____ .. ___ . __ .... , .. __ .. __ .. _ ..... _. ___ ............. _ ... _ .. _ .... _ 17 

Hydrometric pendulum ... __ .. _ ........ _ _ _ ____ .. __ .... _ ........ v. _ ... ____ ...... 18 

Thennometer .. _____ .. _ ...... __ .. ___ . _ ... __ . _ ... _ .. _ ..... _. _ .. _. __ .......... _ .. .. 18 

Pi tot tube . _ .... .. _ .. _. _____ . ____ .. __ .... ________ . _ ...... _ ..... _ .... __ ..... 18 

Current meter __ ...... _ .. _ ...... _ ...... _ .. __ . _ . ____ .... _ .... _ ..... _ .... __ .... _ .... _. . 19 

Slope formula .................... ·--·---- ..... ____ ............................ 22 

Measurement of surface fluctuations ___ .... _ _ _ _ _ ____ .. _ .. _ .. __ ... _ ... ___ .. _ ... __ . 23 

Vertical velocity curves . _____ ..... ______ ... _ ... ____ .... _ . ___ _ .. : __ .. _. _ ....... _ .... _ _ 25 

Pulsation of moving water __ ~ .. _ .... _ . _ ....... ______________ . __ ..... ____ .. _ .. ____ .. 28 

Methods of measuring and computing stream flow . __ . _ _ _ .. __ . ___ .. .. .. _ _ _ _ _ · 31 

Weirs ____ . ____ .. _ _ _ _ . _ . _ . . __ ..... _ .. _ _ _ _ _ . __ .. _ .. _ . _ .. __ . _ .. __ .. ____ .. _ _ _ _ _ _ 31 

Francis's experiments and formula_ .. __ ..... __ ... _ ..... _ ...... _______ . 32 

Fteley and Stearns's experiments and formula ... _ .. _. __ ... ___ . ___ .. _ 33 

Bazin's formula ____ .. ______ ----· _ ··--- ..... _______________ .......... 33 

Current meters __ ....... __ ......... _ .. ___ ....... _____ . ___ .......... _ ... _ .. ___ ...... __ .. 34 

Point and integration methods .. __ ......... __ .... . ___ . _. _ .. __ . _ _ _ _ __ 36 

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

Rating of meters and construction of rating tables __ ...... _ .. _ ........ _. _ 39 

General formulre for computing discharge ..... _____ .. ________ . _______ .___ 44 

Comparisons of results with different instruments and methods.___________ 46 

Surface floats and Pi tot tube _______ ...... _ .. ______ .... ____ . _ ........... _ .. ___ ........ 46 

Pi tot tube and rectangular orifices .... _ ... __ .. _ .. _. _ ..... __ . ___ .. ____ .. _ .. _...... 47 

Double floats and current meter ________ ..... __ .... __ .... ___ .. _. _____ .. ____ ... 47 

Ellis's experiments ... _. _. __ . __ .. _ ..... _ ..... __ . __ ....... _ ...... ____ ... _.. _ .. .. .. 47 

Marr's experiments . _ .. _____ .. ______ .. _ ...... _ . __ .... _ .. ____ . . _ .. ___ .. .. .. . .. 48 

Henry's experiments ____ ... ___ .. __ ........... ____ .... _ ........ ___ ....... __ .. _ ... _ 49 

Gordon's experiments ... _ .. _ .... __ .. ___ . ____ .. ___ .... __________ . .. .. 51 

Float rods and currant meter ... __ ...... __ .. _ .... ___ .............. __ .. _ .. . .. . .. • . . • • . . 51 

New York State canal survey experiments __ ... _. __ ....... __ .... __ .... __ 51 

1\1 urphy's experiments at Cornel1 University ____ ...... _. _. _ .. _____ ...... 53 

Float rods and weir .. _ .. _ .. _ .... ______ ..... ___ ........... _ .. _ .. _________ . _ •. _ _ _ __ _ 53 

Francis's experiments_ .... _ ... ___ .. __ .. ____ ........ __ .. _ ... __ .. __ .. ____ ... _ .. _ 53 

Come~l University experiments _ .. __ .. _ .. _ .. __ ..... ___ • ___ •• _____ • _____ . 54 

fi 
6 CONTENTS. 

Comparisons of results with different instruments and methods-Cf'nt'd. 

Current meter and weir ___ .... _____ ~ _ _ _ _ _ _ _ _ ________ . ______ . __ . -___ - -

Fteley and Stearns's experiments ___ . _ . ___ ... ___ . _____ . _ .... ____ . __ - _ 

Murphy's experiments at Cornell University ____________ .-.-_. __ .. --

Experiments at Cornell University hydraulic laboratory ___ ---- ___ -_. ___ .. - Introductory _ . ___________ .. __ .. _ . ___ . ___ .. ___ .. _ .. ____ . ____ .... _ .. __ . _ . _ 

Description of Cornell hydraulic laboratory .. _ ...... __ .. _ .... _ .. - __ .. _. -. Scope of experiments _ _ _ . ____ . _________ . _ . _ . ________ . ________ . _ . ____ . 

Method of experimentation ____ . __ . ____ . ________ . ___ . __ . _ _ _ _ _ _ _____ -. 

Reduction of experiments. ______ . ____ ... _____ . __ ... __ ... __ . _______ . 

Discussion of results _ _ _ _ _ _ _ _ _ _ _ _ _ ________ . __ .. _____ . _ .. _ _ _ _ _ _ _ _ ____ . 

Comparisons of discharge measurements _. _. -- ___ . ___ .. __ . _______ . 

Velocity curves_ . ________ . _ _ _ _ _ _ _ _ _ _ _ ________ . ___ . _ .. _ . _________ _ 

Mean velocity by integration in verticals. ___ . ___ -- ____ .. ____ . ____ _ 

Rating meters in still and in moving water. ______ .. ___ .... ___ ... __ _ 

Error in using average of bottom and surface velocities for mean 

velocity ___ . _. ____ . _____ ... _ . __ . -. . - . ---- .. -.. --- -- --- ----- --- ·-

Comparison of results by three methods of operating meter _______ . 

Comparison of results obtained in 1900with those obtained in 1901.. 

Effect of method of holding meter in water ___ .. __ .. _ _ _ . __________ _ 

Surface velocity experiments with fioa t rods and with current meters_ 

Application of results to ordinary river gaging __ . ___ . __ . _. __ 

Accuracy of results ________ .. _______ . ____ . _.. _... . ___ .. _. _. ____ _ 

Conclusions ___ . ____ . __ .. _______________________ . _____ . ____ . __ .. _ . 

Index __________ . ____________________________________ . ______________ . _ ~ ___ _ 

Page. 

57 

57 

58 

58 

58 

59 

61 

62 

63 

64 

64 

72 

80 

80 

82 

83 

85 

85 

89 

92 

93 

94 

97 
ILLUSTRATIONS. 

Page. 

PLATE L Price electric current meters. __ ... _. __ . __ ... ____ . _ . __ .. _----.--. . 20 

II. Hydraulic laboratory canal of Cornell University, showing corps 

engaged in making discharge experiments __ .. _ . . . . . .. . . . __ . . -. - 58 

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 

FIG. 1. Double float used by Ellis in Connecticut River survey in 1874_--.. 14 

2. Pi tot tube __ . _____ . __ .. _. _. ___ ... __ . _. _ .. __ ... ____ . _ ... ___ .. _. __ .-. 19 

3. Moore current meter _ _ _ . __ . . ____ .. __ . _ .. _. __ . __ ... ___ . ____ -. -. -- 20 

4. Haskell current meter_ . __ . _ . . _ _ _ _ _ . _ _ _ .. _ .. _ ... _. _ ...... _ .. ___ --. 21 

5. Fteley current meter ____ . . _ .. _ . . . _ . _____ .. . . . . .. ... _ .. ____ . ___ .... _ 21 

6. Self-registering water gage used by United States Lake Survey___ 24 

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

Lake Survey_. __ ... __ .. ____ ..... _ . _____ ..... . __ . __ .. ___ .. _ •. _____ . 24 

8. Hook gage for measuring surface fluctuations . __ ... . _. _______ --.. 25 

9. Sharp-crested weir ___ . _ . _... . . . _ .. _. _ ... ___ ..... __ ... _ .. _____ .- _ . __ . 32 

10. Method of using current meter on large river_. __ . __ ... _·-- ___ .. -- 34 

11. Device for holding meter in place __ .. _ . _ .. _ _ _. _. ___ .. _ ... __ . __ . _ 35 

12. Harlacher's apparatus for moving a meter with uniform velocity.. 36 

13. Details of Harlacher's apparatus for moving a meter with uniform 

velocity .. __ . _. __ . __ ... ___ . ______ . __ .. __ . _. _____ . _ .. ___ . _ .. _ _ _ _ _ _ 37 

14. Diagram illustrating Harlacher's method of computing flood discharge _ . _ . . .. . . ___ .. _______ ... _ . ___ . ___ . _____ . ___ . _____ ..... __ .. _ . 46 

15. Plan and elevation of Cornell University experiment canaL....... 60 

16. Diagram showing difference between meter discharge by ordinary 

method and weir discharge, from measurements in Cornell University experiment canaL ___ . ___ . _. _. _. ___________ .... _ _ _. _ _ _ . 68 

17. Diagram showing difference between meter discharge by six-tenthsdepth and integration methods and weir discharge, from measurements in Cornell University experiment canaL_ ... _. __ .-. _ _ _ 68 

18. Diagram showing difference between meter discharge with different meters and weir discharge in experiments of series E in Cornell University experiment canal ..... _ ... __ . __________ .. __ . ___ . _ _ _ _ 69 

19. Curves of equal velocity in experiment No. 11, series A .. ____ .. _._ 72 

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

Price meter No. 88 ___ ... _ .... ____ . ____ .. ___ .... _ .. _____ . ___ . _ _ _ _ 72 

21. Curves of equal velocity in experiment No.14, series C ----------- 72 

22. Curves of equal velocity in experiment No. 20, series D ... _ .... _ _ _ _ 73 

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

and with small Price meter No. 351 in experiments in series A _. 73 

24. Vertical velocity curves obtained with Fteley current meter in 

experiments in series A __ ... ____ . _. _. _ _ _ _ _ _ __ .....• ___ .. _____ . 74 

7 
8 ILLUSTRATIONS. 

Page. 

FIG. 25. Vertical velocity curves obtained with small Price meter No. 351, 

large Price meter No. 88, and Fteley meter in experiments in 

series B _________ . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ____ .. ____ .. . . _ 74 

26. Vertical velocity curves obtained with small Price meters Nos. 363 

and 351 in experiments in series C _______________________ . _ _ _ _ _ _ 75 

27. Vertical velocity curves obtained with small Price meters Nos. 363 

and 351 in experimenis in series C _________ . ___ . ___ . ___ . _ _ _ _ _ _ _ 75 

28. Vertical velocity curves obtained with Haskell meter No.3 and 

small Price meter No. 363 in experiments in series D _____ . _ _ _ _ 76 

29. Curves showing relation between revolutions 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_------ ---- ---. ---------- ----------- . ------ ------------ -- 89 

30. Vertical velocity curves from simultaneous experiments of series E 

with small Price meter No. 363 and with Haskell meter No.3__ 90 
LETTER OF TRANSMITTAL. 

DEPARTMENT OF THE INTERIOR, 

UNITED STATES GEOLOGICAL SURVEY, 

Washi,ngton, D. C., December 30, 1901. 

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

by Prof. E. C. Murphy, of Cornell University, Ithaca, N. Y., giving 

the results of investigations made by him into the accuracy of stream 

measurements as ordinarily conducted by the hydrographers of this 

Survey. 

Professor Murphy was for svme time resident hydrographer for 

eastern Kansas, and carried on in the field measurements of several 

rivers, being thus by actual practice thoroughly familiar with the 

operations of the hydrographic branch of the Geological Survey. 

Upon his removal to Ithaca Professor .1\f urphy began a series of 

experiment,s, using the facilities offered by the hydraulic laboratory 

of Cornell University. 

While the methods of river measurement at present in use are 

believed to be sufficiently accurate for t,he purposes of ascertaining 

the water resources of the United States, yet it is important to know 

their probable accuracy, and particularly the accuracy of the instruments which are commonly employed. Through such knowledge and 

experience gained from time t,o time it will be possible to improve 

upon the methods, in the interest of greater exactness or wider diffusion of the work. 

I therefore request that this manuscript be published in the series 

of Water-Supply and Irrigation Papers. 

Very respectfully, F. H. NEWELL, 

Hydrographer in Charge. 

Hon. CHARLES D. WALCOTT, 

Director;· Unitefl States Geological Survey. 

9 

ACCURACY OF STREAM MEASUREMENTS. 

By EDWARD C. MURPHY. 

FACTORS CONTROLLING ACCURACY OF STREAM MEASUREMENTS. 

The accuracy of a stream measurement depends largely upon the 

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

measured. There is no special difficulty in measuring the first factor, 

but the second factor-the velocity-is very difficult to measure, chiefly 

for the reason that it is 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 is necessary to measure it at many points, but it is constantly 

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

the discharge (and consequently 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 frequency of the pulsations or of the 

laws governing them. J. B. Francis says: a "It is observed that there 

is a continual change in all parts of these channels, although there 

may be no sensible change in the volume of water flowing and consequently in the mean velocity." Captain Cunningham says: b "'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 velocity varies 

everywhere, largely from instant to instant. * * * It is analogous to the unsteady motion of wind, which is exemplified by the 

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

Henry says: c "All water in motion 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 ma~ing and computing stream measurements. If ~nly a few 

observations of velocity are made, these may all, or nearly all, be 

a Trans. Am. Soc. Civ. Eng., Vol. VII, p. 111. 

b Recent Hydraulic Experiments: Proc. Inst. Civ. Eng., Vol. LXXI, p. 7. 

cJour. Franklin Inst., Vol. LXII, p. 323. 

11 
12 ACCURACY OF STREAM MEASUREMENTS. (N0.64. 

made at a time of maximum impulse, and thus the measured mean 

velocity be too large; or it is possible that most 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 impulse, while others, as the 

current meter, show the average velocity due to all the impulses 

during the observation. 

The 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 aCI·os~, but all as a rule having a general motion downstream. 

The accuracy of a discharge measurement also depends much upon 

the physical features of the stream at. the discharge section or point 

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

reach and far enough from a bend to 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 be easily measurable. The banks should be 

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

should be free from the influence of 1nilldams and bridge piers. In 

addition, economy requires that the section selected be easily aecessible 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 

of bed in some cases and silting in other cases 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 little appears to have been done in the way of determining the degree of accuracy of the measurements. Even when the 
MURPHY.) METHODS OF MEASURING VELOCITY. 13 

experimenter has used 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 on the following pages. 

METHODS OF MEASURING VELOCITY. 

The methods that have beeu used for measuring velocity may be 

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

methods include all ways of ascertaining the velocity of water from 

bodies floating in it, such as surface floats, float rods, double floats, 

etc. 'rhe indirect methods include measurements with the current 

meter, pressure plates, the thermometer, etc., by which the velocity 

of the water is inferred from its impact, its pressure, or its temperature. Measurements by the direct methods are simple, requiring only 

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

over a certain distance, while in the indirect 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 it 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 meter-measure instantaneously the velocity 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 moved with uniform velocity, 

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

results; but since all moving water, even the most undisturbed, has 

these pulsations, velocity measurement's by the indirect methods are 

decidedly more accurate than those by the direct methods. One 

measurement with a current meter is worth several measurements 

with floats. 

There is another reason why indirect measurements are preferable 

to direct 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 distance, and this requires 

the measurement of many cross sections between the upper and the 

lower section, while by the indirect methods the measurement of only 

one area is required. 
14 ACCURACY OF STREAM MEASUREMENTS. [No.M. 

DIRECT METHODS. 

SURFACE 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, but the velocities 

obtaine~ 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 established. The time consumed by the floats in 

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

observed, and the distance divided by the observed time gives the 

surface velocity at that point for that time. 

- ----- ----- ----------. ...... 

This method was used by Dubuat 

in 1779 in gaging the Canal du .Jard, 

in France, and in 1782 in gaging the 

Haine River, Belgium; by Trechsel, 

in 1825, to gage the Outer Aar, near 

Thun; byWampfler,in-1867, to gage 

the Simme Canal, Switzerland; by 

Harlacher, in 1881, to gage the Elbe, 

in Bohemia (at high wat.er 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 float 

somewhat heavier than water con- ~~~M~&k~~.i~:~~S nected to it by a cord or a small 

FIG. 1.-Double float used by Ellis in Con- rope. The office of the upper float 

necticut River survey in 1874. 

is to support the lower float and indicate its position. The connecting cord can 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 

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

high, 8-! inches outside diameter, and 7t inches inside diameter .. 'I'wo 

brass wires were soldered across 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 cord was attached. The surface float was an 

ellipsoid of tin 6 inches in diameter and li 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 
MURPHY.) DIRECT METHODS. 15 

Humphreys and Abbot in gaging the Mississippi River in 1351 and 

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

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

to the axis of the current, and a section at eaeh end of this base was 

marked out at right angles to it. The time consumed by each float 

in passing between these sections and 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 floats were placed in the river from a boat about 100 

feet above the upper section and were picked up by a man in a boat 

some distance below the lower section. At the instant a float passed 

the upper section a· signal was given, the watches were started, and 

the 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 was 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 

ieet. long and the time of run of the floats has been recorded Jn a 

chronograph. 

This method has it's advantages and its disadvantages. In very 

deep rivers, such as the Mississippi, or in streams carrying weeds and 

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

in their report on the Mississippi River, say: h "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 don ble floats were 

found to g:ive 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 rivers, says: c "All the 

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

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

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

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

direction and velocit.y 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 much less than the length of the cord. 

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

a Report on the Mississippi River, by Humphreys and Abbot, p. 224. 

bOp. cit., p. 225. 

cJour. Franklin Inst., Vol. LXII, p.l67. 
16 ACCURACY OF STREAM. MEASUREMENTS. [N0.64. 

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

time, 

This method of gaging was used in the 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 t.he outlets of the Great I ... akes. 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 t.o gage the 

Irawadi River. For comparisons of accuracy of this method with 

others, see pages 47 to 51. 

FLOAT RODS. 

Professor Cabeoa was the first to use the float rod for measuring 

velocity. This was in 1646. 'rhe 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 itsupper 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 writ.er in 1900 in 

the New York State canal survey is as follows: Two surveyor's 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 tothis a boat 

was attached by pulleys, so that a man in the boat could easily move 

himself back and fort.h by pulling on the rope. Another rope was 

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

a boat operated from it in a similar way. 'fhe floats were put in by 

the man in the upper boat, two at a time and about 5 feet apart, and 

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

called to the recorder the position of each. ,As 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 each pair of floats between the chains. A short 

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

The advant.ages and disadvantages of the method may be summed 

up briefly as follows: 

Advantages.-For artificial channels of moderate and uniform 

depth and with floating grass and weeds this is probably the best 

method to use. The advantages of float rods as 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 are not affected by silt 

and weeds; (5) they measure forward velocity; (6) they can be made 

by a common workman; and (7) they are cheap. 

"' See Report of New York Barge Canal, 1901, p. 869. 

b Proc. Inst. Civil Eng., Vol. LXXI, p. 1. 
MURPHY.) INDIRECT METHODS. 17 

Disadvantages.-The rods are affected to some extent by wind; they 

do not give mean velocity, but velocity of impulses; they can not be 

used in deep streams or in streams of rough or irregular bed, and 

·they are expensive to operate. 

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

in 1880; by Francis, in 1852, on a canal at Lowell, Mass.; by Buffon, 

on the Tiber River, in 1821; by Krayenhoff, on the Rhine, in 1812; 

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

in 1881. 

FLOAT FRAME. 

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

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

difficulties in th~ way of the use of this instrument. 

INDIRECT METHODS. 

The following instruments and methods have been 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. 

PRESSURE PLATE. 

In 1779 Gaunthy invented the pressure plate, which consists of a 

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

computed from the weight necessary to keep it vertical. 'rhe tachometer used by Briinings to gage the Rhine and the one used by 

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

Captain Boileau also used a pressure plate in his tachometer. 

BOX WITH HOLE IN SIDE. 

A box with a hole in the side was used by Grandi in 1730tomeasure 

velocity. It was lowered gradually from the surface to the bottom 

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

the amount of water in the box. 

l HYDROMETRIC TUBE. 

This instr ment was used by Captain Boileau in 1850. It consists 

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

one end and a small opening at the other end. The tube 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 is computed. 

IRR 64-02--2 
18 ACCURACY OF STREAM MEASUREMENTS. [No.64. 

HYDROMETRIC PENDULUM. 

This instrument was used by Castelli in 1628. It consists of a ball 

suspended from the center of a graduated arc. The velocity is comput.ed from the weight of the ball and the angle of the string when 

the water impinges on it. 

THERMOMETER. 

Leslie used a thermometer for measuring 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 in 1730. 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 will rise to a convenient height. The velocity is found from 

the difference in the readings of the water columns. Like floats, this 

is an impulse-measuring- instrument, but in using it both maximum 

and minimum impulses are observed and a mean is found. After the 

instrument is in place and the stop cocks R and R' are opened one of 

the observers applies his mouth to the tube 0, removes the air until 

the surface of the water in the tubes stands at a convenient height 

to read, and then closes the upper cock (R). He observes the columns until thP.y reach a maximum height, when he closes 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 column, from which he 

makes the following deduction: If a' is the maximum reading of column A., and b' 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, then a'-b'=d', the difference for the maximum impulse, and 

d' +d" a"-b"=d", the difference for the minimum impulse, and 2 is 

the mean difference of the column readings for the two impulses. 

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

:E ~ is the mean of the values of these column differences (:Ed= 

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

V=c.J 2g:E~, c being the coefficient found by rating and g the accel-

• Rechercheshydrauliques, entreprises par M. H. Darcycontinuees 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 lnstitut Impe 

rial de France, Paris, 1865, Vol. XIX, Pl. XVII, fig. 5. 
MURPHY.] INDIRECT METHODS. 

eration of gravity. The velocity can very quickly be 

found by one accustomed to 

using the instrument. The 

accuracy of V depends on 

that of c and on .J ~ d, the 

greater the number of d's, or 

sets of observations, the more 

nearly accurate will be the 

value of V. 

CURRENT METER. 

The current meter had its 

beginning in the float wheel 

used by Borda and Dubuat 

to obtain surface velocities. 

In 1790 Waltman modified 

this wheel so that it could 

be used below the surface. 

His meter had helicoidal 

blades and an endless screw 

on its axis, which by gearing 

into a train of wheels caused 

a record of the n urn ber of 

revolutions of the wheel to 

be made on dials. It was 

moved up and down on a 1·od 

the lower end of which 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 surface to read 

the revolutions, which was a 

great drawback to its use, as 

was also the fact that dirt in 

the water retarded the train 

of wheels. Lepont sought to 

remove these difficulties by 

bringing the recording apparatus to the surface, away 

from the dirty water and 

where it could be read without lifting the meter. He 

did this by introducing a FIG. 2-Pitot tube. 
20 ACCURACY OF STREAM MEASUREMENTS. [No.64. 

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 

PLAN. W/71f $ECT70N OF CASE SHOWING WH«LWORK 

FIG. 3.-Moore current meter. 

lessened, but the meter had to be 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 difficulties 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 
U. S. GEOLOGICAL SURVEY WATER-SUPPLY PAPER NO. 64 PL. I 

PRICE ELECTR IC CURRENT METERS. 
MURPHY.] INDIRECT METHODS. 21 

is used it is worked by a spring and not by the meter, and, furthermore, it is not necessary to lift the meter to the surface to read the 

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

Fro. 4.-Haskell current meter. 

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

by Henry is shown in fig. 10, page 34; that used by Moore in fig. 3. 

Meters in use at the present day may be divided into two classes: 

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

and {2) those in which it revolves 

about a vertieal axis. The former 

class is illustrated by the Haskell 

and Fteley meters, shown in figs. 4 

and 5, respectively, and the latter 

class by the Price meter, shown in 

Pl. I. Meters of the latter class 

have some advantages over those 

of 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 from 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 the former class, so that both 

low and high velocities can be 

measured more accurately with 

meters of the second class than 

with those of the first class. For 

example, by comparing the rating 

table of Haskell meter No. 3 on 

FIG. 5.-Fteley current meter. 

page 81 with that of small 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 revolutions per second in water having 
22 ACCURACY OF STREAM MEASUREMENTS. (NO. 64. 

-, 

a velocity of 7 feet per second, while the latter requires a velocity of 

about 0.06 foot per second to start it and makes only 3.02 revolutions 

in water having a velocity of 7 feet per second. A rate of 3 revolutions per second can easily be recorded 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 be 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 requires 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 without some electrical device for indicating to the 

observer the revolutions in a given time, and which must be lifted 

out of the water to read the revolutions, is a thing of the past. 'l.,oo 

much time is lost in making the readings. 'llhe acoustic-meter is not 

a success. The clicks are not sufficiently loud to be heard when the 

water is deep and the place noisy. 

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

or mean velocity (any kind of a float gives the velocity of a comparatively few particles at some stage of a pulsation of the water, not 

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

For large streams the choice of instruments 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. 25 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 person, or at most two persons, 

can make the gaging with t.he meter, and the expense of moving the 

equipment from place to place is much greater for the rods than for 

the meter. 

SLOPE FORMULA. 

The velocity of a stream can be computed from measurements of 

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

knowledge of the roughness of the bottom 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 'n + .00281 

s 

J _,-- V= v Rs 1+ (41.6+ .00281) _!1;_ 

s vRs 

•Flow of Water in Rivers and Other Channels, by E. Ganguillet and W. R. Kutter. 
MURPHY.] MEASUREMENT OF SURFACE FLUCTUATIONS. 23 

In this formula V =velocity, in feet per second ; s =surface slope=~, h 

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

radius"=!' F being the cross-sectional area and w the wetted perimeter; and n a ratio whose value varies from 0.009 for a well-planed 

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

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

sewers to large rivers like the :Mississippi, its constants being determined from Bazin's gagings of small channels, from Humphreys and 

Abbot's gagings of the 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 saysa 

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

was 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 measurements of the Ganges Canal, says: b "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, c 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 south 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 current and a corresponding fall on one shore 

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

appreciable slope toward the north." · 

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

MEASUREMENT 01!, 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. d It is necessary, therefore, in accurate 

work to measure the surface fluctuations with great care. Wave 

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

"Trans. Am. Soc. Civ. Eng., Vol. XI, p. 23. 

bProc. Inst. Civ. Eng., Vol. LXXI, p.ll. 

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

dOn some streams there are places where the mean velocity remains nearly constant for several feet variation in stage of river. This is true of the Verdigris River at Liberty, Kans. See 

Nineteenth Ann. Rept. U.S. Geol. Survey, Pt. IV, p. 374. 
24 ACCURACY OF STREAM. MEASUREMENTS. (N0.64. 

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

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

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

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

time, or a moving scale with a fixed index from which the elevation 

of the surface is read. 

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

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

in fig. 6, is a good illustration of instruments of the first class. The 

center pen is connected to a float on the surface of the lake, and its 

r---~--~----J----r--~-n-~n_sJ----J----r----r--~~~ 

6 7 

1/erti'caf.scale 

H,or.i'zontal .$~ale 

NOON I<! 13 14 IS 16 

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

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 

moved at a uniform rate by clockwork. The two outer pens record 

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 
MURPHY.] VERTICAL VELOCITY CURVES. 25 

given by thP, corresponding ordinate of this curve. This figure illustrates the need of an accurate record of the change in 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. 8, is a good illustration 

of a gage of the second class. ·The frame is fastened 

firmly to a post in the water, and the elevat,ion of the 

zero reading is determined. By turning the milled 

nut the hook is raised until its point comes to the surface of the water. This can be done very accurately 

in still water, by means of the little spot, of light on 

the point of the hook. The scale is then read, and 

from it the SJ.Irface elevation is found. 

The water gage used by the United States Board of 

Engineers on Deep Waterways in 1897-98, on the 

Niagara River at Buffalo, N.Y., was of the box-withfloat type. The box was of wood, 7 inches high, 7 

inches wide, and 7 feet long, with a closed bottom and 

a removable cover. The box was fastened firmly in 

the water, with half its length below the surface. 

Water was admitted to it through one or more of three 

!-inch holes, allowing the float to change its elevation 

as the river stage changed and at the same time eliminating the effect of waves. The float, was a 2-quart 

bottle with a 7-foot staff, marked to feet, tenths, and 

hundredths, wedged into it. This staff extended up 

through the cover, and was marked so as to give the 

rise of the water surface above a certain plane as read 

at the cover of the box. 

VERTICAL VELOCITY CURVES. 

The relation between velocity and depth in a vertical section of a stream parallel to the· thread of the 

current, or the vertical velocity curve, is 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. 

FIG. 8.-Hook gage Much effort has been expended in investigating this for measuring 

relation and the change in it for change in river stage. surface fl.uctuaA s might be expected, the results of experiments in ~ 

this direction do not agree. Each investigator adopts a new form of 

curve to fit his observations. In 1791 Waltman made some observations on the Rhine, from which he concluded that the vertical velocity 

curve is a reversed parabola with its vertex below the bed of the river. 

In 1820 De Fontaine found the greatest velocity of the Rhine to be at 
2o ACCURACY OF STREAM MEASUREMENTS. LNo.64. 

the surface. He states that two inclined right lines intersecting about 

mid depth satisfy his vertical-curve observations. In 1824-1826 

Racourt made observations on the Neva River, from which he concluded that this curve is an ellipse whose minor axis is a little below 

the surface. 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 the character of the bed. For the Mississippi 

River, Humphreys and Abbot found it to be a parabola whose axis is 

three-tenths depth below the surface. Henry found it to be an ellipse 

for the 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 mentioned it appears t.hat the 

shape of the vertical velocity curve depends much on local conditions, 

as roughness of bed, slope, ratio of depth to width, wind, obstruct.ions, etc. Two facts must be borne in mind, however: (1) All the 

vertical velocity-curve observations obtained with a single meter 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 closely, 

so that it is quite possible for any or all of these curves to fit more or 

less closely a set of imperfect vertical velocity-curve observations. 

There are two methods of obtaining vertical velocity curves with 

current meters: (1) The single-meter method, and (2) the multiplemeter method. In the former a meter 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 t.he effect of pulsations. This 

requires one or more hours to a vertical, during which time a permanent change may occur in the mean velocity. In the latter method, 

however, this difficulty is overcome, for enough meters are used 

simultaneously to give the whole curve in one operation. 

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

direction of E. E. Haskell, United States assistant engineer, eleven 

meters were used at a time. These were fastened between two cables, 

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 lower 

meter was 1. 7 5 feet above the bottom; the other ten were placed at each 

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

one operation. The observer, with a stop watch in one hand and the 

switch handle in the other, started the watch and at a given instant 

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

end of the observation he stopped the watch and opened the circuits 
MURPHY.] VERTICAL VELOCITY CURVES. 27 

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

made with the meters arranged ns described, and from one to ten 

others of one hundred seconds each with the meters arranged in other 

ways in each vertical. 

There should be some criterion for the rejection of doubtful observations and the grouping of vertical velocity curves. The following 

table gives the position of the vertex of sixty-nine vertical velocity 

curves obtained on the Mississippi River by Humphreys and Abbott, 

and illustrates this need: 

Tab"le showing position of vertex of vertical velocity curves obtained on Mississippi 

River. 

First series. Second series. Total. 

Depth. Number Number Number Number Number Number 

of of of of of of 

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

------------·1------------------

Surface................................. 12 6.'3 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. _____________________________ _ 39 222 30 75 

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 34 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-t.enths depth below the surface. This combination of curves 

so dissimilar is, to say the least, very questionable. 'fhose in which 

the vertex is at or below seven-tenths depth should be rejected, 

or at h~ast 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. 

Vertical velocity curves 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 cases. · · 

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 comQ to the writer's observation the change in stage is 

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

roughness of bed decreases, 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. 
28 ACCURACY OF STREAM MEASUREMENTS. [No.64. 

PULSATION OF MOVING WATER. 

We have already called attention to the fact that one of the reasons 

it is difficult to measure 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 good average value of the velocity in one vertical of a canal. a J. B. Francis 

has made numerous measurements of the velocity with float rods in 

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

taken to have the usual causes of irregularity of motion suppressed. 

'rhe time of run was obtained by the use of an electric telegraph and 

a chronograph, and the depth was very carefully measured with a 

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

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

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

parts of the depth from the same cause."b Adam Baum has made 

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

Bridge of Constance. c He fixed a current meter 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 metm• 

on the variation in velocity in the river Thames. a He noted the time 

of each 100 revolutions, and upon plotting the time and the revolu-. 

tions found that they gave a very irregular curve. The mean 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: 

"Proc.lnst. Civ. Eng., Vol. LXXI, p. 8. 

b Trans. Am. Soc. Civ. Eng., Vol. VII, p.117. 

cProc. Inst. Civ. Eng., Vol. LXXI, pp.456-459. 

d Op. cit., pp. 348,34{1. 
MURPHY.) PULSATION OF MOVING WATER. 29 

Variation in velocity at three points of a vertical of Thames River as found by 

Unwin. 

At 0.5 meter depth; At3me- At6meVariation (Vru-!). a tersdepth; tersdepth; velocity found from- velocity velocity Vm found found 

from 100 from 100 

100revolu- 500revolu- revolu- revolu- At0.5me- At3me- At6 ~ne· 

tions. tions. tions. tions. ter depth. tersdepth .. tersdepth. 

Met.pm·sec. 1tfet.per sec. Met.pe1·sec. Met.per.~ec. Per cent. Per cent. Pel" cent. 1.909 1.877 1.861 1.111 -1.8 +6.6 - :3.6 

1.9!2 1.846 2.030 1.069 -3.6 -1.9 + 0.3 

1.987 1.846 1. 942 0.977 -6.0 +2.6 + 8.9 

1.942 1.846 2.030 1.180 -3.6 -1.9 -10.1 

1.861 1.832 2.030 1.044 +0.7 -1.9 + :!.6 

1.861 1.832 2.060 0.937 +0.7 --3.4 +U.6 

1.887 1.823 1.909 1.021 -0.7 +4.2 + 4.8 

1.861 1. 787 1.909 0.998 +0.7 +4.2 + 7.0 

I 1.861 1.809 1.8{11 0.977 +0.7 +6.7 + 8.9 

1.861 1. 787 2.030 1.094 +0.7 -1.9 - 2.1 

1.942 1.861 2.125 0.900 -3.6 -6.7 +Hi.l 

1.760 1.823 2.030 1.094 +6.1 -1.9 -2.1 

1.831 ............. -----· 2.006 1.021 +2.4 --4.7 + 4.7 

1. 719 ------------ 1.994 1.180 +8.3 0.0 -10.1 

1.942 .............................. 2.086 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 

"V=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 -H per cent and at 6 meters 

depth +16.1 percent and -37.4 per cent. The greatest difference in 

velocity, as shown by two consecutive 100-revolution periods, is 12 

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

velocity measurement of 100 revolutions 0.5 meter below the surface 

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

37 per cent. 

D. F. Henry a has observed t,his 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 ones 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." 

Harlacher b 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. 

Marr's simultaneous observat.ions of velocity in the Mississippi 

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

page 48. 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 consecut.ive periods of one minute each. The depth in 

aJour. Franklin Inst., Vol. LXII, p. 323. 

hTrans. Am. Soc. Civ. Eng., Vol. XII, p. 311. 

•Report on Current Meter Observations, Burlington, Iowa, by Maj. A. McKenzie, 1884. 
30 ACCURACY OF S'l'REA:M :MEASUREMENTS. [N0.64. 

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

meter is 4 feet above the bottom: 

Variation in velocity per minute in Mississippi River at Burlington, Iowa. 

Simultaneous observations in section 

No.1. 

Simultaneous observations in section 

No.2. 

Velocity V~ria- Velocity V~ria- Velocity V~ria- Velocity V~ria- 1 foot t1on 9.1 feet bon 3.6 feet bon 23.6 feet twn belowsur- (Vm-V) belowsur- (Vm-V) belowsur- (Vm-V\. belowsur- (Vm-V\ face (V). Vm · face(Vm). Vm · face (V). Vm -; face (Vm). Vm -;· 

Ft. per sec. Per cent. 2.242 +2.0 

Ft. per sec. Per cent. 1. 724 0.0 

2.267 +0.9 1.675 + 2.9 

2.252 +1.1 1. 761 - 2.2 

2.236 +2.2 1. 744 - 1.2 

2.267 +0.9 1. 797 - 4.3 

2.299 -0.5 1. 766 - 2.4 

2.289 0.0 1. 772 - 2.8 

2.274 +0.6 1.819 - 5.5 

2.211 +3.3 1. 712 + 0. 7 2.2"24 +2.8 1.644 + 4. 7 2.280 +O.a 1.698 + 1.5 

2.239 +2.1 1.915 -11.1 

2.280 +0.3 1.670 + 3.1 

2.289 0.0 1. 775 - 3.1 

2.321 -1.5 1.582 + 8.3 

2.420 -6.0 1.664 + 3.5 

2.445 -6.9 1. 741 - 1.0 2.308 -0.9 1. 717 + 0. 5 2.333 -2.0 1.800 .- 4.4 

2.264 +1.0 1.695 + 1. 7 

2.327 -1.3 1.812 - 5.1 

2.:m -l.O 1.689 + 2.0 2.305 -0.8 1. 792 - 4.0 

2.311 -1.0 1.627 + 5. 7 

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 

2.321 -1.5 

1.704 + 1.1 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 ----------- 1.724 -----------

Ft. per sec. 2.286 

2.353 

2.437 

2.300 

2.404 

2.378 

2.414 

2.392 

2.313 

2.296 

2.383 

2.397 

2.420 

2.361 

2.278 

2.445 

2.459 

2.428 

2.456 

2.460 

Percent. 

+4.8 

+1.3 

-2.3 

+3.5 

-0.9 

+0.2 

-1.3 

-0.4 

+3.0 

+3.8 

0.0 

-0.6 

-1.6 

+0.9 

+4.4 

-2.6 

-3.2 

-1.9 

-3.1 

--8.2 

2.383 -----------

Ft.pe1·sec. Per cent. 1.966 + 2.4 

1.817 + 9.8 

1.985 + 1.5 2.008 + 0.3 

2.065 - 2.5 

2.119 - 5.2 

1.926 + 4.4 

2.008 + 0.3 

1. 983 + 1.5 

2.081 - 3.3 

2.104 - 4.5 

2.276 -13.3 

2.092 - 3. 9 2.008 + 0.3 

2.047 - 1.6 

1.848 + 8.3 

2.024 - 1.0 

2.070 - 2.8 

1. 796 +10.8 

2.055 - 2.4 

2.014 ----------· 

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

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

the surfaCf>:, 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 p_eriods 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 may be in error 7 per cent and a measurement 2 feet above the bottom may be in error 11 per cent. In 

the second section a velocity measurement 3. 6 feet; below the surface 

may be in error 4.8 per cent and a measurement 4 feet above the 

bottom in error 13.3 per ceri.t. 
MURPHY.) PULSATION OF MOVING WATER. 31 

In 1899, w. - measuring the discharge of the St. Clair River, Mr. 

L. C. Sabin, assistant engineer, made some experiments to determine 

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

at the same depth. In the first series of observations the meters 

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

the second series they were 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. r.rhese curves 

have two sets of waves-small ones of fifteen to sixty seconds amplitude and larger ones of three to six or more minutes amplitude. The 

range of velocity as found from the large waves is in some cases 35 

per cent of the mean velocity shown by the meter for te·n minutes. 

The curves for two adjacent meters are at times nearly parallel, but 

they soon diverge and cross each othm~ occasionally. The curves for 

the meters in a line with the axis of the river resemble· one another 

more closely and are more nearly parallel than those of the meters in 

a line across the river. These experiments indicate that the pulsations are very limited in extent 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 th-~ experiments by Sabin 

and others is that velocity observations of short duration are of little 

value unless they are numerous and well distributed over the discharge area. In order to eliminate the effect of the pulsations, each 

observation should extend over a period of from six to t.en minutes. 

Long single observations and rapid fluctuations of water surface 

elevation require that discharge be found from single observations 

in comparatively few verticals, and that the ratio of velocity at this . 

depth to mean velocity be known from vertical velocity 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 COMPUTING STREAM FLOW. 

WEIRS. 

The discharge of a stream can be obtained by causing it to flow 

over a weir or dam the coefficient of which is known, by the substi- · 

tution of observed data in a. weir formula. Three sharp-crested or 

standard weir formulre are in use, viz, Francis'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 discussion of 
32 ACCURACY OF STREAM MEASUREMENTS. (N0.64. 

each formula is here given because of its bearing on the accuracy 

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 of the Board of Engineers on 

Deep Waterways have extended the values of the coefficients of a few 

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

permit more than the mention of them here. a 

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 t-he weir and the velocity of approach are 

the only variables, and these can easily and accurately be measured. The disadvantages are {1) the cost of constructing a weir, 

or the difficulty of finding one in use whose shape closely resembles 

one whose coefficient is known, and {2) the limited range of values 

of the coefficient 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 careful measurements 

of the volume of water passing over small weh~s and the corresponding heads at Lowell, Mass. b His measuring tank was a canal lock 

which had a capacity of 12,138 cubic feet for a depth of 9.5 feet; the 

greatest length of crest was 10 feet; the head on the weir varied from 

5 to 19 inches, and was measured with two hook gages 6 feet 

upstream from the crest; the width of the channel was about 14 feet. 

His formula, derived from these experiments, is as follows: 

Q=i- X 0.622 h2(b-_,lo nh2)V'2 gh2=3.33(b-t0 nh2)h2! 

Q=discharge in cubic feet per second; l1=head on weir, or difference 

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

FIG. 9.-Sharp-crested weir. 

value is 0 when both 

ends of the weir are 

flush with the sides of 

the channel, 1 when one 

side only is flush, and 2 

when neither side is 

flush; g=acceleration of 

gravity. {See fig. 9.) 

The head on the weir 

should be not less than 

0. 5 foot nor more than 

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 entrance under the 

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

a A discussion of these experiments, which were conducted by George W. Rafter, will be found 

in Trans. Am. Soc. Civ. Eng., Vol. XLIV, pp. 220-398. 

bLowell Hydraulic Experiments, by J. B. Francis, p. 133. 
MURPHY.) WEIRS. 33 

measured and the bead corrected for it. The formula for this purpose is h2=[(h+h1)!..:-h1 i] i, h being.the measured head, h1 the head 

due to the velocity of approach= ~~2 and V1= bo~o· (See fig. 9.) 

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

rank in reliability." 

Francis made eighty-eight experiments 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 discharge 

and the discharge computed by his formula was 0. 9 per cent for the 

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

experiments; for the other eleven means tbe difference is less than 

0.4 per cent. 

FTELEY AND STEARNS'S EXPERIMENTS AND FORMULA. 

In 1877 and 1879 Fteley and Stearns b measured the discharge over 

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

weir, from which they derived the following formula for a standard 

weir with end contractions suppressed: 

Q=3.31b [h+1.5 ~1 Jt-o.oo7b. 

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

on weir, V1 =velocity of approaeh in feet per second. (See fig. 9.) 

Their measuring tank was a section of the Sudbury conduit having 

a capacity of 300,000 cubic feet for an increase in depth of 3 feet. 

The head on the weir was measured with a hook gage 6 feet upstream 

V,2 

from the crest. The term 1.5 ~ corrects for ·velocity of approach. 

The head on the weir must be not less than 0.06 foot, and the air must 

have free aceess under the sheet. This formula is not used as generally as is that of Francis or Bazin. It was used by Fteley and Stearns 

to compute the discharge of the weir used in their current-meter and 

weir comparisons. (Seep. 57.) 

BAZIN'S FORMULA. 

In 1886 and 1887 Bazin c made numerous measurements of t,he volume passing over weirs having lengths of from 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=tP [ 1+0.55 (p~h) ] bh~2gh 

0.0148 

and p=0.6075+h (in feet) 

a Hydraulics, by Hamilton Smith, p. 93. 

bTrans. Am. Soc. Civ. Eng., Vol. XII, p. 1. 

o Annales des ponts et chaussees, 1888, p. 416. 

IRR 64--02--3 
34 ACCURACY OF STREAM MEASUREMENTS. [N0.64. 

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 meter to 0.6 meter. 

The air had free access 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 which 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 from a bridge, 

if one can be found in a suitable location. Bridge piers, however, 

FIG. 10.-Metbod of using current meter on large river. 

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 be shallow, taking observations of depth and velocity at 

as many points in the cross section as desired. If the water be deep 

and swift a cable is stretched across the stream at a convenient 

height above the water, and a car or box is suspended from it. From 
MURPHY.] CURRENT METERS. 35 

this car, which is moved back and forth across the stream by the 

observer in it, the depth and velocity of the water are measured. If 

the current. be not swift a surveyor's chain or a cable can be stretched 

across the stream temporarily and the depth and velocity be measured from a rowboat at points marked on the chain or cable. 

In a large river like the Mississippi, where a steamboat can convenFl'G.ll.-Dcvice for holding meter in place. 

iently anchor, a method that has been used satisfactorily is shown in 

fig. 10. a The boat is anchored in the proper place, and a lead weight of 

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 copa Jour. Franklin lust., Vol. LXII, p. 171. 
36 ACCURACY OF STREAM MEASUREMENTS. [No.64. 

per wire being connected to one pole of the battery and an insulat-ed 

wire connected to t,he meter and the other pole. 

On large rivers where boats can not anchor the measurements are. 

made from a boat towed by a steam boat. a . The meter is kept in posi~ 

tion by two lines of range poles at right angles to each other. The 

pilot on the stealnboat steers it so as to keep it in line with one range, 

while the engineer, with his hand on the steam valve and his eye on 

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 to keep the meter in place; b 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 dept~l. c' '"rhe first is the 

better for streams of ordinary size. In the 

device shown in fig. 11 the stay line is attached to the meter and is passed over a 

pulley at the end of the stay pole, being held 

by an assistant. By means of this stay line 

and the vertical cord the meter can be kept 

nearly in posit,ion. . Instead of a stay pole 

a wire cable is sometimes used to keep the 

stay line in place. 

POINT AND INTEGRATION METHODS. 

FIG. 12.-Harlacher's apparatus There are two methods of using a meter 

for moving a meter with uni- in a cross section, as follows: (1) The point form velocity. method, in which the meter is held at certain 

points in the cross section for a stated period of time, usuatly fifty 

seconds, and the number of revolutions of the wheel of the metjer 

during that time are observed, .either by counting the clicks of a 

buzzer or reading a register; and ( 2) the integration method, in 

which, instead of holding the meter 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 

aJour. West. Soc. Eug., Vol. III, No.3. 

b Twentieth Ann. Rept. U. S. Geol. f\urvey, Pt. IV, p. 20. 

o Jour. West. Soc. Eng., Vol. IV, No. ti. 
MURPHY.) CURRENT METERS. 37 

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 decreases. 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 

FIG. 13.-Details of Harlacher's apparatus for moving a meter with uniform velocity. 

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. 45); 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 dept,h in certain verticals, and the mean velocity be found by applying a factor. The 
38 ACCURACY OF STREAM MEASUREMENTS. [No.64. 

three-tenths-depth point a 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 point b is 

employed because the factor which is used to obtain the mean veiocity 

is more nearly constant for it than for any other point on a vertical 

curve. The six-tenths-depth point c is used because it is believed to 

be the depth of the t,hread of mean velocity. 

In the integration method the meter may be moved down several 

times in certain verticals only, as used by Harlacher , d or across the 

stream 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 

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 moved up or down oh the iron tube AA by the rope 

D attached to the clrum F. E is a bracket holding the pulley e. G 

is an arm supporting the drum F, and f 3 (fig. 13) is a dial on which is 

registered the depth. The fan f 4 (fig. 13) and the gearing f 5 regulate 

the rate of motion of the meter; f 6 "is a crank lever for raising the 

meter, and f 8 a ratchet wheel for arresting the motion. I {fig. 12) is 

an electric battery, and H {fig. 12) is the registering 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 consists of obtaining the ratio of 

the velocity at any point in the depth of the stream (called the index 

point), as, for_ example, the three-tenths-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• 02, 03, etc., be the coefficients for the component parts, 

F1, F 2, F 3, etc., of the discharge area F; V1, V2, V3, 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 = 01 F 1 ~ + 

02F 2 V2 + 03F 3 V3 + ................. · ......................... (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 VH v2, Vs, etc., at the 

a Jour. West. Soc. Eng., Vol. III, No.3. 

b Report on Current Meter Observations, Burlington, Iowa, by Maj. A. McKenzie, 1884. 

cProc. Inst. Civ. Eng., Vol. LXXI, p. 60. 

dibid., Vol. LXVII, p. 358. 

•Jour. West. Soc. Eng., Vol. HI, No.3. 
MURPHY.] :RATING OF METERS. 89 

index points, using the set of values of the coefficient~ which correspond with the observed river stage. 

Coefficient work can be done with one current meter, but it can be 

done more rapidly with two or more meters. When two meters are 

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 eaeh point. The two 

meters are occasionally held at the same dept,h 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 simultaneous readings of the two meters. For example: The 

index meter at three-tenths depth indicates 2. 34 revolut.ions per second. The other meter, at eight-tenths depth, indicates 2.05 revolutions per second. The chart shows the velocit.y ratio for these meter 

speeds to be 0. 89. From the velocity ratio at each tenth of the depth 

the ratio of the mean velocity in the vertical to the index velocity, or 

C, is found. 

This coefficient method of gaging is better and more accurate for 

large streams than M1e slower one in which velocity observations are 

made at several points in each vertical, on account of the rapid 

changes of surface elevation of the stream. 

RATING OF METERS 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 they should 

be eliminated or reduced to a minimum. 

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 (4} by 

attaching the instrument to a long arm and revolving it about avertical 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 2 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 meter 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 
40 [No.64. 

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. rrhe rating table 

should not be extended beyond the limits of velocity used in the 

rating. 

The relation between distance passed over by tbe 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 revolutions of wheel per second is of the second 

degree and 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 t.his line be nearly stra_ight between the limits of the 

observed revol~tions its equation is assumed to be of the form 

y=a+bx, y being velocity, x revolutions per second, and a and b constants. If t.he results indicate a curved line its equation is assumed 

to be of the form y=a+bx+cx2. 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 x and the ratio y to x (see fig. 29, p. 89) instead of x 

and y. The reason is that the ratio y to x changes rapidly as x 

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 curve, is the most accurate, but it requires the 

most time.. If the meter is to measure low velocities to within 1 per 

cent, the second m('thod must be used. It gives n observation equations of the form y-a+bx=v if the relation be linear, or y-a-bxcx2=v if it be a parabolic curve. vis a small quantity ca~led 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 
lllUltPHY.) ltATING OF METERS. 41 

of the constants are those that make the sum of the squares of the 

residuals a minim urn. 

Squaring each of these n equations and adding, we have 

~v =v +-t, +v + . . . = [y' -a-bx' -cx'2]2+ [y" -a-bx" -cx"2

] 2 

· +[y"'-a-bx"'+cx'"2] 2+ 

Taking the first derivative of this equation with respect to a, b, and c 

and placing these equal to 0, we have 

~ 2) d--v-= -2 [y' -a-bx' -cx'2] -2 [y" -a-bx" -cx"2] da 

~v2 

cl db =-2x' [y'-a-bx'-cx'2]-2x" [y"-a-bx"-cx"2] 

~v2 

d de = -2x'2 [y'-a-bx' -cx'2] -2x"2 [y" -a-bx" -cx"2] 

=0 

From these normal equations the values of a, b, and c can be found. 

For the linear function these equations become two in number and 

have the form a~x+b:EaP=~xy 

na+b~x =~Y 

and a and b are found from these equations. 

This relation between revolutions per second and velocity, whatever 

it may be, is not constant. Below are given the ratings of a Price 

meter, obtained by J. C. Bailey, United States assistant engineer. a 

Results of four ratings of a Price meter used in 1892 on Niagara River. 

Number Meter coefficients. 

Date. ofobser- Velocity. Remarks. 

vations. a b 

~~\~:~:~~~~:::~~~~~ 20 

Ft. per sec. 2.5to7.3 4.239 +O Still water; base 150 feet long. 34 2.1 to 6. 7 4.256 +0.001 Do. 

49 1. 7 to 7. 7 4.0!6 +0.207 Do. 

May 17---------------- 43 2.0 to 8.0 4.130 +0.067 Still water; base 300 feet long. ----·-- 4.168 +0.0848 

Values computed from two ratings of current meter on April 29 and May 4, 1892. 

[April29, V1=4.256R+0.001; May 4, V2=4.046R+0.207.] 

R Vt v2 v2-V1 V2-V1 

---v;- ---------------

0.05 0.274 0.409 0.135 0.314 

0.10 0.487 0.612 0.125 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 

0.4.5 1.967 2.028 0.052 0.026 

0.50 2.189 2.230 0.041 0.018 

a Engineering News, Vol. XXIX, 1893. 
42 ACCURACY OF STREAM MEASUREMENTS. [No.64. 

The foregoing table shows that if on May 4 velocity measurements 

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 31.4 per cent. It is true that neither set of values of a and 

b was determined for low velocities. This, however, 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 examined 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. rro illust,rate 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 0.174 foot per second. 

This is 2.04 per cent of 0.17. Hence if the computed revolutions 

were either 0.166 or 0.174 the error introduced by using this rating 

tab~e would be 2.4 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 greatest percentage error in rating table of srnall Price rneter No. 

363, which gives velocity to only two places of decirnals. 

Revolu- Error Revolu- Error 

.tions per Velocity. 0.004 tions per Velocity. 0.004 

·second. ---v· second. --v· 

Ft. per sec. Per cent. Ft. per sec. Per 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 

0.1fi 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 methods to rate the Pitot 

tube which they used in their hydraulic 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. 

a Recherches hydrauliques, by Darcy and Bazin, 1865, pp. 63-70. 
MURPHY.) RATING OF METERS. 

Results of Pitot tube ratings by Darcy and Bazin. 

First method." Second method. b Third method. e 

No. of' Value ex- of coef- peri- ficient. ment. 

----

2 0.987 3 1.024 4 0.981 5 1.013 6 1.006 7 0.988 8 1.012 !) 1.008 10 1. 008 11 1.009 12 1.007 13 1.015 H 1.039 15 0.99t 16 1.007 17 1.023 

------- --------- ------- --------- ------- --------- ·------

----·-- ------- ------- .................. --·---- ................. 

----·-- ----·--- ------- --------- --- --- --------- ------- --------- -------- --------- ------· --------- -------- --------- ............... ................... 

~~-

1.006 

Num- I 

Veloc- I Value ber of ity of of coef- ex peri- boat. ficient. ments. 

----~--

Meters. 8 0.609 1.040 8 0.69'Z 1.(153 

8 0. 785 1.032 8 0.938 1.033 8 0.980 1.040 8 1.120 1.015 8 1.231 1.028 4 1.333 1.032 4 1. 38.-5 1.048 4 1.470 1.029 4 1.500 1.040 4 1.611 1.033 4 1.661 LO'Z7 4 L 775 1.042 4 1.819 1.031 4 1.863 1.027 ................. 1.930 1.039 

-------- 1. 976 1.025 

~~:~~~J 2.034 1.037 

.. -------- ---·---- -------- -----·--- -------- -----·-- --------- ................ ·------- --------- ·------- -·-·-·-- --------- ............. -- -------- -------- -------- ----·--- ~ --- ---...... 

------ -------- --------- -------- -------- --------- -------- -------- -·------- ----·-·-- ------- --------- ... ............. ................. ------·--

---

1.034 

a By surface floats. 

bIn still water. 

c In moving water. 

Nnm- Designation 

of experi- ber of ment. ex peri- ments. Series. No. ------

2 51 1 1 51 2 3 51 3 1 52 1 3 52 2 1 52 3 1 58 4 1 59 4 1 60 2 1 61 4 1 62 4 2 63 3 1 64 1 1 64 2 3 65 4 3 66 1 1 66 2 4 68 4 1 71 6 

-------- 72 5 

-------- 73- 4 ................. 74 4 

-------- 84 2 

-------- 84 3 

·------- 85 1 

--·----- 85 2 

--·----- 85 3 

-------- 88 1 

----·--- 88 2 

-------- 88 3 

-------- 88 4 

d Rectangular covered wooden channel. 

Value Mean 

of coef- Velocficient. ity. 

~~- ~~-

Meters. 1.021 . 0.508 

1.010 0.768 1.018 1. O'ZS 1.029 0.376 1.000 0.542 1.006 0.694 1.005 1.429 

0.969 2.318 0.968 2.571 0.966 1.267 0.965 1.979 

0.988 2.199 

0.996 0.856 0.988 0.948 

0.978 1.511 1.015 1.464 0.984 1.675 0.976 1.497 

0.968 1.810 1.017 1.679 

0.967 1.612 1.014 1.229 1.014 1.033 0.984 1.246 0.998 1.011 0.997 1.218 0.990 1.473 0.995 0.894 

0.986 0.921 

0.980 0.955 

0.993 1.010 ---

0.99B 

e Rectangular open wooden channel covered with cloth. 

fTrapezoidal open wooden channel covered with cloth. 

g Semicircular. 

h Rectangular. 

43 

Channel. 

Shape. Width. -----

Meters. 

(d) 0.8 ( d} 0.8 (d) 0.8 (d) 0.48 (d) 0.48 (d) 0.48 (d) 1.994 

(d) 1.994 

(d) 1.994 

( •) 1.994 

( •) 1.994 

( •) 1.994 

( •) 1.994 

( •) 1.994 

( •) 1.994 

( •) 

I 

1.994 

( •) 1.994 

(f) 1.984 

(g) 1.40 (g) 1.40 (g) 1.40 (g) 1.40 (h) 1.990 

(h) 1.990 

(h) 1.990 

(h) 1.990 

(h) 1.990 

(h) 1.990 

(h) 1.990 

(h) 1.990 

(h) 1.990 

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 surface of 

the water. Cis found from v=C.J2g~d,v being known from the 

floats. In the second method the tube was fastened in front of a 

boat and was drawn through still water at different observed velocities. In the third method the instrument was held 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. 

'rhe value found by the second method (the one now commonly used) 

is ·the largest of the three and is rejected on account of the action of 

the boat on the instrument. r:rhe pull on the boat as it was drawn 

through the water tipped the point of the tube down slightly, making 
44 ACCURACY OF STREA.M MEASUREMENTS. [No.64. 

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 from the mean of all the observations by the first method are 

+1.8 per cent and -2.5 per cent. The value of C found by the third 

method is· 0.993, obtained from thirty-one measurements of discharge 

of the experiment canal. The tube was held at many 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 second, 

or from 1. 64 feet to 8. 20 feet per second. 

GENERAL FORMULIE FOR COMPUTING DISCHARGE. 

Whatever method is used in computing discharge, the depth must 

be known at a sufficient number of points in the cross section to 

determine the cross-sectional area with the required degree of accuracy. For a small stream it should be known at each foot of width, 

for large streams at each 5 or 10 feet of width. -

The cross-sectional area (F) is found from the following formula: 

b F'=- [d1+4 (d2+d4+d6+dn-1) +2(d3+d5+d7+dn)+dn+1]. 

d11 d2, d3, etc. ,being depths and b the distance between the points where 

the depths are measured. 

The genera~ formula for the discharge per second is 

Q=F'l V1+F2l·.,..2+F's Vs+F'n 17;1· {1) 

F'1, F'2, F'3, etc., are the component parts of the cross section, and 

l.,..1, 172, · 173, etc., the mean velocity in each of these parts. If the 

width of these component parts is b and the mean depth in each is 

d11 d2, d3, this formula can be written 

(2) 

If d1 =d2=d3.:_, that is, if the channel is rectangular in cross section, 

then formula (2) becomes 

Q=bd ( V1+ V2+ V3+-). (3) 

The component velocities are found (1) from a single observation at 

some 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 velocity in this vertical is then the area 

inclosed between the vertical curve and a vertical line representing no 
MURPHY.] IfORMUL.£ FOR COMPUTING DISCHARGE. '45 

velocity divided by the depth. Harlacher's method of integrating a in a 

vertical gives each component velocity very readily and quickly. Any 

component velocity is Rf, R being the observed revolutions, T the 

observed time in seconds, and C the number, which changes from 

revolutions to velocity. 

In measuring 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 measurement if possible. 

The discharge measurements of the Niagara River made in 1897 

and 1898 by the United States Board of Engineers on Deep Waterways b 

from 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. 

'l"'he 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 onethird 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. 

T. V. Moore in his discharge measurements of the Thames c assumed 

the vertical velocity curve to be a parabola, and computed its area 

d' from the formula A=6[Vs+4 Vm+ Vb], dbeingthedepth, Vs thesurface velocity, Vm the velocity at mid depth, and Vb the bott.om velocity. 'l,he discharge per second flowing between the end sections he 

. h 

computed from the formula V -[.~ A 1 + 4 ~.A + 2 ~As], h being the 

distance between the consecutive sections, ~A1 the sum of the two end 

sections, ~A2 the sum of the odd sections, and ~As 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, n1ultiplied the velocity at mid depth in each component area 

by 0. 95 to find the mean velocity in that area. ct In computing the 

discharge of the Mississippi River in 1882 ·the velocity at mid 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. e From 1885 to 1887 the 

velocity at six-tenths depth was observed in the component areas, and 

this was taken as t.he mean velocity in each area. 

aProc. Inst. Civ. Eng., Vol. LXVII, p. 358. oProc. Inst. Civ. Eng., Vol. XLV, p. 220. 

bJour. West. Soc. Eng., Vol. IV, No.6. dTrans. Am. Soc. Civ. Eng., Vol. IV, p. 303. 

•Jour. West. Soc. Eng., Vol. III, No. a 
46 ACCURACY OF STREAM MEASUREMENTS. (N0.64. 

Harlacher's method of computing flood discharge where the surface 

velocity only could be measured is illustrated in fig. 14. a The surface 

velocity was measured at a sufficient number of points (1, 2, 3, etc.) 

in the cross sect.ion ACB to determine the surface velocity curve 

ADB. The line ACB shows the depth at each point and is plotted 

from soundings taken immediately before or after the flood. 

FIG. 14.-Diagram illustrating Harlacher's method of computing flood discharge. 

The openings between EF and G Hare bridge piers, the measurements being made from a bridge. The product of the surface velocity 

Vs and the corresponding depth tis found for a sufficient number of 

points, depending on the irregularity of the bottom and the curve 

.AEFG HB drawn. The discharge per second is the area between the 

line AB and the curve AEFG HB, less the piers, multiplied by 0.85. 

COMPARISONS OF RESULTS WITH DIFFERENT INSTRUMENTS AND METHODS. 

SURFACE FLOATS AND PITOT TUBE. 

On page 43 we have given the results of three ratings of a Pitot 

tube by Darcy and Bazin.b In the first method the surface velocity 

was found from surface floats and a Pitot tube, as already described. 

Ninety-two experiments were made. The results are combined, according to velocity, into seven groups of eight experiments each and nine 

groups of four experiments each. The value of the coefficient as found 

from the first 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. 

a Proc. Inst. Civ. Eng., Vol. XCI, p. 399. 

b Recherches hydrauliques, by Darcy and Bazin, 1865, pp. 63-70. 
I 

MURPHY.] COMPARISONS OF RESCLTS. 47 

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 discharge of the rectangular orifices admitting water to the canal was determined by 

experiment for different 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 ninetyone in the canal 2 meters wide. The points of measurement were 

nearest together where the velocity changed most rapidly. The results 

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 METER. 

ELLIS'S EXPERIMENTS. 

In 1874 T. G. Ellis made numerous velocity measurement•s of the 

Connecticut. River at Thompsonville, Conn., with current meters and 

with double floats like that shown in fig 1. 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 River in 18'74. 

Mean velocit~. in feet per second, at various depths. 

Observations. Mean. Varia-

~~~~ 0.1 o. 2 o. 3 o. 4 u. 5 o. 6 o. 7 I o. 8 o. 9 fo~~ tion. 

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

Meter below av. P.ct. 

FI~:\oc~ro;~v-. · 1.15 1.19 1. 2'2 1. 22 1.19 1.14 1.11 1.03 0.94 0. 79 0.46 1. 063 } 25.8 

velocity 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 aboveav. 

velocity 1.86. _ 2.96 3.08 3.12 3.06 2.99 2.91 2. 78 2.62 2.42 2.16 1.4-7 2. 735 } Float above av. 5. 7 

velocity 1.86 ... 3.26 3.24 3.17 3.17 311 3.01 2.94 2.80 2.60 2.35 1. 78 2.891 

All meter observations. ____ 2.0.') 2.12 2.15 2.13 2.08 2.01 1.93 1.81 1.67 1.47 0.96 1.887 } All float obser- 12.0 vations ____ .. __ 2.38 2.38 2.35 2.35 2.30 2.23 2.15 2.04 1.90 1.60 1.18 2.1H 

a Rept. Chief Eng. U. S. A., 1878, Appendix B. 
48 ACCURACY OF STREAM MEASUREMENTS. [NO. 64. 

It is seen from the foregoing 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 difference between the meter and float velocities increases 

as the velocity decreases. 

Ellis gives also the following values of the ratio of mean velocity 

in a vertical ( Vrn) to mid-depth velocity in that vertical ( V~ D) and 

the ratio of distance below the surface of mean velocity ('m) to total 

depth (D). 

Mean ratios frortt vertical velocity curves obtained by Ellis on Connecticut River 

in 1871,. 

Observations. 

Meter at low velocities.--- .•. ____ -----. __ .... _________ ---- ------ _ ..... ------ Floats at low velocities ------ __ ------ _________ ----· .... ------ ------ _________ _ 

M~if~t i~i~:r~~itr:: :~~~~~- ~·: ~ ~~ ~ ~: ::~ ~: ::: ~~ ~ :::: ~: ~ ~:: :::::: ~ ~ ~ ~ :::: ~: ~ :~~ Mean of high velocities ___________________________ . _____ ------ _____________ _ 

Mean of meter measurements_ ... ___________ ... ___ .... __ .... ---------------- Mean of float measurements. ____ ... __ . ______ ------. _____________ ------------ Mean of all measurements. ________ ------ _________ ... ____ ---------------- ___ _ 

Vm+VtD 

0.933 

0.918 

0.930 

0.939 

0.961 

0.944 

0.937 

0.947 

0.940 

m+D 

0.656 

0.622 

0.652 

0.628 

0.637 

0.629 

0.638 

0.632 

0.636 

From the foregoing table it is seen that ~7J varies from about 0.92 

rn 

to 0.96 and D 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. a 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 16.4 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 chronograph 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 into equal parts. One pen of the 

chronograph recorded 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 each 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: 

"Report on Current Meter Observations, Burlington, Iowa, by Maj. A. McKenzie, 1884. 
MURPHY.) COMP .ARI$0NS OF RESULTS. 49 

Comparison of velocity by double floats and current meters from measurements by 

G. A. Marron Mississippi River at Burlington, Iowa, October, 1879. 

Mean velocitl'[ found Mean velocity found 

Number from 200-foot run. Difference from 50-foot run. Difference 

of float. Float Meter (Vm-Vf). Float Meter (Vm-Vf). 

(Vf). (Vm). (Vf). (Vm). 

Ft. per sec. Ft. per sec. Ft. per sec. 1. _____ 2.543 2.604 +0.001 Ft. per sec. 2.660 Ft. per sec. 2.597 Ft.persec. -0.063 2 ...... 2.741 2.546 -0.195 2.976 2.657 -0.319 3 ______ 2.634 2.500 -0.114 2.674 2.630 -0.044 4, _____ 2.446 2. 43.t) -0.011 2.456 2.481 +0.025 

iL ..... 2.850 2.468 -0.382 2.847 2.590 -0.257 6 ••.... 2.672 2. 700 +0.028 2. 778 2.649 -0.129 

7----- 2.514 2.545 +0.001 2.674 2.484 -0.190 

8 ...... 2.832 2.457 -0.375 2.857 2. 749 -0.108 

9 ..•... 2.476 2.625 +0.149 2.569 2.821 +0.252 10~----- 2.829 2.758 -0.071 3.012 2.!i23 -0.189 

------------·------- 2.654 2.566 -------·--·· 2.750 2.648 -----·-·---- I 

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 

se~ond 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 number 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 cent. We may note also that we have 

here forty mid-depth velocities in nearly the _same vertical 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 cent to +12.1 per cent, 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. Henry also gives a comparison of velocity measured with 

double floats like that shown in fig. 1 and current meter, made on 

the St. Clair River in 1869. a The results of the comparison are given 

in the following table: 

aJour. Franklin Inst., Vol. LXII, p. 322. 

IRR 64-02--4 
50 ACCURACY OF STREAM MEASUREMENTS. [No.64. 

Comparison of t'elocity by double floats and current rneter frorn measurement.<J by 

D. F. Henry on St. Clair River in 1869. 

Depth Velocity of current. of 

Number Dir{'ction and obser\·a-1----------,-----1 

of obser- velocity of tion be- I 

vations. wind. low sur- Float!'~. Meter. Difference. 

Miles per hour. 50 ...... 3.26up _______ _ 62 ...... 1.92up ______ __ 

56 ...... 1.27up ........ 50 ...... 0.48up ______ _ 54, ______ 0.29 down __ __ 31. _____ 0.53 up .... __ __ 

37. ..... 0.80up ....... . 29 ...... 2.18 down __ __ 12 ______ 4.85 down ____ · 7 ...... 0.74up ______ __ 

face. 

~---1---1 

Feet. Ft. per sec. Ft. per .~ec. Ft. per sec. 1 3. 619 3. 655 -0. 036 

5 3. 759 3. 783 -0.1!24 

10 3. 703 3. 674 +0. 029 15 3. 590 3. 516 +O. 074 

20 3. 598 3. 405 +0. 193 25 3. 637 3. 441 +0. 196 

30 3. 546 3. 279 +0. 267 35 3. 556 3. 166 +0. 390 40 3. 636 3.142 +0. 494 

45 3. 542 2. 985 +0. 557 

It iR 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 met~er. While the action of t,he upper float on the 

lower float may not account for all the difference between the float 

and meter 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 Rurface float will therefore move more slowly than the lower float for 

dept,hs 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 1ipper float will move 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 

floats and current meter in a small canal at Ogdensburg, N. Y. a The 

floats were run over a distance of 200 teet 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 do1tble floats and current meter from measurements 

made by D. F. Henry in small canal at Ogdensburg, N. 1"., 3 feet below surface. 

Number Velocity. 

of observations. Floats. 'Meter. Difference. 

Ft.pe1·sec. Ft. per 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 

aibid., p. 259. 
MURPHY.] COMPARISONS OF RESULTS. 51 

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 smaller velocity than the floats. 

Henry also gives a comparison of velocity found with floats and a 

propeller meter in the 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 fifty 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, and t.hat may 

have retarded the floats somewhat. 

GORDON'S EXPERIMENTS. 

In 1873 Gordon made comparisons of the discharge of the ,lrawadi 

River at Saiktha, Burma, as measured with double floats and with 

current meter. From these he concluded that the double-float discharge was about 10 per cent too large. He therefore reduced all 

discharges found with double floats by tliat amount. 

FLOAT RODS AND CURRENT METER. 

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 similar 

rods and methods, 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 York State canal survey during the 

summer of 190fJ. 

Place. Date. I V'r V"r Vm Q'r ~ Q"r I Qm ~:;,~ s:::~ s~~; -TQ'r Q'1· Q"r 

--- Ft.per Ft.per Ft.pa Cn.jt. Ou~~ Cn.jt. ------

1900. sec. sec. sec. per sec. per sec. per sec. Per ct. Per ct. Per ct. Lockport---- ____ Sept. 14 __ .. ____ 1.440 1.531 ·--- ____ 805.70 799.85 ____ ____ ____ ____ +0. 73 

Rochester _______ Sept.20 -------- 0.704 0.736 ________ 235.12 251.57 -------- ________ -7.00 

E~~:::::~:::: -~-~~~~~- --~~~~- 8:= --~>~929- -~~--~~- ~:~ ·sio:sa· ~~·-~~- :~~~:::: --=-=a:i4 

Do ___________ .... do ... ---- ___ 0.899 0.939 -------- 307.08 317.54 ________ -------- -3.4!:i 

Boonville. _______ Sept.25 1.073 0.813 -------- 2'Z7.22 227.51 ________ -0.1:1 _______________ _ Do ___________ .... do ___ -------- 0.850 1.079 ·------- 238.81 2'28.66 ________________ +4.25 

Do _______________ do ___ -------- 0.836 1.111 ________ 233.54 234.70 ________________ -0.49 

Glens Falls ... __ . Oct. 8 0. 821 0. 690 . ____ . _ _ 164. 73 172. 77 161. 50 -4. 88 + 1. !J! +6. 52 

Do _______________ do .... 0.756 0.640 -------- 149.66 158.57 155.23 -5.92 -3.72 +2.11 

V'r=mean velocity found by party No.1, with rods. 

V"r=mean velocity found by party No.2, with rods. 

Vm=mean velocity found with meter, using six-tenths-depth method. 

Q'r=discharge found by party No.1, wi.th rods. 

Q"r=discharge found by party No.2, with rods. 

Qm=discharge found with meter, using six-tenths-depth method. 
52 ACCURACY OF STREAM MEASUREMENTS. [No.64 

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 

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 immersion of 

80 to 90 per cent of the depth, and 13 meter observations of 50 seconds 

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 43 feet 

and the depth 7.5 feet. The flow was undisturbed for a half mile 

above the section of measurement, but there was a sharp curve less 

than 100 feet below t,he point where the lower rod-measuring party 

was stationed. In the first comparison 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 observations 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 party 

No. 2, with a depth of immersion 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 a half 

mile below the place selected. The partjes 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 143 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 method. 

The Glens Falls comparisons were made on the Glens Falls feeder, 

near Glens Falls. At the place selected for the tests the feeder is 32 
MUltPHY.l COMPARISONS OF RESULTS. 53 

feet wide and 6 feet deep, with nearly vertical sides. There is a bend 

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 measurements were made from a bridge about 100 feet 

from each of the points where the rod measurements were made. ,..rhe 

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 minutes, party No. 1 passed 68 rods, party 

No. 2 ran 108 rods, and 28 meter observations of fifty seconds each 

were made. 

The method of making these comparisons is the same as t.hat used 

in the canal discharge measurements, which is described on page 16. 

The Rochester and Glens Falls comparisons are not so satisfactory 

as those at Lockport and Boonville. In tjhe former the measurements 

were made too near a curve. ,..rhe large variation in the time of run 

of the individual rods indicates this fact, and surface-level fluctuations and passing boats int.erfered somewhat with the work. There is 

a possibility of leakage from the feeder between the points of measurement 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 tlian those of 

meter with rods. It must not be concluded from the Rochester comparisons that because the rod discharges agree closely and the meter 

discharge differs from the rod discharge 7 per cent that this error is 

all due to the meter. The two sets of velocity measurements 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 9-ifference is due to errors in the rod discharge measurements. 

MURPHY'S EXPERIMENTS AT CORNELL UNIVERSITY. 

In connection with the writer's experiments at Cornell University 

to determine the relative accuracy of measurements by the weir and 

by the current meter, the results of which are discussed on pages 58 

to 95, surface velocity experiments were made with float rods and 

with the current meter, the results of which are given on pages 89 

to 92. 

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.~~. 

This wooden canal or flume was 27.75 feet wide where the first 63 

experiments were made and 14 feet wide where the remaining 52 

"Lowell Hydraulic Experiments, by J. B. Francis, p. 170. 
54 .ACCURACY OF STREAM MEASUREMENTS. [No.64 . 

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, 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 ill. 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 11.4 per cent below this 

curve in experiment No. 1. 'rhe rods used were not all of the _proper 

depth of immersion, and Francis derived the following formula for 

computing the correet discharge: Q'''=Q"[1-0.116( v'l)-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 and 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 velocity 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 canal survey 

of 1900 a series of experiments was made at the hydraulic laboeatory 

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 ::,t.andard weir. These experiments were planned by the 

consulting engineer of the New York State canal survey, Mr. 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 t,he sections of the canals fluctuates rapidly on 

account of lockage of boats and irregular feed of water to lower sections. It was therefore necessary to make discharge 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 center, 

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 
MURPHY.) COMP ARI!;ONS OF RESULTS. 55 

levels. In the laboratory experiments the conditions were duplicated 

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 measurements of the State 

canals and feeders. 

Pl. II shows the laboratory canal and the observers employed in 

making t,he tests. A description of the laboratory and of the method 

of obtaining standard weir discharge will be found on pages 59 to 64. 

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 so as to give the desired depth of water in the channel. 

As soon as the flow became steady 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 under 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 ~n the 

velocity. ~rhe number of rods used in an experiment varied frmn 

fifty to one hundred and fifty. Meter party No. 1 measured the discharge by the six-tenths-depth and the integration methods, and then 

assisted the rod-measuring party, four stop watches being used and 

the number of rods run in a given time nearly doubled. During each 

experiment the head on the weir, the depth of water in the canal, and 

the slope of the surface were read every thirty seconds and were 

checked occasionally by readings of the hook gage. The time of run 

of each rod was plotted on squared paper, using distance from side 

of canal as abscissre 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: 
56 ACCURACY Olf STREAM MEASUREMENTS. lNo.64. 

Comparison of float rod and weir velocity and discharge measurements at Cornell 

hydraulic laboratory. 

Rod gagings in laboratory canal. Mean error ----~-- -----------1 Error of dis- of disa Q) ~ ImmerRion, I Immersion, charge re- charge re- o ~ .... 75 per cent. 90 per cent. ferred to ferred to 

.!::~ . $ ---,---!standard weir. st~ne1:.rd 

l»Q'd ~r;:l v v ~·:!;j§ ..-... e- e-

-~ro as Cl ~ l~~i- c~~ge l~i- c~~sge 75 per 90 per 75per 90per 

~·$~ ~ per per per per ~':: cf:~ ~~ ~':~ Ql 1!: ~ ~ sec- second. sec- second. mer- mer- mer· merDate. 

> ~ ond. ond. \ sion. sion. sion. sion. -----!---'----~-- --------------------

2

Clu4.· 

58

.tt

8

1900. : Feet. Feet. Feet. Cu. ft. Feet. Cu. jt. Per. ct. Pe1·. ct. P. ct. P. ct. October 24 .•••• 

Do--------- Do .. _____ _ 

Do.-------

October 26 ..... 

Do--------· 

October 27 _ ... 

Do---------

Do---------

Do ........ . 

Do---------

Do---------

October 31 •.... Do ........ . October 29 .•••. November 1 ... 

140.514 A:~ ~:~ A:~~ i~:3U ·o~949- ·i4i~004- 2=~:~ ·=-=o~af }1. 32 71.670 0.484 9. 222 0. 49(1 72.621 0. 476 70. ()46 -1.33 +1. 57 °- 75 

38. 308 0. 269 8. 789 0. 276 38. 990 0. 272 38. 425 -1. 78 -0. 31 

1~: ~~ A: gro ~: ~r A: ~g 1~: ::J A:~ 1~: ~~ =~:; =i: ~~ 3. 96 2. oo 

178.553 1.473 7.54.3 1.510 183.185 1.525 184.832 '1-2.59 -3.52 '} 

30.089 0. 254 7. 376 0. 266 31. 5431 0. 255 30.239 -4. 83 -0. 50 

196. 387 l. 983 6.163 2. 067 204. 695 2. 044 202. 407 -4. 23 -3. 06 r ~~i: ~ A: ~g ~: ~~ A:~ ~~: ~ A: rJ ~: rfl =!: ~~ =~: ~ . 22 2. 95 

50.309 0. 535 5. 847 0. 555 52. 176 0. 549 51. 612 -3. 71 -2.59 

198. 258 1. 475 8. 365 1. 537 2?6· 554 1. 507 202. 523 -4-.18 -2.15 r ~:~ 8:~ag ~:~ 8:~~~ ~:~U ·o~roi" -67~288- =g:~ ·=-=a~of -68 2· 78 

31. 140 0. 235 8. 255 0. 249 33. 04.3 0. 242 32.114 -6.11 -3. 13 -----

3.54 2.14 

It is seen that the discharge obtained wit,h the rods is larger for all 

depths, 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 discharge, 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 2.14 per cent for the 90 per cent depth of immersion. 

The greatest variations from these means are +1.14 per 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. 54) 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 cent to 2.5 per cent, the 

former for a head on weir of 1 foot, the latter for a head· of 2. 5 feet. 
MURPHY.] COMPARISONS Ol!, RESULTS. 57 

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 

accura~y is only attained, however, by many observations, equivalent 

to six or twelve gagings, with the rods started 2 feet apart from side to 

side of canal. 

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. a 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 

rectangular gat,es, 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. Two 

methods of operating the meter were employed, viz, the point and 

the integration. When the point method was used the meter 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 .moving the meter 

while integrating was from 0.1 foot to 1 foot per second. The results 

for t,he 8-vane meter are as follows: 

Oompari.<Jon of discharge measured with 8-vane Fteley meter and over weir. 

Number Depth of Ratio of Variation of com- No. of parisons Rate of in- center of speed of Mean ve- of meter experi- included tegration. meter meter to locity of discharge ment. from speed of water. from weir in experi- surface. water. discharge. ment. 

Feet. Ft. per sec. Percent. 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 i.5 0 2.93 -0.4 6 1 (J 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 16 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 

The results of experiments Nos. 2 to 6 show a remarkably close 

agreement between measurements by this meter and those over the 

•Trans. Am. Soc. Civ. Eng., Vol. XII, p. 301. 
58 ACCURACY 01!' STREAM MEASUREMENTS. [No.64. 

weir. The length of an observation, thirty seconds, is too short to 

give a good average indication of the velocity. The discharge varied 

somewhat during the experiment. The depth of water in the conduit 

being small, any error in the depth must have introduce(l considerable error in the result. We would not expect, therefore, so close an 

agreement, which appears aU the more remarkable when it is seen 

from the following table that the discharge shown by two weirs may 

differ by 3' per cent: 

Values of 1n in formula Q = tnlh "/"Jgh, as fmmcl b1J Bazin and l)]J Fteley and 

Stearns." 

Values of m. 

Head on I I 

Fteley andl !!_!1--m2 

weir (h). Bazin 

I 

1nt-1n2 m1 Stearns 

Crn2). (mt)· 

I 

Meter.~. Meters. Meters. I .lfeters. Pe1· cent. 0.1428 0. 41~9 0.42911 

I 

0.0141 3.29 0.1969 0.4166 0.4263 0.0097 2.28 

0.2<l97 0.4191 ll.4259 0.0068 1.60 0.3008 0.4218 0.4266 0.0048 1.12 0.3530 0.4-247 0.4276 U.(l0'29 0.68 0.3957 0.4-272 0.4285 l 0.0013 0.33 0. 4434 0. 4296 0.4295 0.0001 0.02 0.4888 0.4323 0.4-:.HO ~0.0013 ~0.33 

I 

It is seen that for heads on the weir of from 0. 5 foot to 1 foot the 

Yariation in 1n is from 3 to 1 per cent. 

MURPHY'S EXPERIMENTS. 

The results of numerous weir, current-meter, and other experiment,s 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. 

EXPERIMENTS AT CORNELI .. UNIVERSITY HYDRAULIC 

LABORATORY. 

INTRODUCTORY. 

This investigation was begun by the writer in May, 1900, 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 9 to April I, on account of freezing weather, and was completed in May, 1901. Its object was to compare the discharge of the 

Cornell University experiment canal as obtained with a sharp-crested 

weir with that obtained with current meters operated by different, 

aAnnales des pouts et chaussees, memoires et documents, 1888, p. 416. 
U. S. GEOLOGICAL SURVEY WATER-SUPPLY PAPER NO. 64 PL. II 

HYDRAULIC LABORATORY CANAL OF CORNELL UNIVERSITY, SHOWING CORPS ENGAGED IN MAKING DISCHARGE EXPERIMENTS. 
MURPHY.] CORNELL HYDRAULIC LABORATORY. 59 

methods, and thus determine the accuracy of velocity and discharge 

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 thejr 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. Gardener S. Williams, in charge of the hydraulic 

laboratory, for many valuable suggestions and for the use of a chart 

for converting head on the Cornell Universit.y 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 in 

Pis. II, III, and IV and fig. 15, of a canal 16 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 th6 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 and the water be allowed to pass out 

of the canal at the end instead of under the side gates. In the upper 

chamber are two sets of baffles 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 4-inch by 12-inch timbers placed horizontally, with the wide face toward the current and spaced from 8 to 

12 inches apa1·t. 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 iE 

similar in construction, except that the l-inch by 6-inch strips arf 

placed vertically and are spaced 10 inches from center to center 

Twenty-eight feet below the weir is a baffie made of l-inch by 6-incl 

strips placed 3 inches from center to center, with the narrow side 
60 ACCURACY OF STREAM MEASUREMENTS. [No.64. 

toward the current. 'I'o still further quiet the waters after passing 

too weir, when the depth is small and the velocity large, a second 

baftle was constructed of l-inch by 6-inch pieces placed vertically, 

spaced 2 inches from center t,o center and fastened on the upper side 

of the baffle just described. 

Air is admitted under the falling sheet of water through 12-inch by 

10-iuch passages in the concrete, one on each side of the weir. The 

head on 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 

(P, P, P, fig. 15) perforated for 3 feet of their length with t-inch 

holes 6 inches apart around the pipes. These are placed 27 feet 

upstream from the weir, with their axes parallel with the axis of the 

ELEVATION 

·~ 

I 

I 

Pl.AIV 

~ ~ 

& l ~ "' ~ ~ 

,..,,-\ ,, \ 

~~ -~ 

~ 

"2 

~-~ n p p• 

cii 

- .... ~- 2-'3'- -•+ ---280'- ----.+ -290'--+(.-.3{)4-~ ......... -·.356~-- --+ 

"K".ehouse 

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 approximately 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 t,he depth of water in the canal. 
U. S. GEOLOGICAL SURVEY WATER·SUPPLV PAPER NO. 64 PL. Ill 

FLUME, PENSTO CK, AN D WHEEL HOUSE OF CORNELL HYDRAULI C 

LAB ORATORY CANAL. 
MURPHY.] EXPERIMENTS AT CORNELL_ UNIVERSITY. 61 

SCOPE OF EXPERIMENTS. 

The experiments naturally divide themselves fnto 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 model 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 d llfing 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 meters 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 was always held 

with a rod, the small Price meter was held with a cable, and the large 

Price meter with a cable in some of the experiments and with a rod 

in other experiments. About 3-!- inches of mud had accurnnla~d on 

the bottom of the canal above the model dam. Aftet· 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 and aftter the model dam had been removed. They are with 

high velocities and shallow depths, the scarcity of water at the time 

restricting the depth somewhat. · In all these experiments except 

Nos-. 6 and 8 the tail gates were open, so that there was no backwater. ~.rhe 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. 'rhe Fteley and the-' large Price 

were held with rods, the small Price was held with a rod in some of 

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 was 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 six-tenths-depth and integration methods, and small Price No. 

351, operated by the ordinary method. The former was held with a 

cable, the latter with a rod. 

'rhe experiment& of series D were made 220 feet below the standard 

weir, with Haskell meter No. 3 and small Price meter No. 363, each 
62 ACCURACY OF STREAM MEASUREMENTS. [N0.64. 

held with a cable. The range of depth was from 5 to 9.5 feet, and the 

velocities from 0.25 foot to 2 feet. The water surface was like that in 

series. C-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 

tlu~ 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. The depth in this series varied from 4.6 feet to 9.3 

feet, and the mean velocity from L 5 feet to 3 feet per second. It was 

· designed to extend the results of the previous year to the higher 

velocitiies. The discharge measurements were made in pairs, as in 

series D, so as to compare the results of two 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, withput swirls. To quiet it and enable the surfac:e elevation 

to be 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 veloc~ty 

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 station the veloq_it,y would be about the desired 

rate. The tail ga,tes were th~n opened or closed somewhat, as the 

case required, until the water reached the desired depth and remained 

st,eady. 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. vVhen 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," already described. When the ordinary. 

method of operating t.he meter 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 revolut.ions 

were read on a recorder. In all the other experiments except those 
U. S. GEOLOGICAL SURVEY WATER-SUPPLY PAPER NO. 64 PL. IV 

CORNELL HYDRAULIC LABORATORY CANAL, SHOWING DISTURBED WAT E R SURFACE 

DURING EXPERIMENTS I N SERI ES 8, 
MURPHY.) EXPERIMENTS AT CORNELL UNIVERSITY. 63 

with the Fteley meter the revolutions were obtained from indications 

of an electric buzzer. When the meter was· operated by the sixtenths-depth method it was held at about six-tenths depth below the 

surface in eight verticats, 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 verticals 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 t.he 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 boUom) and 1 foot from the side of the canal, and was 

passed slowly to the :surface at 4.5 feet from the side, then to the 

bot.tom 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 beginning and end was noted and the total number of revolutions were counted. rrhe meter was then carried back over the same 

path at about the same speed, and the time of passage and the number of revolutions were obtained as before. The mean time and the 

mean number of revolutions of these two passages across the canal 

are used as a single ~xperiment. When 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. vVhen this method was 

used in series E the meter was moved 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 means 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 

t.he mean canal gage reading in feet the difference in elevation of the 

canal bottom and the zero of the scale. The diRcharge when the 

ordinary method was used was computed from the vertical velocity 

curve for that experiment (see figs. 23 to 28). The observations were 

usually taken in t.he 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 

bottom. When observations in any vertical were missing. as in vet:-· 
64 ACCURACY OF STREAM MEASUREMENTS. [No.64. 

ticals 7 and 11 in series C, they were supplied by interpolation. The 

mean number of revolutions at the depth of each observ&tion for these 

eight 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 comparisons 

of series A to D. The standard weir discharge (third column) is 

the mean 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. '"fhis is not strictly true for the larger discharges, but it is near enough for practical purposes. The true 

velocity is obtained by dividing the weir discharge by the crosssectional area at the meter station. 'l.,he other columns are selfexplanatory. 

Comparisons of discharge over Cornell University standard weir with rneasure· 

rnents by current rneters. 

Date. 

---

1900. 

Mar;g~~~ 

May7 ... MayS ... Do .. May 9 .. . Do .. . ·no .. . Do ... May15 .. Do ... .May 16 .. Do .. . Do .. . Do .. . 

~ 00 Q) ;a 

.§ ,_,...:. 

..... 0> ,.., 

(!) 

~ ~';;' t< 'db£ (!) 

..... ~~ 'd..c:l 0 p<:.l 

0 «! 

z .p 

rD. ~~ ---

Cu. ft. 

pe1· sec. 1. ___ 147.991 

2---- 65. O'.M 

3.--- 78.481 

4.. -- 162. 684 5 ____ 100.379 

6 . -- - 193. 624 

7---- 131.178 8. ___ 131.037 

9 ____ 131.072 

10 ____ 148.556 

n ____ 119.947 

12 --·· 74.137 

13.--- 93.407 14 .. __ 74.137 

15____ 93.386 

,..,..,. ~ 

alcilo 

~ :p ll= ...... 0 a:! (I) 

.... .:oo OQJ,_, 

,.c:lO(I) 

~ ~ Q).s a 

A 

~~ 

Feet. 

7.996 

7.167 

7.258 

8.104 

7.542 

8.369 

7.845 

7.848 

7.845 

7.984 

7.729 

7.281 

7.484 

7.280 

7.484 

SERIES A. 

Meter observations. 

I»"" r..; .pQ) 

'8~ Q) 

.p Q) aJS. a ~ .... >:1 cii.Q "0 

~C'~ 'd 

,_,._,oo .s 8 ~ 

-----

Feet 

p.sec. (") 

1.166 L. P. 88. 

o.573 .... do __ _ 0. 683 Fteley _ 1. 268 S. P. 35L 

0.841 .... do -- 1.462 .... do·--

1.056 .... do ... 1.056 L.P. 88. 

1. 055 Fteley . 1.175 .... do ... 0. 980 8. P. 351. 

0.643 L.P. 88. 

0.788 ·---dO ..• 0. 643 Fteley _ 0. 788 ..•• do ... 

.6 

000 Variation. .... !=I Ordinary Integration 00 

,..,:;:: method. method. Q)cil 

.t:J~ 

a~ p<ll Q-Qo Q-Q1 

-

z --

Vo ---

Ql --V1 --Ql 

--

~ --~ 

Feet Cu: ft. Feet Cu. jt. 

p. sec. per sec. p. sec.. per sec. Per ct. Per ct. 76 1.097 138.478- -------- + 6.43 29 0.447 50.714 ------- -------- +22.01 31 0.677 77.780 ------ --- ---- + 0.90 ------- 38 1. 267 162. 464 1. 252 160. 62 + 0. 14 + 1. 26 

20 0. 790 94.318 . ------ ----- --· + 6. 03 

35 1.435 190.109 ------- -------- + 1.81 

18 1. 036 128. 657 1. 031 128. 04 + 1. 92 . +2. 32 

18 0. 982 122. 000 1. 006 124. 98 + 6. 90 +4. 63 

18 1.148 142.570 ---·--· ---------8.77 

~ 6:= ~Y::~ ·o:97s- ·ii9:oo· + ::~ ·+o:26 

36 0.533 61.432 ------- -----··- +17.14 

32 0.744 88.110 ----·----------+5.72 29 0. 642 73.985 . ------ .. ------ + 0. 20 32 0.834 98.804 ------- ---------5.80 

a L. P. =l~rge Price; S. P. =small Price. The figures given are the meter numbers. 
MURPHY.] EXPERIMENTS AT CORNELL UNIVERSITY. 

Comparison8 of discharge over Cornell University standard weir with measure· 

ments by current meters-Continued. 

00 

~ :B >= Q) "',...:, 

a .... Q> <1)._,. 

-~ ~Q) 

Date. Q) !ll.l Po 

1>1 'd::'il "' Q) "'..= 

"0 ~0 

'd 

~ 

0 ol 

~ z rfJ. 

---

Cu. ft. 

1900. per sec. May 19.---------·-- 1 50.366 Do ______________ 2 50.260 Do ______________ 3 50.154 

May 21 ....... ------ 4 65.625 Do ______________ 5 65.625 

Do ....... ·---·-·· 6 66.896 Do _____ .. __ ·----- 1 21.616 Do ______ -------- 8 66.731 

Do .... ·--------- 9 33.060 

May 22.------------ 10 21.369 Do. _____ -------- 11 94.410 

Do ...... -------- 12 94.410 Do ______ ---- ____ 13 57.854 Do. _______ ------ 14 57.854 Do ______ --------. 15 43.761 Do ________ ·----- 16 43.761 Do __________ ---- 17 29.598 Do ________ ·----- 18 29.598 

Do .. ------------ 19 18.932 Do. _______ ------ 20 18.932 

SERIES B. 

Meter observations. 

l=l"' 

E.~ .... <1) i.. 

Q) "'""' $ Q)Q) ~ 

~a 1»-+'> .pO ~ OrJi 

~""' ·~ (!) Q) orn ..... >= Ordinary method. 

s 00 ..... ~>:l s~ ,...:;:: o .... 0 ~~ ..... Q)ol ..=~~ 0 .a~ 

-+'>i=lo Q)a 'd P,~Q) a ::l..,. 

~ Q)Orll 

~~ p 

0 z Vo Qo ------------------

Feet Feet Feet Cu. ft. per sec. pe1·sec. (a) 

1.115 2.823 S.P.351 16 per sec. 2. 790 per sec. 49.774 

1.115 2.823 Fteley 16 3.599 64.206 

1.110 2.824 L.P. 88 16 3.103 53. '190 

1.299 3.157 Fteley 24 3.344 69.502 

1.299 3.157 L.P. 88 24 3.085 64.118 I 

2.000 2.091 Fteley 24 2.500 80.000 

0. 786 1.719 L.P. 88 16 1.538 19.341 

2.029 2.056 .... do ... 24 1.900 61.682 

0. 741 2. 766 Fteley 16 3.273 32.295 

0.550 2.428 ____ do. __ 16 2.9<l5 25.916 

l. 885 3.13U .... do. 24 3. 789 114. 2.1)0 

1.885 3.130 L.P. 88 24 3.102 93.556 L 198 3.018 Fteley 24 3.720 71.305 

1.198 3.01S L.P . .S8 24 2.947 56.589 

0.953 2.870 S.P.351 16 2.698 43.055 

0.953 2.870 Fteley 16 3.474 52.944 

0.693 2.671 S.P.351 16 2.425 26.876 

0.693 2.671 Fteley 16 3.137 34.768 

0.464- 2.553 S.P.351 8 2.290 16.983 

0.464 2.553 Fteley 8 2.932 21.744 

Varia· 

tion. 

Q-Qo 

~ 

---

Per ct. + 1.11 

-27.75 

- 7.26 - 5.91 + 2.30 

-18.09 

+10. 54 

30 + 9.07 + •) ""· -21.28 

-21.01 

+ o.ol I 

-23.2 7 + 2.18 + 1.62 

-20.98 

+ 9.19 

-17.47 

-10.30 

-14.84 

"L.P. =large Price; S. P.=small Price. The figures given are the meter numbers. 

IRR 64-02--5 
Comparison of discharge over Cornell University standard weir with measurements by current mete1·s. 

SERIES 0 

Meter observations. Variation. 

Number Standard Small Price No. 351, Small Price No. 363. Small Price 

of weir Depth of True ve- ordinary method. Small No.363. 

Date. experi- discharge water in locity (F) 

Price 

canal at Integra· No.351, ment. (Q). at meter Ordinary method. meter (QQQo) . section. Vo Qo tion . Q-Q6 Q-Ql 

section. method, Q Q v6 Q6 (QI)• -------

1900. C1~.jt.per C1t.jt.per Cu. ft. per Cu. ft. per sec. Feet. Ft. per. sec. Ft. per sec. sec. Ft. per sec. sec. sec. Pe1· cent. Per cent. Pe1· cen October24 •••••••••••••••••••••••••.••• 1 216.131 9.460 1.409 1.446 219.836 1.465 222.980 220.393 - 1.77 -4-.11 -0. 

Do ..••.•••••••••••• ~--···.--------- 2 140.515 9.374 0.932 0.969 146.060 0.985 14~. 528 143.099 - 4.13 -6.13 -5. 

Do .....•••••••..•••..•••.••....•... 3 71.681 9.338 0.477 0.493 73.050 0.487 73.167 71.514 - 2.38 -2.08 -1. 

Do.---- •......•...••.•••••••• ------ 4 38.254 8.910 0.265 0.259 37.420 0.278 40.113 33.330 + 2.03 -6.00 -16. 

October26 .•...•• -----· ••••••••..•••••• 5 178.553 7.673 1.444 1. 44o9 179.130 1. 489 184.075 174.679 - o.sa -3.09 -5. 

Do .. ------------------------··--·-- 6 125.298 7.640 1.018 0.999 122.974 1.047 128.880 120.789 + 1.85 -2.78 -5. 

October 27-------·····--------. ····---- 7 61. Z72 7.582 0.502 ......................... ........................ 0.522 63.771 6l.o27 ----···---- -4.88 -4 . 

DO------···--------------------·-·· 8 31.176 7.557 0.255 0.215 26.180 0.258 31.488 28.070 +16.01 -1.04 -22. 

Do ..••.••..•..•......••..•••.•••... 9 50.310 6.005 0.515 0.494 48.208 0.540 52.696 46.451 + 4.17 -5.92 -7. 

Do .••...•..•••.••••.••••••••••••.•• 10 196.387 6.278 1.940 1.890 192.799 1.989 201.367 188.232 + 1.83 -1.46 -4. 

Do ......•.•••••••••.•••...••.•••••. 11 132.414 6.399 1.283 1.251 129.078 1.at8 135.991 123.816 + 2.52 -3.18 -4. 

Do ......•••••.•••...•.•.••.•••••••• 12 91.056 6.319 0.893 0.847 86.318 0.920 93.758 83.872 + 5.20 -5.08 ~ 2. 

October 29 .••••••.••••••••••••••••••••• 13 65.319 8.476 0.478 0.464 63.325 0. 49'2 67.146 60.459 + 3.07 -2.35 -2. 

October 31. ••.••.••••••.••••••••••••••• 14 198.258 8.470 1.454 1.460 199.115 1.514 206.480 187.795 - 0.44 -3.71 -6. 

Do .•.••.•..•..•••.•••.••••...•••••• 15 125.301 8.508 0.915 0.890 121.921 0.949 130.001 114.522 + 2.69 -3.75 -9. 

November 1 .•••...•••••••••••••••••••• 16 31.223 8.455 0.229 0.201 27.364 0.240 32.674 25.186 +12.37 -2.47 -39. 

-------

6 

4 

30 

~ 

~ 

> 0 

0 

<:::1 

~ 

> 0 

~ 

0 

~ 

00 

1-3 

~ 

trJ 

> Is: 

Is: 

trJ 

> 00 

<:::1 

~ 

trJ 

~ 

trJ 

~ 

1-3 

r'l 

~ 

~ 
Comparison of discharge over Cornell University standard weir w'ith measurements by current meters-Pontinued. 

Date. 

1900. 

December 6 ••••.••..••••••••. 

Do--····-················· December 7 

Do --- Do .........•••.... 

Do--·······---------------

Do----------·········----- DecemberS 

Do .....••••.••...... Do 

Do ........••.... Do 

Do 

--

Do .....••.•••.....•••.••.. 

Do •.••.•••...•.........•.. Do .•••.••••••• 

SERIES D. 

Meter observations. 

Nu~ber I ~':,'/:'"d I Depth of True ve- Ordinary method. Six-tenths- experi· discharge water in locity (JT) Kind of depth ment. (Q). c~~~e~t at meter meter. a Vo Qo method 

section. section. . (Q6). 

----

Cu.ft.per sec. Feet. Ft. per sec. Ft. per sec. ou.tttar976· Ou.ft.per sec. 1 233.2112 9.505 1.528 S.P.363 .... 1.519 ............................. 2 233.262 9.505 1.528 Hask.3 ..... 1.484 226.380 ...... 23ifi2() 3 ~29. 731 9.317 1.535 ..... do •..... ...................... ................................. 4 117.673 b9.536 0. 768 ..... do •••••• 0.832 b127.421 b 126.498 

5 117.673 b9,536 0. 768 S.P.363 •... 0. 794 b121. 601 b 119.301 

6 95.176 b9.524 0.622 Hask.3 ..... 0.676 b103.401 b 105.846 

7 25.176 b9.524 ............................. S.P.363 .... 0.563 b99. 883 b 97.892 

8 221.749 7.245 1. 905 Hask.3 ••... 1.864 216.932 218.680 

9 221.749 7.24.5 1.905 S.P.363 •... 1.867 217.281 222.521 

10 191.165 7.217 1.649 Hask.3 ..... 1.675 194.183 200.209 11 191.165 7.217 1.649 S.P.363 ... 1.651 191.400 192.793 

12 110.186 7.183 0.955 Hask.3 ..... 1.022 117.919 118.802 

13 110.186 .. ----- .............. 0.955 S.P.363 .... 0.955 110.188 110.858 

14 56.717 7.113 0.496 {Hask.3 .•... .............................. ............. ---- .......... 53.244 

\8. P.363 .... -.................. ....................... 58.270 

15 57.071 5.154 0.689 Hask.3 ..•.. 0.730 60.455 62.277 

16 57.071 5.154 0.689 S. P.363 •..• 0.672 55.651 57.308 

aS. P. =small Price; Hask. =Haskell. The figures given are the meter numbers. 

b Hook gage broken; depth not accurately measured. 

I Variation. I 

Integra- tion Q-Qo Q-Q6 I Q-Q1 

method -Q- Q Q 

(Qt>· ___ , ___ 

Ou.ft. per Per cent. 

~:~?f" :j~~ sec. 

235.082 +0.55 

239.968 +2.95 

235.828 - 4.09 -2.66 .......................... -8.2R - 7.50 .. ....................... -3.34 - 1.40 ............................. -8.63 -11.21 . ......................... -4.93 - 2.84 ······---- 228.340 +2.13 + 1.38 -3.08 

------------ +2.01 - 0.35 .................... 202.647 -1.58 .... 4. 73 -6.00 ............................ +0.20 - 0.84 ........................ 119.609 -7.01 - 7.84 -8.55 .. ....................... 0.00 - 0.68 

-------............ ... .............. - 6.14 . ........ -- ~- . -.... 62.277 ......... -5.94 ··--·- = ~:ig 1····:.:9~io .......... ·--·-· +2.49 - 0.42 

~ td 

~ 

.:::. 

t?;j 

>1 

~ 

t?;j 

t?;j 

~ 

tz 

~ 

rJJ 

>-

~ 

a 

0 

~ 

tz 

t:=J 

1::'"1 

t"'l 

c::: 

~ 

H 

<: 

t:=J 

~ H 

~ 

~ 

0':> 

-:t 
68 ACCURACY OF STREAM MEASUREMENTS. (N0.64. 

It is seen from the foregoing tables that the meter discharge differs 

from the weir discharge all the way from 0 to 40 per cent. One might 

say, without careful examination, that the current meter must be a 

very unreliable velocity-measuring instrument; but when we examine 

these results carefully and plot them according to velocity we find the 

case very different. Take first the results by the ordinary method. 

S-1 nO# >J63 

t1 : ...... 0 d 

Len>e ~ 0.88 :s-11 -.,, OJ51 

1\ ~ 

0~ d 0 (~ _o d 0 

0 "--

- No 

1'/'elej 

0 '1ft - _o' 

)-, / 0 

0 I.Yc .................... ~ -.....,~ 

0 

0 .. I 0 

- .Fro. 16.-Diagram showing difference between meter discharge by ordinary method and weir 

discharge, from measurements in Cornell University experiment canal. Line 0-0' represents 

weir discharge. 

These are plotted for each meter in fig. 16, using mean velocity as 

abscissre and percentage difference as ordinates. It is seen that nearly 

all of these points fall on well-defined lines. The few exceptions are 

those in which the depth is small and the errors of depth and position 

of meter have a large effect on the measured discharge. The discharge obtained with the Fteley meter differs more from the corre0 0 

c ....-! f.- ~ 

I ~ 

lntq_ '8ti0n f'etho /nte~ '8tlon meth if I 

I 0 

& 0 e k-1 !...--- .-;-

"·I(> 

~ ~a depth imeth 4'1i defdh 

~ - 2 3 2 . 1.1 Small Price mt?t(u'NtJJ6J Ht6.slr~/mfltW'No..J 

Velocity~ 'eet pe,. !;t!ccnt~ 

Fro.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 0-0' represents weir discharge. 

sponding weir discharge than that obtained with the other meters. 

This is because it had never been rated. The constant we have used 

in reducing the observations with this meter-viz, 1 revolution per 

second at 1 foot velocity= 1.072-was obtained from observations 

by students. It is not, however, much in error for this velocity, 

but is largely in error for other velocities. The rating obtained from 

these weir experiments is given in the table on page 81. For the other 
MURPHY.) EXPERIMENTS AT CORNELL UNIVERSITY. 

three meters the percentage error is small for velocities above 1 foot 

per second. For the Price meters the error is positive and increases 

rapidly as the velocity decreases. For the Haskell meter the error is 

negative and increases, negatively, rapidly as the velocity decreases. 

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 quantity is only 

a 1-per cent error in a quantity ten times as large. The rating tables 

as derived from these curves and as found by moving the meter 

through still water are given in the table on page 81. ~xperiments 

with depths of 0. 75 foot or less (Nos. Hand 17 to 20 of series B) are 

not plotted in the diagram (fig. 16), as the probable 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 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-tenthsdepth and the integration methods. 

It is seen that the meter discharge by 

these methods is greater than the weir 

discharge: being 4 or 5 per cent greater 

for velocities above 1 foot per second. 

ln the integration method, for small 

velocities the difference increases very 

rapidly as the velocity decreases. It 

Snt. p,.;"'"t!le~ No. 3$1 

OU,..Z1,7,J.:75,?7,Z!I..Jf..3.J, 3$,1nd37 -.-..r 

'i,,~ j •ju u v 

FIG. 18.-Diagram showing difference 

between meter discharge with differ 

ent meters and w:eir discharge in experiments of series E in Cornell University experiment canal. Zero line 

indicates weir discharge. 

is seen from figs. 16 and 17 that while the ordinary method 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; 

~rhe results of t.he discharge measurements 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. 
70 ACCURACY OE' STREAM MEASUREMENTS. [No.64. 

Comparison of dischm·ge over Cornell University .<;tandard weir with measure- ments by current rneters. 

SERIES E. 

: Depth of True ve- Standard No. of ! water in locity at weir dis- Meterdisexperi- Date. '[ canal at meter sec- ha charge ment. meter sec- tion. c rge ( Qw ). ___ 

1 

____ ~~on.___ _ (Q). 

1901. 1 April L. .. 2 ..... do ____ _ 3 April2 ___ _ 4 ..... do ____ _ 5 _____ do ....• 6 _____ do ____ _ 7 ..... do ____ _ 8 ..... do. ___ _ 9 April5 __ _ 

10 ..... do .... . 11 ..... do .... . 12 _____ do. ___ _ 

13 _____ do .... . 

14 ..... do .... . 15 ____ .do .... . 16 _____ do .... . 17 ..... do ___ _ 18 _____ do ..... 19 ..... do .. ___ _ 

20 ..... do ..••• 

21 April6 .... 22 ..... do ____ _ 

23 April10 .. __ 

24 ..... do ..... 2.') .... do ____ _ 

26 .... _do ..... . 27 ..... do ___ _ 28 _____ do .... 

29 Apri11L .. 30 ..... do ..... 31 ..... do. __ _ 32 ..... rlo ____ _ 

33 ..... do ..... 34, ..... do. __ _ 35 _____ do ____ _ 36 _____ do ____ _ 

37 ..... do ____ _ 

38 ..... do ..... 

39 Apri112 .. . 40 ..... do .... . 41 .•... do .... . 42 ..... do ____ _ 43 _____ do ..... 44 ..... do ____ _ 

45 ..... do ..... 46 _____ do ____ _ 

47 ..... do ____ _ 48 ..... do ____ _ 49 ...•. do. ___ _ 

50 ..... do ..... 

Feet. 

9.075 

9.075 

6.079 

6.079 

7.453 

7.453 

5.742 

5.742 

7.409 

7.409 

6.295 

6.295 

5.628 

5.628 

5.294 

5.294 

4.892 

4.892 

4.617 

4.617 

4.808 

4.808 

8 744 

8. 744 

7.874 

7.874 

6.889 

6.889 

6.129 

6.129 

5.483 

5.483 

5.185 

5.185 

5.003 

5.003 

9.256 

9.256 

9.344 

9.344 

8.934 

8.934 

8.297 

8.297 

7.806 

7.806 

7.266 

7.266 

6.439 

6.439 

Ft. per sec. 1.472 

1.456 

2.208 

2.187 

1. 744 

1.710 

2.137 

2.171 

1.869 

1.883 

2.137 

2.177 

2.377 

2.438 

2.611 

2.602 

2. 764 

2.827 

2.936 

3.019 

2.985 

3.006 

1.670 

1.657 

1.846 

1.862 

2.108 

2.073 

2.34,0 

2.320 

2.596 

2.604 

2. 725 

2. 758 

2.816 

2.834 

1.522 

1.538 

1.486 

1.541 

1.613 

1.543 

1.646 

1. 700 

1. 775 

1.803 

1.879 

1. 943 

2.132 

2.182 

Cu.jt.pe1· sec. 

204.41 

204.41 

208.88 

208.88 

200.81 

200.81 

197.64 

197.64 

222.67 

222.67 

2'Z0.33 

220.33 

219.38 

219.38 

221.96 

221.96 

222.81 

2'22. 81 

224.75 

224.75 

230.36 

230.36 

230.75 

230.75 

229.28 

:2.l. 28 

229.91 

229.91 

227.16 

227.16 

2'~.01 

225.01 

224.06 

224.06 

222.60 

222.60 

223.40 

223.40 

224.63 

224.63 

221.39 

221.39 

221.39 

221. 3.Q 

221.49 

2'21. 49 

221.21 

221.21 

221.03 

221.03 

Cn.jt.pe1· sec. 

214.08 

212.33 

216.28 

214. ~2 

208.85 

204.77 

197.02 

200.15 

222.68 

224.3.5 

216.00 

220.03 

214.82 

220.33 

2'22.02 

221.27 

217.32 

222.27 

218.32 

224.50 

230.66 

232.30 

234,. 68 232.85 

233.61 

235.64 

233.25 

2'49.38 

230.25 

2'28.28 

228.59 

229.30 

226.98 

229.73 

226.37 

227.82 

226.38 

228.71 

223.11 

231.37 

231.58 

221.53 

219.50 

226.70 

2!?2. 69 

226.19 

219.34, 

226.81 

220.43 

225.61 

Variation 

(QQ~w). 

PPr cent. 

-4.73 

-3.87 

-3.54 

--2.55 

-4.00 

-1.97 

-0.31 

+1.27 

0.00 

-0.75 

+1.96 

+0.14 

+2.08 

-0.43 

-0.03 

+0.31 

+2.46 

+0.24 

+2.86 

+0.01 

-0.13 

-0.84 

-1.70 

-0.99 

-1.89 

-2.77 

-1.45 

+0.23 

-1.36 

-0.50 

-1.60 

-1.91 

-1.30 

-2.53 

-1.69 

-2.34 

-1.33 

-2.38 

+0.ti8 

-3.00 

-4.60 

+0.07 

+0.81 

-2.40 

+0.54 

-2.07 

+0.85 

-2.53 

-0.27 

-2.07 

Diff~rencein 

meter Kind of meter. a discharges. 

Pe1·cent. 

Hask.3 ... } 086 RP.36.'L_ · 

Hask 3 ... } O. 99 S. P. 363 .. Hask. 3 ... } 2_

03 S. P. 363 .. Hask. 3 ___ } 1 58 8. P. 363.. · Hask. 3 ___ } 0 75 8. P. 363.. · Hask. 3 _ . } 1 82 8. P. 363.. · Has}r. 3 ___ } 2 5 S. P. 363.. ·• Hask. 3 ... } 0 3 S.P.363.. · Hask. 3 ... } 2_

22 S.P. 363 .. Hask. 3. __ } 2_

85 S. P.363 .. 

,-1.60 

S.P.351. } 8. P. 363 .. 

8. P. 351..} S.P. 363 .. S. P, 351 .. } S. P. 363 .. S. P. 3.51 .. } 8.P. 363 __ 

S. P. 351 .. } 8.P. 363 .. S. P. 351 .. } 8. P. 363 .. S. P. 3.51 .. } 8. P. 363 __ S. P. 351 __ } 

S. P. 363 .. 8. P. 351 .. } 8. P.363 .. 

0. 71 

0.71 

0.88 

1.68 

0.88 

0.31 

1.23 

0.65 

1.05 

0.90 

Hapsk. 3 ... } 3_68 8 .. 351 .. 

S. P. 35L_} 4 67 Bask. 3___ · 

-EC~~35i::} ~- 21 

Hask. 3. __ } 2_

61 S. P. 351 .. Hask. 3 ... } 3 38 S. P. 351.. · Hask. 3 ... } 1 80 S. P. 351.. 1 

___ ·_ 

I 3.22 

aS. P. =small Price; Hask. =Haskell. The figures given are the meter numbers. 
:MURPHY.) EXPERIMENTS AT CORNELl. UNIVERSITY. 71 

The principal results of the foregoing comparisons have been condensed in the following table: 

Table showing percentage variation between weir discharge and meter discharge, 

and between meter discharge by different instrwrnents of expe1·irnents in series E. 

Experiments. 

lto2Q _____ 

Do _____ 

21 to38 ____ 

Do _____ 

39 to 50 ____ 

Do _____ 

Kind of meter. 

Haskell No. 3 -. 

S. Price No. 363 

8. Price No. 351 

S. Price No. 363 

S. Price No. 351 

Haskell No. 3 __ 

Difference between standard weir 

discharge and meter discharge. 

Difference in discharge of simultaneous meter meas- urements. 

Max. Min. Mean.a Range. Max. Min. Mean. ltange. ---1------1-----------

Per ct. Per ct. Pe1·ct. Per cent. Per ct. Per ct. Per ct. Per ct. -4.73 0.00 -0.33 -4.73 to +2.86 ·------- ----~--- -------- _______ _ 

-3.87 +0.01 -0.76 

-1.89 -0.13 -1.38 

-3.87 to +1.27 2.85 0.34{ :~:~:} 2.51 

-1.89 to -0.13 ___ . ____ -------- .. __ ---- ------ _. 

-2.77 +0.23 -1.56 

-4.60 -2.07 -2.78 

-2.77 to +0.23 1.68 0.31 { :8:~} 1.37 

-4.60to -2.07--------------------------------

+0.85 -0.27 +0.40 +0.85to -o.21 4.67 1.so{ :g:~n 2.87 

"Regarding signs. 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 per 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 meter, 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 

expected, however, since there are a number of possible errors in the 

former which are not in the latter. Errors in measuring head, depth, 

calibration o_f weir, velocity, and rating of meter affect the 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 these 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 by 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. 
72 ACCURACY OF STREAM MEASUREMENTS. [No.64. 

VELOCITY CURVES. 

Curves of equal velocity in the cross-sectional area of observation 

" .vI ' r-~ 

If. . . -r--

. . D -~ """" ~ ~':f· v 

1'.• ce: . ~~ 

D 

.<": 

*~·~ ~ 

wi r11.1:. "' .... 

J----: ..--r-... :~ ._ 

r---f-." .. 11!!.:£ CldWS i":!'""''ly -::: ::::: 

"-' 

~' ...- .\ . ~ 

/.~ 

.. A' 

/"'- ,..,. 

'lHO 

I~ 'P 

.. v~ 

~ 

#. -

,qJ 't ~~~c. 

... 

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. 'rhey are 

FIG.l9.-Curves of equal velocit.y in experiment No. 11, self-explanatory. Fig. 20 

se:ies A. illustrat,es a case of small 

I 

\ z !!~~';;; 1\ v . .., ../ 3.6!J 

·.~ ~ -~ ~ ~ .. ,.,__~~ // . - """~'- . ~~~~~3 .. ~r:;v"" .~i#"" 

· -~~~· ~R~ ·-:'""~~vfA' D.........._.! . ;·--.IS 8 10 2 . .$0~ ... ~ .?.~· 1.8 -3.0 " .M .. ,. WJdth can a~ (t. V•IDcity,Ft.sH. 

~ r---.--.. 1'-r--.. · / 

.L v A 

.....-- ..... e· 

_/ 

~ 

I 

~ ;:~~ ;-ity / P.Fi'~ 

depth, high velocity, and 

no back-water effect. The 

maximum velocity is at 

the surface, nearly midway between the banks . 

In figs. 19, 21, and 22 the 

maximum velocity is below the surface and not 

mid way between the 

banks. It is less at the 

center than 3 or 4 feet from 

FIG. 20.-Curves of equal velocity in experiment No. 12, either side. This is true 

series B, with large Price meter No. 88. of all the experiments of 

"'' B :t.J t.$1 . lSg ~ 

.. ( 

\ s/.6'\o 4 Cvrv ""'~ 

.. ~ "\. ~ 1-:s '"" 1-:s /7!\ '3 

~'~ ~ 

z ~'--, 

·~ "~ !<! .. t:J!J ,.t{.t Ji!O 139 

':-..... ,, :-;q;~ ~ 

0 2 .. ~,q #, rt 

14 v.: r--:: 

~,. -- --- ·8 

"'A\ 

'""" c/ty 

I 1.63 

. ~~.~I 

"" 'r-l.! l(l 

'\ r=!'QJ " -J 

I-' y" 

0 f' /.,. 

... 

~\ 

~ 

;,t~o i!fY 

._I{!!!!. ~ 

/ 

~ . .se~ / 

Vel city, 

~ 

\ 

j 

1 

l 

I 

v 

/S 

series A. We tried admitting the water to the 

upper chamber of thecanal in various ways, by 

opening some of the gates 

and closing or partly closing others, but the distribution of velocity appeared to be nearly independent of the openings 

through which the water 

was admitted to the can~l. 

Horizon tal velocity 

curves are shown in these 

same figures (19 to 22), the 

FIG. 21.-Curves of equal velocity in experiment No.14, velocity curve at sixj ii ~ f~! fiffy 1\'\ ~ 

---- \ \ 

/ B 

/.0 

A ./ c I\\ 

series c. The dots are for small Price meter No. 351; tenths depth below the 

heavy black squares for small Price meter No. 363. 

surface being shown, and 

also the curves for surface and bottom. In these figures the velocity 
HURPHY.j EXPERIMENTS AT CORNELL UNIVERSITY. 73 

near the north side of the canal is somewhat less than that near the 

south side. This is true of all the experiments of series C and D. It is 

due to the north side of the canal being 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. 

Vertical velocity curves for these four series of experiments {A to 

D) are shown in figs. 23 to 

28. Each of these curves 

is the mean of observa- .~ ~- ,s. ,Se 1\ ui ~ 

tions in the eight verticals ~r.,OIIt-t-'~-"":+--+,.<,o~' -~--,'+-""+-+-l-\-:-!!/./"HI--,/.""H--+--1-+--<»--+--+--i ""' ,a. ,_()6 1.011 \_ .,.,. 1 /.tHo 

1, 3, 5, 7, 9, 11, 13, and 15 •l--+a,~!:J!'d"~oi~C'<~Vtvq-e'IJi1'<;!-+'f-:-+---f--+--+--H--f-l--i 

feet from the south side ~ V I !/ 

of the canal. For series ~"l~ /.t}g f" ~ ~ 1/~ ./! 

C and D, figs. 26, 27, and :-~ ~ __.L J-r'~ .P ~'/ 28, the observations ob- ~~v4 ~- ';""f-"'!.- L 

tained with small Price 0 "' • w.:-th,H.. IO '" •• ··.v~>ts:g 

~~1--.-.-.--.~~-~~-r~~-r-.-.-~-. 

meter No. 363atsix-tenths t: .-.;"..t=:f:::-:::.~V ..... - -.... ~ 

depth are shown by the lit- J1V .L ?" r------...._ ....-~ ~: 

tlesquares. Asarulethey sV z:::~:,~ -Z.~r-';'"Z .. ""....," 

fall outside the curve, FIG. 22.-Curves of equal velocity in experiment No. 20, 

meter No. 363 indicating series D. The dots are for Haskell meter No.3; heavy 

black squares for small Price meter No. 363. 

a somewhat greater velocity than meter No. 351. This fact is also shown by the corresponding 

curves of figs. 1() and 17. The two sets of velocity curves {full and 

dotted) of fig. 28 were found from simultaneous velocity measurements. Two parties measured velocity in the same section at the 

same time. One party, with the Haskell meter, started near the south 

No.I N ~ ~~ • 

-""""' 

=- - . ~~ No.2 

--

~~ ~ ~~ ~ . "' 6 

~ s ..,_, 

! If J/ ej / 17 

I 7 1/ 

.8 I L 

z ~ I ,~), } ;. J .s/•, / ) 

"' _..V J) / v / I . /,_ I / / Ifill> 

I 

.,..,..... v ~ K / v .8/ v 

iB I /v ~ "'/ .!J '" 

oclt ~ ... I. 6 [7 Jl_ 

FIG. 23.-Vertical velocity curves obtained with current meters in experiments in series A. 

Nos.l, 2, 8, 12, and 13are for large Price meter No. 88; Nos. 4, 5, 6, 7, and 11 are for small Price 

meter No. 351. 

side of the canal and worked toward the north side; the other party, 

with the Pric~ meter, started at the north side and worked toward 

the south side. It is seen from these curves {fig. 28) that the bottom 

velocities agree more closely than those at the surface, and that the 

Haskell meter gives a much larger surface velocity than the Price 

meter. We should expect a little difference, since the revqlving head 
74 ACCURACY Oli' STREAM MEASUREMENTS. [No.64. 

of the Haskell meter is larger than the wheel of the Price meter, and 

its center being farther below the surface it must revolve faster. But 

the difference in velocity is much greater than this little difference in 

depth of axis would indicate. (Seep. 91.) 

The shape of these curves evidently depends on the depth and 

velocity. For depths not exceeding 1 foot it is a nearly straight line, 

IN. 

~ "' . ~ 

~15 

1 . .4; 3 ~:' 

I . .. . I. I. I. • 1.~ i~ 1/ ~ I. lil 1/ I I ~ ·"' 1,61 7 v / v . 7 t 8 

I 1/ I / .v. v _..,.....~-"" / / // ............. y" V&o 1fr,l sec. 

FIG. 24:.-Vertical velocity curves obtained with Fteley current meter in experiments in 

series A. • 

with the maximum velocity at the surface and the mean velocity at 

mid depth. For depths of 8 or 9 feet and small velocities the curve 

is very flat, with the maximum velocity at two-tenths to three-tent,hs 

depth and the mean velocity at sixty-five-hundredths to seven-tenths 

depth below the surface. The radius of curvature decreases as the 

velocity increases. In ·an of these curves the least velocity is at the 

bottom. Nos. 6 and 8, series B, fig. 25, show thP, effect on the vertical 

I 

s I u._.e 

~ 

~f _M 10 I~"' ~ ~· ~19 Af2o _..:..--~ 

~ v / y-; v v 0 / Z2 

~or ~ No.I ~2 No-15 o./6 I 

... ~ IS il .-::;:::. ~ .........-" v / / 7 ~ , s . .J~ lG 

~ ~ v v 30 J:.: vs v _,.v ob:::== 3 .-: ......... J 2 I! I! !I 

ti ..§ No. tl 2 • 

! "'"'1. = 't il ~ 2 2 2 2 r ~Ft 

I j z.....-:l VJ 6 3. 

v 

.0 ~ 'f. if 

v v _.... / / / 29 ~~ ~ 

_..Y ~ v ,...... v v - ~ ~ f::---- 0 

- ~elo lyfl sec. 

Fig. 25.-Vertical velocity curves obtained with current meters in experiments in series B. 

Nos. I, 15,17, and 19are for small Price meter No. 351; Nos. 3,5, 7, 8, 12, and Hare for large Price 

meter No. 88; Nos. 2, 4, 6, 9, 10, 11, 13, 16, 18, and 20 are for Fteley meter. 

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 discharge at the lower end is to force the thread of 

maximum velocity from the surface to a depth of two-tenths or more. 

'"rhe table on page 77 gives the position of the threads of maximum and 

mean velocity taken from the curves shown in figs. 23 to 28. It is 
MURPHY.) EXPERIMENTS AT CORNELL UNIVERSITY. 75 

difficult to locate the threads with accuracy, since very little change 

in the shape of the ci1rve would make a great change 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 

or more per second, however, the threads can be located with a fair 

..... ~ ~ ~ ~ ~ ~~ \ \ d ~ -~ ~ 

7 

. ~ ~~ I~ ~ \ \ _'l 6 1\ ;:: 

.,.. . j 9 0 I 

$I} 

. "' .I 2 ~ 1 ~ . . t ~ f ~ 1 y s " 

2 I la .I I l/ /12 J lL 1 

If f s If I~ 

I lL 2 /t>.L, .. 5 v l 2 ,/ - J / • lJ-V IQ 

~I--~ 1.1 1.2 1--v:.c r"~' ec. ~ 

FIG. 26.-Vertical vel0city curves obtained with current meters in experiments in series C. 

Heavy round dots are for small Price meter No. 3M: the square blocks are for small Price 

meter No. 363. 

degree of accuracy. The position of the thread of maximum velocity 

as found from serjes A is eighteen-hundredths depth below the surface; for series B it is one-tenth depth; for series C, thirt,y-eighthundredths depth; and for series D, twenty-four-hundredths depth. 

For the mean of C and D, in which the conditions are nearly the same, 

it is thirty-one-hundredths depth. The position of the thread of mean 

J .~/6 ~ ~ " \ No 9 ~ ~ ~~ .,j!~ 

$ 

5 ""' i'\ \ '\ - ~ 

.\ \ I,) . ,. . ... I l ' eo .J 

1: I J ) i / . . .1~ 

~ .; . ..-'~ ~ J 2 

/. ....tv L-<v / v I J ~ v v ~ r-- 1/ v """ / ~ !.--f.-- YeA~ ~ .... .......... 

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. 

velocity as shown by this table is sixty-six-hundredths depth for series 

A, fifty-four-hundredths depth for series B, and sixty-six-hundredths 

depth for series C and D. It is seen that the threads of mean and 

maximum velocity are nearer the surface in series A than in series Cor 

D, although the depths ·do not differ much. This is probably due to 

the influence of the Croton model dam, the long upstream slope of 
76 AOOURAOY OF STREAM MEASUREMENTS. [No.64. 

which has had the effect of forcing the thread of maximum velocity 

up to thirteen-hundredths depth. As the ratio of width to depth 

~ 

\~ ,a ~ ~ ~ I : ' - Hesk '/No. - Smell Pri'~ "'"j6 

l r I ~vw .. No. .No.9 7 No-12 No./0 .., I I I ~ ,"\ I I~ - . 0 r=1 . 1 I 

T I/ /; \ f No./5 I I o.IG s 'j I I I 

I I ~ ""''~o I I /.' 

·rr ~,. /' .I I ,I // 0 le I 

"'l /J I 1/ I /I! ;· IP. I 

~ I 

/( /j }o 0/ ) j{ / o/ -;4 I 

54 f~\ j/ 

-~ /·/~ ~/ ~'l~ ~JI .. toch<rt ~ .s ·" ·' 8 .. m 1.$ .8 . 9 , .. .. 1.6 J.6 1.7 ,. 1.9 .6 .7 

FIG. 28.-Vertical velocity curves obtained with Haskell meter No. 3and small Priee meter No. 

363 in experiments in series D. Open circles are for small Price meter No. 363, point method; 

heavy black dots are for Haskell meter No.3, point method; heavy black squares are for small 

Price mete:.; No. 363, six-tenths-depth method. 

changed from 16 to 2 the thread of mean velocity moved from fiftyfour-hundredths depth to sixty-six-hundredths depth below the surface. 
Table showing position of threads o.f rnaxirnurn and rnean velocity in Cornell University experirnent canal as found frorn current-rneter dis-

~ charge rneasurernents rnade in May, Novernber, and Decernber, 1900. 

No. of 

experiment. 

---

1 

2 

3 

4: 

5 

6 

7 

8 

9 

10 

11 

12 

18 

14 

15 

16 

17 

18 

19 

20 

---------

Series A. Series B. Series C. Series D. 

Velocity Depth Ratio Ratio Velocity Depth Ratio Ratio Velocity Ratio Ratio Velocity Depth Ratio 

(d;). (~). (~t). (~)· Depth 

(V). (D). (d~n). (~)· (~t). D. (Vo). (D). (Vo). (D). (Vo). (D). 

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

Feet per Feet per Feet pet· Feet per 

second. Feet. second. Feet. , second. Feet. second. Feet. 

1.17 8.00 0.81 0.35 2. 79 1.12 1.00 0.4.0 1.4.5 9.4.6 0.65 0.31 1.52 9.51 0. 75 

0.57 7.17 0. 77 0.29 3.60 1.12 1.00 0.49 0.97 9.37 0.61 0.32 1.4.8 9.51 0.80 

0.68 7.26 0.92 0.28 3.10 1.11 1.00 0.4.9 0.4.9 9. 34. 0.52 0.27 ---------- 9.32 ---------- 1.27 8.10 0.89 0.29 3. 34. 1.30 1.00 0. 4.2 0.26 8.92 0.62 0.28 0.83 9. 54. 0. 79 

0.84 7.54. 0.80 0.49 3.09 1.30 1.00 0.38 1.4.5 7.67 0.70 0.33 0. 79 9. 54. 0. 84. 

1.46 8.37 0.75 0.30 2.50 2.00 0.85 0.44 1.00 7.64. 0.72 0.33 0.68 9.52 0. 77 

1.06 7.85 0.84 0.41) 1.54 0. 79 1.00 0.45 ----o.-22· 7.58 .................... ---------- 0.65 9.52 0.80 

1.06 7.85 0.75 0.31 1.90 2.03 0.85 0.37 7.56 0.60 0.28 1.86 7.25 0.82 

1.06 7.85 0.95 0.43 3.27 0. 75 1.00 0.47 0.49 6.01 0.60 0.28 1.87 7.25 0.69 

1.18 7.98 0. 79 0.37 2.95 0.55 1.00 0.50 1.89 6.28 0.71 0.32 1.68 7.22 0. 77 

0.98 7.73 0.71 0.36 3. 79 1.89 1.00 0.40 1.25 6.40 0.66 0.32 1. 6.1 7.22 0. 72 

0.64 7.28 0. 75, 0.30 3.10 1.89 1.00 0.43 0.85 6.32 0.60 0.31 1. O'Z 7.18 0. 72 

0.79 7.48 0.65 0.21 3.72 1.20 1.00 0.46 0.46 8.48 0.56 0.27 0.96 7.18 0.70 

0.64 7.28 0.86 0.39 2.95 ].20 1.00 0.49 1.46 8.47 0.65 0.31[.-- .. -- .. - 7.11 ---------- 0. 79 7.48 0.84 0.33 2.70 0.95 1.00 0.48 0.89 8.51 0.53 0. 27 0. 73 5.15 0. 70 

.................... --........ ---- ................... ~ .. -.. ---.... - 3.47 0.95 1.00 0.48 .................... ---------· 0.623 0.30 0.67 5.15 0. 70 

---------- ---------- ...................... ..................... 2.43 0.69 1.00 0.50 ---------· ---------- 0. 755 0.37 ---------- ......... ............ ...................... 

--------- .. -....... ---- .................... ---------- 3.14 0.69 1.00 0.50 ----·----- ---------- --------·- ·--------- ................... .................... .................... 2.29 0.46 1.00 0.50 ---------- ......................... ---·------ ------- -- -....... -~ ---- ~ .... -.. -.... -- ........................ ..................... ....................... ---------- ---------· 2.93 0.46 ].00 0.50 .................... ...................... ------ ---- ................... ....................... ... .................. ..................... 

---------- -----------0.815 -0.343 .......... ----·-··--1-0.985 -0.4.57 .................... ------ ---- 0.69 0.341---------- ...................... 0.755 

- - ------- --

V =velocity found from the weir. 

Vo=velocity found with meter by ordinary method. 

dm=distance above bottom to thread of maximum velocity. 

d' =distance above bottom to thread of mean velocity. 

Ratio 

(~)· ---

0.29 

0.4.7 .................... 0.4.2 

0.4.2 

0.39 

0. 34. 

0.36 

0.32 

0.34 

0.33 

0.33 

0.36 

---------- 0.33 

0.44 .................... 

---------· 

----------

----------

U.37 

~ :>:1 

~ 

~ 

t?=.l 

~ 

"d 

t?=.l 

~ ~ 

t?=.l 

z 

;-3 

m 

p.. 

;-3 

Q 

0 

~ 

z 

t?=.l 

t:"' 

t:"' 

t:1 

z 

H 

~ 

t?=.l 

~ m 

H 

f-3 

~ 

-::t 

-"T 
78 ACCURACY 01!' STREAM MEASUREMENTS. [No.64. 

The first of the following tables gives the mean, maximum, and 

bottom velocities in the experiments of 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 middepth velocity is much more nearly constant, and hence is better to 

use than that of mean velocity to bot~om velocity. The second table 

gives the ratio of mean velocity to three-tenths-depth velocity, and of 

mean velocity to six-t,enths-depth velocity in series A, C, and D. The 

ratio at three-tenths rlepth is seen to be more nearly constant than 

that at six-tenths depth. 
Velocities at various depths and 1:elocity ratios in Cornell Unit,ersity experiment canal as found from standard weir and current-meter 

' discharge measurements. 

Series A. Series C. Series D. 

No. of Depth Velocities in feet per sec.* Ratios. Depth Velocities in feet per sec.* Ratios. Depth Velocities in feet per sec.* Ratios. experi- (D) in (D) in (D) in ment. feet. VJ:t v feet. Vb v feet. Vb 

v Vm Vb(t) VtD v VtD v Vm Vb(t) VtD v VtD v 17m Vb(t) V~D v Jl+ViD 

---------------------------------------------------- 1 s.oo 1.17 1.::16 0.80 1.24 0.69 O.l:IO 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 0.89 0.96 9.32 1.54 -····· ------·- .................... .............. ----.. - ~ - 4 8.10 1.27 1.37 1.01 1.33 0.80 0.96 8.92 0.27 0.29 0.22 0.29 0.82 0.94 9.54 0. 77 ............... .. -.. ·~ ....... ~ ~- -- ... --- .............. .. ................. 5 7.54 0.84 0.87 0.64 0.85 0. 76 0.99 7.67 ]. 44 1.54 1.12 1.52 0. 78 0.95 9.54 0. 77 6 8.37 1.46 1.55 1.22 1.53 0.82 0.96 7.64 A:g~ 1.~·-~- 0. 78 1.06 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 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:oi' "'1:65' "i:96' o.'s6-- '"0:9f 

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 7.98 1.18 1. 24 0.83 1.20 0.70 0.98 6.28 1. 94 2.17 1.42 ~.(17 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 A:~ 18:~~ 0.97 12 7.28 0.64 0. 71 0.49 0. 70 0. 77 092 6.32 0.89 0. 98 0.63 0.96 0. 71 0. 93 7.18 0. 96 1.01 0.80 0.97 

13 7.48 0.97 0.89 0.65 0.88 0.83 0.90 8.48 0.4~ 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 0.87 0.56 0.85 0. 71 0.93 8.51 0.92 0.95 0.67 0.95 0. 73 0.97 5.15 0.69 0.71 0.59 0.68 0.86 0.9» 

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 

-~-

*Correct velocities found from standard weir. t Velocity 2t inches above the bottom. 

N01'E.-V=mean velocity; Vm=maximum velocity; Vb=bottom velocity; V.rp=mid-depth yelGcity. 

a: 

d 

I" 

"d 

;c 

~ 

~ 

~ 

"'0 

~ 

~ 

i:= 

~ 

z 

1-3 

00 

> 1-3 

a 

0 

~ ~ 

t"l 

rot 

0 

~ 1-' 

<1 

t?;l 

~ 00 

1-' 

1-3 

~ 

-1 

~ 
80 ACCURACY OF STREAM MEASUREMENTS. lNO. 64. 

Vt!locity 1·atios in Cornell University experiment canal as found with current 

rneters in May, November, and Decernber, 1900. 

Series A. Series C. Series D. 

No. of ex peri- Veloc- Ratio Ratio Veloc- Ratio Ratio Veloc- Depth Ratio Ratio ment. ity Depth 

(~)- (~)- ity Depth 

(~)- (~)- ity 

(vo). (D). (vo). (D). (vo)- 4DJ. (~)- (~)- -------------------------------

Ft.per Ft.per Ft.per sec. Feet. sec. Fee~. sec. Feet. 

1 •...... 1.10 8.00 1.082 1.050 1.45 9.46 1. O'Z2 1.009 1.52 9.51 1.059 1.012 2 _______ 0.45 7.17 1.062 1.036 0.97 9.37 1.029 1.017 1.48 9.51 1.071 1.002 a _______ 0.68 7.26 1.066 0.997 0.49 9.34 1.037 1.022 -------- 9.32 ------- ------- 4 _______ 1. 27 8.10 1.060 1. 014 0.26 8.92 1.001 0.981 0.83 9.54 1.031 0.988 5 _______ 0. 79 7.54 1.073 1.010 1.45 7.67 1.057 1.021 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 1.034 1.000 

7------- 1.04 7.85 1.040 l.OOJ 0.50 7.58 ------- ------- 0.65 9.52 1.046 1.010 

g _______ 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 lQ _______ 1.29 7.98 1.083 1.025 1.89 6.28 1.127 1.042 1.68 7.2"t 1.038 1.010 n _______ 0.94 7. 73 1.050 1.021 1.25 6.40 1.094 1.045 1.65 7.2'~ 1.039 1. 018 

12------- 0.53 7.28 1.103 1.043 0.85 6.32 1.090 1. 056 1.02 7.18 1.060 1. 02.3 

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 1.0.30 0.89 8.51 1.025 1.042 0. 73 5.15 1. 041 1.011 

16- ·----- ---· .. --- -------- ------- ------- 0.20 8.46 1.139 1.0.30 0.67 5.15 1.045 1.015 ----- ------ ----·--

1.077 1.021 1.069 1.035 1.048 1.010 

v0 =.velocity obtained by ordinary method. 

v3 and v6 =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: 

Cornparison of rnean velocity obtained by the ordinary point method and by integration in verticals in Cornell University e::cperirnent canal. 

Date. 

1901. 

!~~H ~ =: ~ ~~~-- = ~~~== ~ ~ ~ ~= = = = ~::::~ = = == Apri15 _ ------------------ ___________ _ Apri111 .•. -·-. _____ ----------- _. ____ _ 

Depth. Kind of meter. 

Velocity. 

Point 

method 

(Vp). 

Integration 

method 

(Vt)-

Feet. Ft. per sec. Ft. per sec. 9. 08 Haskell No.3 _ _ 1. 468 1. 460 

6.08 _____ do__________ 2.208 2.225 

7.41 ..... do__________ 1.883 1.921 

9. 26 S. Price No. 351. 1. 522 1. 568 

Per cent. 

+0.6 

-0.8 

-2.0 

-3.0 

It will be seen that t~e agreement is close, the greatest difference 

being 3 per cent. 

RATING METERS IN STILL AND IN MOVING WATER. 

The results of meter and standard-weir comparisons are given in 

the tables on pages 64 to 67. With a few exceptions, already mentioned, these are shown graphically in figs. 16, 17, and 18, pages 68 

and 69. The straight lines 0-0' represent in each case the weir dis--

charge and the curved lines drawn through the plotted points repre-
MURPHY.] EXPERIMENTS AT CORNELL UNIVERSITY. 81 

sent the percentage variation of the meter discharge from the 

corresponding weir discharge. The meter discharge is computed 

from a rating table prepared from ratings in still water. If we 

assume that the weir discharge is correct, then these curves show the 

percentage difference between a rating in still water and a rating in 

moving 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 velocit.y 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 the velocity 

in still water. For the Haskell meter (a propeller instrument) the 

velocity is less in moving 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 

rating tables for moving water, and they would agree closely with 

the weir discharges. New vertical velocity curves have been 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 current rnete1·s in still 'Water and in moving wate1· in Cornell University experirnent canal. 

Revo- Small Price Larg0e. 88P.rbice Haskell Fteley. b Revo- Haskell 

lutions No. 351.b N< No.3.c lutions No.3.c Fteley.b 

per 1----~-----1---~---1---~----1----~---1 per 1----~--11--~-----1 

second. JT Vw V Vw V Vw V Vw second. V Vw V Vw 

~--- ---- --·ido0.15 

0.20 

0.25 

0.30 

0.35 

0.40 

0.45 

0.50 

0.55 

0.60 

0. 6.') 

0.70 

0. 75 

0.80 

0. 8.5 0.90 

0.95 

1.00 

------·- ...................... ------ ------- ............... ------- .................... .................. 1.10 1.30 1.28 1.18 

--0~284" -------· ................ .................. ................. ------- ------- .................... 1.20 1.40 1.39 1.29 

0.318 ------ ................... .................. ------- ------- ------- 1.30 1.50 1. 49 1.39 

0.397 0.437 0.54 0.660 ------ ------- ----··- ------- 1.40 1.60 1.60 1.50 

0.510 0.552 0.70 0.804 ------ ------- ------- ·------ 1.50 1.71 1. 70 1. 61 

0.625 0.664 0.86 0.950 --- -- ------- ............... ------- 1.60 1. 81 1. 81 1.72 

0. 741 0. 776 1.0:3 1.097 ------ ------- ------- ------- 1. 70 1. 92 1. 92 1.82 

0.857 0.887 1.19 1.244 ------ ------- ------- ------- 1.80 2.02 2.03 1.93 

0.972 0.998 1.35 1.392 ------ ------- ------- ------- 1.90 2.13 2.14 2.04 

1.088 1.109 1.52 1. 550 ------ ------- ------- ------- 2.00 2.2a· 2. 24 2.14 

1.204 1.220 1.68 1.709 0. 70 0.647 0.536 0.552 -- ---- ............ ------ ------ 1.319 1.332 1. 84 1. 874 0. 75 0.698 0.589 0.598 ................ ............. ------ ---·-- 1.435 1.447 2.01 2.042 0.80 0. 751 0.643 0.644 ............... ------ ------ ------ 1. 550 1.562 2.17 2.207 0.85 0.803 0.697 0.690 -------- ------ ------ ------ 1.660 1.677 2.34 2.373 0.90 0.855 0.750 0. 735 -------- ------ ------ ------ 1. 782 1. 796 2.50 2.538 0.95 0.907 0.804 0. 779 -------- ............ ............ ------ 1. 897 1.915 2. 66 2. 702 1.00 0.960 0.858 0.822 -------- ............ ------ ------ 2.013 2.033 2.83 2.868 1.05 1.014 0.911 0.864 -------- ------ ------ ------ 2.129 2.150 2.1:19 3.034 1.10 1.068 0.965 0.905 ·------- ------ ------ ------ 2.244 2.266 3.15 3.199 1.15 1.121 1.018 0.946 ---... ~--- ------ ·----- ------ 2.36 2.38 3.32 3.366 1.20 1.174 1.072 0.987 ..................... ............. ................. ................ 

a Recent experiments with a Fteley meter do not verify this statement. 

b Meter held with rigid rod. 

c Meter held with cable. 

1. 07 

1.15 

1. 2'.3 1.30 

1.38 

1. 45 

1. 53 

1.60 

1.67 

1. 74 

--------

--------

--------

................. 

--------

--------

--------

--------

---·----

___ .,. ____ 

--------

NoTE.-V=velocity, in feet per second, from still-water rating; Vw=velocity, in feet per second, from moving-water rating. 

IRR 64--02--6 
82 .ACCURACY OF STREAM MEASUREMENTS. (NO. 64 . 

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 meter will 

measure a velocity of 0.23 foot per second, as t.he 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 pe~ 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 

pr~bably made on the assumption that tliis 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 on the weir. Recent 

experiments seem to indicate this fact. These two causes, however, 

account for only a comparatively small part of 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 in the direction of the current, 

is probably dne to the stream lines becoming more 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 more 

nearly in the direct.ion of the axis of the canal. 

ERROR IN USING AVERAGE OF BOTTOM AND SURF ACE VELOCITIES FOR 

MEAN VELOCITY. 

The following table gives the mean velocity and the average of the 

velocUies 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 bot.tom velocities instead of the 

mean velocUy. It is seen that in all these experiments except two 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 percent. 
l\IURPliY.) EXPERIMENTS AT CORNELL UNIVERSITY. 83 

Table showing relation between mean 'oelocity and ave·rage of sttrface and botton~ 

t'elocitie.'5 as found f1·orn. Conwll University standard weir and from current 

meters in Cornell experiment canal. 

No. of 

experiment. 

1 

2 

3 

4 

5 

6 

7 

g 

9 

10 

11 

12 

13 

14 

15 

16 

v 

Feet per second. 

1.16.! 

0.573 

---------- 1.268 

0.841 

1.462 

1.056 

1.056 ........................ 

---------- 0.980 

0.643 

0. 788 

----------

............................ 

~ --.. -.. -- --

Series A. 

V' 

Feet per second. 

0.987 

0.416 

---------- 1.100 

0. 749 

1.384 

0.965 

0.946 

-------·--

---------- 0.887 

0.476 

0.687 

----------

----------

____ .. _____ 

V-V' 

-v v 

Feet per Per cent. second. 

+15.3 1.400 

+27.5 0.932 

0.477 + 6.1 0.265 

+10.9 1.444 + 5.4 1.018 + 8.6 0.502 

+10.4 0.255 

---------- 0.515 

---------- 1.914 + 9.5 1.283 

+25.9 0.893 

+12. 7 0.478 

---------- 1.454 ---------- 0.915 ... -... ~ ... --- ~ - 0.229 

V ~mean velocity found from standard weir. 

Series C. 

V' V-V' 

--v 

Feet pe1· 

second. Per cent. 1.412 -0.2 

0.954 -0.2 

0.468 + 0.2 

0.231 +12.8 

1.364 + 5.6 

0.940 + 7. 7 

''''(ij77' ---------- +30.6 

0.435 +15.5 

1. 730 + 9.6 

1.129 +12.0 

0. 759 +15.0 

0.422 +11.8 

1.311 + 9.8 

0. 784 +14.3 

0.179 -+ 21.8 

Series D. 

v V' 

Feet per Feet per second. second. 

1.528 1.436 

1.528 1.436 ............................ ---------- ------------ -----"- ........................ _______ ,. __ 

---------- ....................... 

---------- ---T8o7· 1. 905 

1. 905 1. 779 

1.649 1.613 

1.649 1.590 

0.955 0.973 

0.955 0.897 ........................ 0.689 ----ii~7of 

0.689 0.659 

V-V' 

-v 

Per cent. 

+6.2 

+6.2 

----------

---.. -- - -- ~ 

... ....................... 

----------

........................ 

+5.2 

+6.6 

+2.2 

+3!1) 

-1.9 

+6.1. 

---------· -2.2 

+4.3 

V'=mean of velocities 0.5 foot above bottom and 0.5 foot below surface, as found by meters, 

uncorrected. 

From the foregoing table, and from the table on page 79, in which 

is given the ratio of bottom velocity t.o mean velocity, it appears that 

bottom velocit,y is not a desirable quantit,y to use in computing 

discharge, for it varies between too wide limits. In a stream with a 

stony or gi'avelly 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 RESULTS BY THREE METHODS OF OPERATING METER. 

rrhree methods of operating meters have been used in these experiments, viz, the ordinary method, the six-tent.hs-depth, and the integration. A detailed account of the manner of operating the meter 

by each of these methods has been given on pages 62 to 63. The time 

required to make 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. 6~) 

give for each meter a well-defined line which agrees with the weir 

line (0-0') within about 2 per cent for velocities greater than 1.5 feet 

per second, the meter discharge being less than the corresponding 

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. [N0.64. 

defined a line (fig. 17) for each meter as do those by the ordinary 

method, the meter discharge being from 1 to 6 per cent greater than 

the corresponding weir discharge, and the mean being 3.5 per centfor 

small Price meter No. 363. If the observations with the latter meter 

had been taken at sixty-four-hundredths 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 mean 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 the 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 showing effect of variation of speed of meter in integration method. 

No. of experiment. Date. Depth. 

True Velocity velocity Speed of of water meter byrne- by weir per ter ( Vl) 

( V) per second. per second. second. 

Kind 

of meter. 

----[----------1--------------- ----1-----

1900. 

3 k::::: ______ ..... 

-~~!a.~==~=~~==~~~:========== do _____________________ _ 

4 ........... d0-------------·-------- 5 .•••••..... do----------·-----------

?:::::~ -~~-~~ ==== ====== :::::::::::: 

~====== ~~lo~:r:M::::::::==~====== 10 ......•.... do----------------.·---- 11 ...•••..... do---------------------· 

12.----- ---·.do .. ---· •....••......... 13 .....• October26 ----------------- 14. _____ ..... do_·---·-----· ......... . 15 ...... October 27 ....... ··-··----· ltL ....••.... do------·------·---- ... . 17 ... ___ ...... do •....•. ----- ........ .. 18 ........... do ...... ---------------- 19 ........... do-----· ........• .: ..... . 20 ........... do ____ ------ ............ . 21. ..... October 29 _ ------------ ... . 22 ...... October 31 .....•.••...•..•.. 

23 ........... do ...... -------------- .. 24 ...... November! ........... : .. . 25 _____ December 6 .............. .. 

26 ........... do----------------------

27------ December 7 ____ ...... ------ 28 •••••• December 8 .............. .. 

29 .•••••••••• do ...... ---------------- 30 ..••••...•. do---····-···· ..•....... 31 ••.•••.•••. do---- ................. . 

Feet. 

8.10 

8.10 

8.10 

7.54 

7.54 

7.85 

7.85 

7. 73 9.46 

9.37 

9.34 

8.92 

7.67 

7.64 

7.58 

7.56 

6.01 

6.28 

6.40 

6.32 

8.48 

8.47 

8. 51 8.4.-6 

9.51 

9.51 

9.32 

7.25 

7.22 

7.18 

5.15 

Feet. 

1.268 

1.268 

1.268 

0.841 

0.841 

1.056 

1.056 

0.980 

1.409 

0.932 

0.477 

0.265 

1.4441 1.( 

0.5L 

0.251> 

0.515 

1.940 

1.283 

0.893 

0.478 

1.454 

0.915 

0.2"Z9 

1.528 

1.528 

1.535 

1.905 

1.649 

0.955 

0.689 

Feet. 

0.101 

0.152 

0.270 

0.079 

0.055 

0.056 

0.043 

0.032 

0.118 

0.142 

0.164 

0.107 

0.137 

0.135 

0.143 

0.128 

0.142 

fl.180 

' 154 l.188 

0.151 

0.293 

0.258 

0.185 

0.253 

0.284 

0.243 

0.252 

0.295 

0.254 

0.179 

Feet. 

1.268 

1.235 

1.200 

0.834 

0.842 

1.028 

1.008 

0.978 

1.429 

.0.982 

0.48.'l 

0.308 

1.519 

1.079 

0.522 

0.312 

0.555 

2.030 

1.338 

0.920 

0.492 

1.552 

1,00'Z 

0.319 

1.540 

1.572 

1.576 

1.962 

1. 748 1.039 

0.752 

Percent. 

0.00 

+ 2.60 + 5.35 

+ 0.09 - 0.01 

+ 2.65 

+ 4.54 + 0.02 

-1.42 

- 5.36 - 1.68 

-16.23 

-5.20 

- 5.99 - 3.99 -22.35 

- 7.77 - 4.64 - 4.29 - 3.02 

-2.93 

- 6.74 - 9.51 

-39.30 

- 0.78 - 2.87 - 2.6d - 2.99 - 6.00 - 8.79 - 9.14 

(&) 

S.P.351. 

Do. 

Do. 

Fteley. 

-Do. 

S.P.351. 

L.P.88. 

S.P.351. 

S.P.363. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

Hask.3. 

Do. 

Do. • Do. 

Do; 

Do. 

aS. P. =small Price; L. P. =large Price; Hask. =Haskell. Figures given are the numbers of 

the meters. 
MURPHY.] EXPERIMENTS AT CORNELL UNIVERSITY. 85 

Table showing effect of speed of meter on observed velocity as found by the integration 

method in experiments of table on page 84. 

Experiments Nos. 9 to 25, omitting Nos. 12, 16, and 24. 

Speed of meter 

0.10 to 0.14. 

Feet per second. 

0.118 

0.137 

0.135 

0.130 ....... -.... ---- ----------

------ ........ 

Speed of V-V1 meter -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 

Pe1·cent. 

-5.36 

-1.68 

-3.99 

-7.77 

-4.29 

-2.93 

-6.33 

Speed of meter 

0.18 to 0.30. 

Feet per second. 

0.180 

0.188 

0.293 

0.258 

0.253 

0.234 

---- --· ---

Percent. 

-4.64 

-3.02 

-6.74 

-9.51 

-0.78 

-4.94 ...................... 

Experiments Nos. 1 to 8. 

Speed of meter 

0.05 to 0.15. 

Feetpe1· 

second. 

0.056 

0.043 

0.032 

0.101 

0.079 

0.055 

0.061 

Pe1·cent. 

+2.65 

+4.54 

+0.02 

+0.00 

+0.09 

-0.01 

+1.22 

Speed of meter 

0.15 to 0.30. 

Feet per second. 

0.152 

0.270 

----------

----------

----·-----

-·-·o:2if 

Percent. 

+2.60 

+5.35 

--·-------

------ ---- ·---------

.. +3:97"" 

This ratio is positive for all the experiment,s of series A and is negative for those of C and D. This difference of sign is due to two causes: 

(1) The meter was moved faster in the experiments of C and 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 from 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. lf-j (page 68} and 18 (page 69), 

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 t,o change in rating of the meters, for an increase in the friction in a meter would reduce 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 sect,ion 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 ce11t of the canal discharge. It must be 

borne in mind in this connection that t,he discharges obtained in 1900 

for velocities greater than 1.4 feet were in shallow water, and therefore are not so reliable 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 

its axis was free to move about a horizontal axis; in the former cases 
86 ACCURACY OF STREAM 'MEASUREMENTS. [No.64. 

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 at.tached 

to the under side of the meter, keeps the axis of the revolving wheel 

farther from 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 position considerably in a swift current. 

It was in order to measure the velocity close to t,he bottom and keep 

the meter at a desired place during the observation that in many of 

the experiments the meter was held with a rod. In oi·dinary river 

gaging, however, the Price and Haskell meters are held with cables 

and the meters are rated in still water suspended from a car and 

cable. The question then arose: ''Is the rating table for a meter used 

suspended from a cable applicable to the same n~eter 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 same course in the opposite direction; the third eolumn 

gives the number of revolutions observed in this average time; the 

seventh column gives for each of t.hese cases the difference between 

the observed velocity and the velocity computed from the old rating 

table of April 23, 1900, for the same meter 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 reducing the 

Cornell experiments is given on page 81. By comparing the eorresponding quantities in the seventh and tenth columns of this tabJe it 

will be seen how much more closely the values in the new rating table 

fit t.he observations than do those of the old one. The tenth eolumn 

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=0.0±7 +2.313x, y being 

velocity in feet per second and x revolutions of Ineter wheel per second. From the sevent,h column of the table on page 87 it is seen that 

the observed velocities are larger than the computed velocities, indicating more friction in the meter on December 30, 1900, than on April 

23, 1900. 

The "most probable" linear relation between x and y for this case 

of the meter held with a cable was found to be y=0.067+2.:321x. The 

differences in the tenth column show that this line does not fit the 

observations. It crosses the curve given by the observations twice as 
MURPHY.) EXPERIMENTS AT CORNELL UNIVERSITY. 87 

y increases from 1 to 8 feet per second. The rating table was prepared by using this line as a basis, applying corrections as indicated by 

the corresponding difference of the tenth column, and also that the 

rating table will difference smoothly. The numbers in column 12 

show how closely the observed velocities agree with those computed 

from the new rating table with the meter held with a cable. 

It should be noted that the smallest observed velocity is about 0.5 

foot per second in one case and 0. 35 foot in the other case. 

Observations and computations of a rating of small Price meter No. 351 held by 

rigid 1·od, made at Chevy Chase, Md., December 30, 1900, 

1. 

No. of 

observation. 

---

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

2and 3. 4. 5. 6. 7. 8. . 9. 10. 

----------- Length of run, 100 feet. Revo- Ob- Com- lutions Differ- Resid- Revo- per served puted ence x2 xy ual 

lutions second velocity velocity (y-yl), (v). Time. of me- (x). (y). (yl ).a 

ter. 

-----------

Feet per I Ft. per 

---------

Sec- Feet per onds. second. second. lsecond. 

9.25 43.00 4.648 10.811 10. 815 -. 004 21.604 50.245 +.059 

10.5 42.50 b4.048 b9.524 9. 4D5 +.119 

16.0 43.00 2.688 6.250 •. 231 I +.01, 7.225 16.800 -.014 

22.5 43.00 1.911 4.444 4.414 +.030 3.652 8.493 -.022 

35.0 42.25 1.207 2.857 2. 797 +.060 1. 457 3.448 +.018 

45.0 42.00 0.933 2.222 2.183 +.03!J 0.870 2.073 +.017 

53.0 42.00 0. 794 1.887 ~J~ I t:8ig· 0.630 1. 498 . +. 003 

54.5 42.00 0. 774 1.835 0.599 1.420 -.003 

68.0 41.75 0.614 1.471 1.461 +.010 0.377 0.903 +.004 

8.5. 5 4.1.75 0.488 1.170 1.174 -.004 0.2:38 0.571 -.006 

106.5 41.00 0.385 0.939 0.944 -.005 0.148 0.362 +.001 

113.0 41.00 0.363 0.885 0.891 -.006 0.132 0.321 -.OO'Z 

154.0 40.50 0.263 0.649 0.669 -.020 0.069 0.171 -.006 

197.0 39.50 0.201 0.508 0.522 -.014 0.040 0.102 -.004 

220.0 39.00 0.177 0.455 0. 56ll 

1 

... 014 0.031 0.081 -.001 

290.0 36.90 0.126 0.341 0.351 -.010 0.016 0.043 -.003 ------ 15.572 36.724 37.088 86.531 

"Computed from rating table prepared from rating of Apri123, 1900. 

b Omitted in computing ::S x and l: y. 

11. ---

v2 

---

.003481 

.000196 

.000484 

.()()()324. 

.000289 

.000009 

.000009 

. 000016 

.000036 

.000001 

.000004 

.000036 

.000016 

.000001 

.000009 

.004911 

NOTE.-Observation equation, y-a-bx=v; normal equations, a l: x+b ::t x 2 =::txy, na+b l:x=:Ey. 

For these observations these become 15.572 a+37.088 b=86.531, 15 a+l5.572 b=36.724. The solution 

/::Sv2 of these gives b=2.313 and a=.047. The mean error of a single observation is 'V n-l =.019. 

The probable error of result is 6,745 ~ n (~~l) =.003. 
88 ACCURACY OF STREAM MEASUREMENTS. (No.64 

Observations and comptttations of a, rating of small Price meter No. 351 held by 

cable, made at Chevy Chase, Md., December30, 1900. 

1. 2 and 3. 4. 

---

5. ---

6. ---

7. ---

8. ---9. ---10. ~~~ Length of run, 100 feet. Revo- Ob- Uom· ComNo. of lutions served puted Differ- Resid- puted Differobser- Revo- per veloci- veloci- ence x2 xy ual veloci- ence vation. Time. lutions second ty ty (y-y'). (v). (y~~. b 

(y-y"). 

of me- lX). (y). (y'). a 

ter. 

-------------------------------- Sec- Ft. per Ft.pe1· Ft.per Ft.pe1· 

onds. second. second. second. second. 

1 10.5 42.00 4.000 9.524 9.300 +.224 "if500" ----......... -+~04if "T98-- -------- 2 12.5 42.5C 3.400 8.000 7.900 +.100 27.200 +.02 

3 16.5 42.50 2.576 6.061 5.967 +.094 6.636 15.613 +.015 6.04 +.O'Z1 

4 21.5 42.75 1.990 4.651 4.588 +.063 3.960 9.256 -.034 4.68 -.021) 

5 26.0 42.50 1.6.35 3.846 3. 767 +.079 2.673 6.288 -.015 3.83'1 +.009 6 29.0 42.50 1.465 3.448 3.383 +.065 2.146 5.051 -.02() 3.443 +.005 7 31.0 42.25 1.363 3.226 3.151 +.075 1.858 4.397 -.oot 3.290 +.017 

8 41.0 42.50 1.037 2.439 2.411 +.028 1. 075 2. 529 -.G34 2.451 -.012 

9 50.0 42.50 o.850 2.000 1.990 +.010 0. 723 1. 7(X) -.039 2.024 -.O'M 

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 1.4.30 -.tXJl 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 12.5. 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.(i97 + 017 

17 171.0 36.00 0.215 0.51:)5 o.sr.m +.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 +.022 0.541 +.OO'Z 

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 

a Computed from rating of April 23, 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 tl!ese 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 remembered that the values given in this table for velocities less t,han about 0.5 foot per second are only approximate, since 

t,he observat,ions do not extend below 0.35 foot per second. We may 

say that if the rating table 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 l.i3 per cent to 8.5 per cent for velocities 

from 1.5 feet to 0.5 foot per second. 
MURPHY.) EXPERIMEN'fS .AT CORNELL UNIVERSITY. 89 

Table .<;hawing percentage difference in velocity as shown by small Price meter No. 

S51 when rated in still water on a rigid rod and on a cable. 

Speed of] V Fe Vr-Vc I Speed of Vr Vc I Vr-Vc meter. r Vr meter. Vr 

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

R.pe1·sec. F.pe1·sec. F.pe1·sec. Per cent. R.persec. F'. pe1· sec. F. per sec. Pe1· 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. 7R1 5.4 0.75 '1. 782 1. 796 0.8 

0. 3.5 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 

I 

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 

Vr =velocity with meter rated on a rigid rocl. 

Vc =velocity with meter rated on a cable. 

Small Price met,er No. 351 was again rated three times on May 9, 

1901. It. was held (1) with a cable, using an IS-pound sinker; (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, hut 

thEJ result.s are plotted in fig. 29, using R= 

revolutions per second as abscissre and 

K=j;=ratio of velocity to revolutions as 

ordinates. It is seen that these rating observations give a separate curve for each 

s 

7 

. 

., ') 

, 

A 

f' \ 

\ 

~ 

D \ 

of these cases. ~rhe value of K for any 

value of R for one curve is very different ~ 

from that for the other curves for velocities less than about 3 feet per second. For 

example, for R=0.3, K='J. 755 for case 1 

,. 

0 

~ \ \ 

,\ \ ~ ~ 

" 

I~ 

&_ ' ....... ~ ~ E 

Ht:vt:11uf;on.s per.~ "' 

(curve AE), ~.585 for case 2 (curve BE), Fw. 29.-Curves showing relation 

and 2.485 for case i3 (curve DF). The co- between revolutions of meter and 

efficient 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 K, the velocity decreases as 

the freedom to tip about a horizontal axis 

and to swing around a vertical axis decreases. Or, stated in the other way, in 

a current of a given velocity the revolutions increase as the freedom of motion 

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-pound sinker being 

us~d. 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. 

decreases. Each of these 

cases therefore requires a separate rating table. 

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 eurve near the surface optained with 
90 ACCURACY 0}""' STREAM MEASUREMENTS. [No.64 

a small Price meter 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 indicates 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 surface as possible. For 

the three meters used in these surface velocity observations the distance of the center below the surface was as 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. 

----- -- ---., 

~ 5 

?' 4 

~ 

/• 

9 Nos. """ ~ I =~ ·,o 

I 2.7 ~-9 3.0 3.1 3:2 as a,. I M~ 6 I rJ 

: I 

-· - I 

6 

I • ti=if! j ··~ ~- 5 I 

I ] ,rr I I ' I 

I f:· },' J 

1 i' /,/ ,y ~ ~ ;f' \ /, ~- , ~~ I / 

~-~~ l..-A .,/"' ~~-&, I.~ I 

y 

lA 

-·· • 8 ... ... .. .6 z.o z . 

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. 

In order to investigate this matter further the surface velocity of 

a part of the canal was measured simultaneously 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 thick were also used. These were 

started near the center of the canal18 feet above t,he upper wire and 

timed over a run of 60 feet. Any that 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 11 feet from the 

south side, and the revolutions were counted for periods of forty 

seconds. The results of the experiments are given in the following 

table: 
MURPHY.] EXPERIMENTR AT CORNELL UNIVERSITY. 91 

Comparison of surface V!'.locity measured with float rods and with current meters. 

Small Price meter No. 351. Haskell meter No. 3. I ~¥~~[ Velc;>city N~r~~r Velc;>city ~¥1f~[ Velc;>city N~~ker Velc;>city I 

observa- Wltb second With observa- with second With 

tions. floats. periods. meter. tions. floats. periods. meter. 

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

Feetpe1· Feet per Feet per Feet per second. second. second. second. 

11 3.122 10 2. 794 13 3.083 13 3.171 

12 3.076 12 2.806 12 3.144 121 3.187 

13 3.030 13 2.818 10 3.135 --~~~-165 

36 3.076 35 2.806 35 3.121 35' 

I 

3.174 

During the foregoing observations the depth of water in canal was 

6.04 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 from 

2 to 8 feet from the south side of canal; that which is compared with 

the Haskell meter velocity is found from the float.s passing the lower 

wire from 8 to 14 feet from the south side of canal. It is seen that in 

each experiment the float velocity is greater than that of the Price 

meter 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 small 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 24 

feet below the lower wire at points from 0 to 7 feet from the center, 

and the revolutions were counted for 50-second periods. 

The mean surface velocity shown by the small Price meter from 

thirty-two 50-second periods is 1. 967 feet, and the corresponding float 

velocity obtained from ten floats passing from 2 to H feet from the 

south side of canal is 2.146 feet. The corresponding surface velocity 

shown by the Fteley meter is 2.074 feet, and by the floats from 8 to 14 

feet from the south side of canal, 2.137 feet. The float velocity is 

8.:~ per cent greater than the Price meter velocity and 2.95 per cent 

greater than the Fteley meter velocity. The difference between the 

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 
ACCU:n.AcY OF STREAM MEASUREMEN'rS. [No.64. 

the surface for about the same length of time. The mean velocity at 

2-! inches 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 indicated 

velocity increased 7.4 per cent, as the meter was lowered 1-! inches. 

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 dept,hs below the surface. rrhe 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: 

Velocities near the surface of Cornell University experiment canal as found with 

small Price meter No. 351 and with Haskell meter No. 3. 

Small Price meter No. 351. a Haskell meter No. 3. b 

Number of run. Depth below surface, in inches. Dept~~~~cl;.!~rface, 

2.5 4.5 8.5 4.5 6.5 8.5. 1 6.5 

--------------1----1---:-----------

Second ...... ·-------------·-----------...... 0. 482 

Third-·-········-------·----------------- ... 0.556 

Fourth .......•........................ ------ 0. 936 

Fifth .....•.......... -----................... 1.297 

Sixth ----- .......................... -------- 1.480 

Seventh ....................... _____ ·------. 1. 611 

0.490 

0.1)95 

0.958 

1.281 

1.457 

1.556 

0.482 

0.575 

0.958 

1.320 

1.389 

1.533 

0.942 

1.299 

1.434 

0 

0.592 

1.015 

1.348 

1.450 

1.552 

0 

0.615 

1.032 

1.325 

1.392 

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 

1.412 

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 surface to 8 or 9 per cent at 2.5 inches 

below the surface. 

APPLICATION OF RESULTS TO ORDINARY RIVER GAGING. 

It has been s4own 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 
MURPHY.] EXPERIMENTS AT CORNELL UNIVERSITY. 93 

he attained in ordinary river gaging, as the conditions are not so 

favorable for accurate work. rrhe 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 measure with accuracy, but frequently there are one or more 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 measurement 

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 the total 

discharge 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, how~ 

ever, Prof. G. S. Williams believes that the actual discharge of the 

Cornell weir will not differ from that computed by Bazin's formula 

by more than 1 per c~nt 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 t.~1e 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 inaccuracies will be 

found, as all the results are not obtained in exactly the- same way; but 

they are believed to be substantially correct. 
94 ACCURACY OF STREAM MEASUREMENTS. (N0.64. 

In comparing the results of these experiments with results obtained 

by other experimenters it must 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. 57) 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. 53) it is 0. 5 foot, and 

in Marr's (p. 48) 2.4 feet. For these and highet· velocities our meter 

results by the ordinary method agree closely 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. 51). The large disagreement between meter and weir is for the low velocities, a field into 

which apparently few experimenters have entered. 

CONCLUSIONS. 

The conclusions to be drawn from these experiments may be briefly 

summarized as follows: 

(1) Discharge m~asured 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 

64 to 67 and 70.) 

{2) For velocities less than 1. 5 feet per second the discharge found 

with the Price meters is less than the corresponding weir discharge, 

and the difference increases rapidly as the velocity decreases. (See 

tables on pages 64 to 67.) 

(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. ~rhis difference 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 method, with an error of not more than 

1 per cent under favorable conditions, a velocit,y observation lasting ... 

fifty seconds being taken in each 2. 3 square feet of discharge area. 

( 5) When t.he 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 m~asure velocities of 1 foot per second and less more accurately than either the large Price meter or the 

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. 
MURPHY.) EXPERIMENTS AT CORNELL UNIVERSITY. 95 

(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 

dept.h. (See fig. 17.) 

(10) rrhe integration method 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 3G) 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 use 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 that 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-onehundredths depth. (See table on page 77.) 

(12) rrhe position of the thread of mean velocity varies from fivetenths depth for small depths to seventy-three-hundred_-ths depth for 

the larger depths. For the thirty-one experiments by the ordinary 

method of series C and D it is sixty-four-hundredths depth below the 

surface. (See table on page 77.) 

(13) rrhe 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 mean 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 for series 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 from -2.2 per cent to +30 per cent less 

than the mean velocit.y shown by tJ1e weir. (See table on page 83.) 

(17) A small Price meter will revolve faster in moving water of a 

given velocity when held with a rigid rod than when held with a 

cable. (See table on page 89.) Hence the same rating table will not 

answer for both. 

(18) rrhe 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. 

INDEX. 

Page. 

Abbot and Humphreys, method of using 

double floats adopted by---------- 14--15 

quoted_________________________________ 15 

vertical velocity-curve work oL ______ ~. 27 

Bailey, J. C., meter ratings by ____________ 41-42 

Baum, Adam, cited __________ -------------- 28 

Baumgarten, cited------------------------ 26 

Bazin, weir experiments and formula 

of ________________________________ 38-34,58 

Bazin and Darcy, cited ____________________ 2il,42 

experiments of------ __________________ 46--47 

Pitot tube ratings by __________________ ·12-44 

Pitot tube used by, view of___________ 19 

Boileau, Captain, cited ____________ -·--____ 26 

hydrometric tube invented by_______ 17 

Boright, W. P., acknowledgments to_____ 54 

Boonville, N.Y., experiments at _________ 51-58 

lirewster, meter designed by _______ ------ 20 

Brfinings, pressure plate used by_________ 17 

Ca beo, Professor, use of float rods by_____ 16 

Cass, C. D., acknowledgments to_-------- 59 

Ca3telli, hydrometric pendulum used by_ 17 

Coefficient work, fea~uresof: _____________ 38-89 

Connecticut River, floats used in survey of _________________________ ---------- 14 

measurements of ______________________ 47--48 

method of computing flow of.________ 45 

Cornell University, hydraulic laboratory 

at, description of_ _________________ 59-60 

hydraulic laboratory canal at, views 

showing ______ ------------- ______ 58,60, 62 

Murphy's experiments at _____________ 58-95 

Murphy's experiments at, diagrams 

showing results of ________________ 60,68, 

69, 72, 73, 7 4, 75, 76, 89,90 

Cornell University experiments, accu- racy of _______ ------ ________________ 93-94 

current-meter and weir, comparisons · of ________________________________ 64--71,94 

float-rod and current-meter surface 

velocity experiments ______________ 89-92 

float rod and weir, comparisonsof. ___ 54-57 

meter, method of holding, effect of __ 85-89 

meter, operation of, effect of-------- 83-85 

methods of conducting_----- __________ 62--63 

object of. _______________ ------------ ___ 58-59 

rating of meters in ______ -----· ________ 80-82 

reduction of ____ ------ _________________ 68--64 

I:esults of _______________________________ 64--95 

river gaging, application of results to_ 9'.2-93 scope of. _______________________________ 61--62 

surface velocity experiments. ________ 89-92 

velocity curves ______ ------------ ______ 72-80 

IRR 64-02--7 

Page. 

Cornell University experiments-Cont'd. 

velocity, mean, and average of bottom 

and surface, relation betwe•OJn ____ 82-83 

velocity, mean, by integration inverticals_______________________________ 80 

weir and current meter, comparisons 

oL _____________________ ------ ____ 64-71,94 

Cunningham, Captain, cited _______ . ______ 16,28 

quoted--------------------------------- 11,23 

Current meter, accuracy of measure- ments with _______ ----- _ _ ____ _ _ ____ 13 

advantages and disadvantages of_____ 22 

device for holding in place, view of__ 35 

double floats and, comparisons of ____ 47-51 features oL ____________________________ 19-22 

float rods and, comparisons of________ 51-53 

Harlacher's apparatus for moving, 

views showing _______ ---------- ____ 36,37 

method of holding, effect oL ____ 85-89,94,95 

methods of using ______________________ 34-39 

operation of, effect of _ _ _ _ _ _ _ _ 83-85, 85-89, 94 

rating of ______________________ 39--44,80-82,94 

rating tables of. _____ ------ ____________ 81-82 

revolutions of, relation between velocity of water and________________ 89 

speed of, effect of ______________________ 84-85 

surface velocity experiments with __ . 89-92 

variation in measurements with______ 71 

velocity of water and revolutions of, 

relation between ____ --------______ 89 

views of __________________________ ------ 20,21 

weir and, comparisons of__ 57-58, 64-80,94, 95 

Darcy and Bazin, cited _______________ ------- 26,42 

experiments of _______________ --------- 46--47 

Pitot tube ratings by------ ______ ------- 42--44 

Pitot tube used by, view of------------ 19 

De Fontaine, cited _______ ------_----------- 25-26 

Discharge, formulm for computing_----- 44-46 

Discharge-measurements, factors controlling accuracy of ______ ----- ________ 11-18 

methods of making and computing __ 31--46 

Double floats, adaptability of. _______ ----- 22 

current meter and, comparisons of __ 47-51 

features and use of. _____ -------------- 14-16 

view of ___________ ------ ______ ---------- 14 

Dubuat, float wheel used by-------------- 17 

Ellet, C., quoted------- ______ -------------- 23 

Ellis, T. G., cited-------------------------- 23 

experiments by------------------------ 47-48 

floats used by, description of--------- 14 

method of computing discharge used 

by---------------------------------- 45 Float frame, features of_ ________ ----_____ 17 

97 
98 INDEX. 

Page. 

Float rods, adaptability of._______________ 2'4 

current meter and, comparisons of. __ 51-53 

features of. .. _. __ ... ___________ . _______ 16--17 

surface velocity experiments with . _. 89-92 

weir and, comparisons of .. _ ... __ ... -~ 53-57 

Float wheel, features of. ____ ._____________ 17 

Floats, accuracy of measurements with.. 13 

Flood discharge, Harlacher's method of 

computing _____________ .___________ 46 

Flow of water, measurement of, application of Cornell experiments to .... 92--93 

measurement of, factors controlling 

accuracy of------------------------ 11-13 

methods of measuring and computing ....... __________ ....... _________ 31-46 

Francis, J. B., float-rods and weir experi- ments of. __________ . __________ . ____ 53-54 

quoted ___________________________ . _____ 11,28 

weir exper~ments and formula of ____ 32-38 

Fteley and Stearns, experiments of ... 8.3, 57-58 

Fteley meter, accuracy of measurements 

with ........ _. ____ .... _ ............. 90,91 

rating tables of ______ ...... ____________ 81 

vertical velocity curves obtained with, 

diagram showing ...... ____ ._ .. ___ . 74 

view of. ____________ . _____ ._____________ 21 

Fuertes, E. A., acknowledgments tJ. ____ 59 

Funk, cited------------____________________ 2G 

Ganges Canal, pulsation of water in _ ... _ 28 

Gaunthy, pressure plate invented by____ 17 

Glens Falls, N.Y., experiments at ____ 51,52-53 

Gordon, experiments by ____________ ------ 51 

Grandi, velocity-measuring device used 

by---------------------------------- 17 

Harlacher, apparatus designed by, for 

moving meter, description of.____ 38 

apparatus designed by, for moving 

meter, views of. _____________ ------ 36,37 

cited_------ ________________ ---·· .... ____ 29 

method of computing flood discharge 

used by----------------____________ 46 

method of computing flood discharge 

used'by, diagram showing________ 46 

method of using meter adopted by._. 38 

Haskell, E. E., vertical velocity-curve 

work by------------------ __________ 26--27 

Haskell meter, accuracy of measurements with ______ 69, 71,73-74,88,89-92,94 

Price meter and, comparisons of _____ 21-2'4 

rating tables of. ______ .... __ .__________ 81 

vertical velocity curves obtained with, 

diagrams showing .. _ ... _ .... ____ . _ · 76, 90 

view of. __________________________ .----- 21 

Henry, D. F., cited________________________ 26 

experiments by----------------------- 49-51 

meter designed by-------------------- 20-21 quoted _______________ . ______________ 11,15,29 

Hirn, float frame used by ..... ------______ 17 

Hook gage, view of________________________ 25 

Humphreys and Abbot, method of using 

don ble floats adopted by_ . _ _ _ _ _ _ _ 14-15 

quoted_------------ ______ ------________ 15 

vertical velocity-curve work of. ______ 26,27 

Hydrometric pendulum, features oL.... 18 

Hydrometric tube, features of----------- 17 

Ira wadi River, experiments 011.------ ____ 51 

Kuichling, E., reference to--------------- 54 

Page. 

Kutter, slope formula devised by ________ 22-2'~ 

Lepont, meter designed by--------------- 19-2(} 

Lockport, N.Y .. experiments at ____ 51-53,~.4--55 

McKenzie, A., cited----------------------- 29,38 

Marr, G. A., experiments by ________ 29-30,48-49 

Meter. See Current meter. 

Mississippi River, experiments on ... _._ .. 48--49 

method of computirg flow of_________ 45-

method of measuring flow of. ________ 14-15-

method of using meter on., .. ______ 35--36,38 

method of using meter on, view showing . __ .... ______ ... _. ___ . __ . _ .. _ _ _ _ _ 34 

pulsation of water in __________________ 29-30 

vertkal velocity-ctu·ve work on .. ____ 26,21 

Moore, T.V., method of computing discharge used by .. ___ .. _ ....... _____ 45 

Moore current meter, view of____________ 2(} 

Neva River, vertical velocity-curve observations on .... ____ ...... ___ .____ 26 

NewelL F. H., acknowledgments to. _. __ .. 59 

letter of transmittal by __ . ___ .. _ ... _ _ 9 

New York State canal survey, experiments of ... _ .. _. ___ . ___ . ________ ... 51-53 

Niagara River, meter ratings in. ____ . ___ 41-42 

method of computing flow of.________ ,45-

Paul,E.G., meter ratings by------------- 86 

Pitot tube, features of ________ .... ________ 13--19 

ratings of ________________ --------. _____ 42-44-

rectangular orifices ltnd, comparison 

of---------------------------------- 41 

surface floats and, comparison of.___ 4~ 

view of_________________________________ 19 

Pressure plate, features of________________ 11 

Price, W. G .. , method of using meter employed by--------------------______ 38 

Price meter, accuracy of measurements 

with ___________ 69;71, 73-74, 83-B4, 89-93, M 

ad vantages of . ____ ________ ____ ____ ____ 21 

Haskell meter and, comparisons of ... 21-22 

method of holding, effect of_ ........ _ 95 

ratings and rating tables of .. 41-42,81,87-89 

vertical velocity curves obtained 

with, diagrams showing .. 73, 74, 75,76,90 

views of.. __ ... ___ ----.. -- ...... ·._.----- 2(} 

Pulsation of water, features of .. 11-12,13,28-31 

Racourt, cited._----- ____ .... ______ -------- 26 

pressure plate used by---------------- 11 

Rafter,Geo. W.,referenceto experiments 

by----~--------·-------------------- 32 

Rating tables, comparison of, for different meteril. ------ ____________ ------ 81-82 

construction of. ______________ --------- 39-44 

Rectangular orifices, Pi tot tube and, comparison of. _____________ -----------· 47 

Rhine River, pulsation of water in ....... 28,29 

vertical velocity-curve observations on ___________ -.---- .... ____ ... _ ... --- 25-26 

River gaging, application of Cornell experiments to --------------.------- !l2-93 

factors controlling accuracy of.------ 11-13 

methods of _____ ------------------------ 31-46 

Rochester, N. Y.,experimentsat _________ .01-53 

Sabin, L. C., velocity experiments by... 31 

St. Clair River, experiments on---------- 49-51 

pulsation of water in----------------- 31 

vertical vekdty-curve observations 

on_---·· .•.... ___________ ----·------ 26 
INDEX. 99 

Saxton current meter, utility of ___ . 

Page. 

15 

Slope formula, method of measuring ve- locity by _________________ : _________ 22-23 

Smith, H., jr., quoted-----________________ 33 

Stearns and Fteley, experiments of ___ 33,57-58 

Surface floats, features and use of_______ 14 

Pitot tube and, comparison oL_______ 46 

Surface fluctuations, hook gage for measuring, view of_____________________ 25 

measurement of _______________________ 23-25 

Tachometer, features of ____________ -~---- 17 

Thames River, method of computing flow 

of __________________________________ _ 45 

pulsation of water in __________________ 28-29 

Thermometer, method of measuring velocity by _____ ---------- _______ . ___ 18 

Torrance, C. E., acknowledgments to____ 59 

United States Board of Engineers on Deep 

Waterways, method of computing 

discharge used by ____________ --·__ 45 

water gage used by _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 25 

United States Lake Survey, water gage 

used by---------------- ____________ 24-25 

Unwin, Professor, velocity experiments 

by---------------------------------- 28-29 Velocity, difficulty in measuring_ _ _ _ _ _ _ _ _ 11 

float-rod and meter experiments on 

surface.--------_-----_----- ________ 89-92 

mean and average of surface and bottom, relation between __ . _ .. _____ • 82-83 

0 

Page. 

Velocity-Continued. 

methods of measuring ____ 13-25,31-58,62-95 

revolutions of meter and, curves 

showing relation between _ _ _ _ _ _ _ _ 89 

threads of______________________________ 95 

variation in ________________ 28-31, 72-SO, 82-9'2 

Velocity curves, diagrams showing______ 72, 

73, 74, 75, 76, 90 

features oL ______________________ 25-27, 72-SO 

Verdigris River, Kansas, features of_____ 23 

Waltman, cited ________________________ ,___ 25 

meter designed by ______ ______ ____ ____ 19 

Water gages, self-registering, features 

of _________________________________________ 24-25 

record made by-------------__________ 24 view oL ______ ------ ______ ______ ____ ____ 24 

Weh-, current meter and, comparisons 

of ______________________ 57-58,64, W, 94,95 

discharge over, diagrams showing 

difference between meter discharge and _________ ------------ ____ 68,69 

float rods and, comparisons of ________ 53-57 

methods of measuring stream flow 

over------ ____ ------ ____ -------- ____ 31-34 

sharp-crested, view of---------------- 32 

Weser River, vertical velocity-curve observations on ________________ ------ 26 

Willhms, G. S,, acknowledgments to____ 59 

cited _______ ---------------------------- 93 

reference to----------------------·---- 54 
t