The Hydraulics of 

Overland Flow 

On Hillslopes

GEOLOGICAL SURVEY PROFESSIONAL PAPER 662-A

The Hydraulics of 

Overland Flow 

On Hillslopes

By WILLIAM W. EMMETT

DYNAMIC AND DESCRIPTIVE STUDIES OF HILLSLOPES

GEOLOGICAL SURVEY PROFESSIONAL PAPER 662-A

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1970
UNITED STATES DEPARTMENT OF THE INTERIOR 

WALTER J. HICKEL, Secretary

GEOLOGICAL SURVEY 

William T. Pecora, Director

For sale by the Superintendent of Documents, U.S. Government Printing Office 

Washington, D.C. 20402 - Price 75 cents (paper cover,)
CONTENTS

Abstract.._________________________________________

Acknowledgments__ _ ______________________________

Introduction.______________________________________

Description, of the problem_______________________

Review of the literature._--_-----_______________

Scope of the investigation________________________

Laboratory apparatus and techniques of measurement-__ 

Laboratory equipment.__________________________

The laboratory flume__________________________

Simulation of rainfall__________________________

Discharge measurements.________________________

Depth measurements.___________________________

Surf ace-velocity measurements. __________________

Other measurements.___________________________

Field sites and description of measurements.___________

General location.._______________________________

Geology and soils.______________________________

Vegetation.,_ __________________________________

Topography__ --__-----_______________________

Artificial rainfall__--------_____-______________

Runoff measurements,__________________________

Sediment samples_______________________________

Surface-velocity measurements- __________________

Flow pattern of overland flow-_-_--____-_________

Depth measurements.___________________________

Page

Al

1

1

1

2

3

4

4

4

5

6

6

6

6

7

7

8

9

10

10

12

12

12

13

13

Page 

Analysis of results and discussion. ______-_____--____-_ A14

General__ _ _________________---__-------__--- 14

Laboratory tests with uniform flow.______________ 15

Laboratory tests with artificial rain _______________ 19

Field investigation of overland flow.______________ 25

Comparison of field results to laboratory data______ 28

Probabilistic approach to overland flow and the shape of

hillslopes. _________-_-_-___-_-_--_-__-__-----_--- 31

Hydraulic changes downslope___-_______-_-____-- 31

Application to the shape of hillslope profiles_______- 34

Erosion and sediment transport___________-__-__---- 36

Rills and dynamic equilibrium________-______--- 36

Erosion and laminar flow--___------------------- 42

Summary of findings.____-_______-__-__-----------_- 44

References. __________-_--__-_------__-___---------- 45

Summary of data:

A, Vegetation type and relative density of cover at 

field sites..___________._ _____ _- 48

B, Example of data from measurements of surface 

velocity, Pole Creek Site 3________-___ 50

C, Example of data from depth measurements, Pole

Creek Site 3__________._____ 51

D, Summary of laboratory data for uniform flow 52 

E, Summary of laboratory data for artificial rainfall 53 

F, Summary of field data for overland flow sites.___ 66

ILLUSTRATIONS

FIGURES 1-8. Photographs of: *"£e

1. General arrangement of laboratory equipment-------..----------------- --___- -- A4

2. Details of sprinkling apparatus and appearance of artificial rain over the flume area... 5

3. Pole Creek Site !___-______________________________________________ ____-_ __ 7

4. Pole Creek Site 2__-____.___________________________________--- -- 7

5. Pole Creek Site 3_-_________________________________________-_.-_-----_.------------------ 8

6. New Fork River Site 1__-_____________._.___-_____.-----__------_____________-_-___-_- 8

7. New Fork River Site 2_____________________________________________________.___--- 9

8. Boulder Lake Site 2______________________________________ __ _-_ 10

9. Hillslope profiles of field sites_____________________________-________----------------- - ----- 11

10. Hydrographs of runoff for New Fork River Site 1____________.---___--_-__--__---_ ------- 13

11-24. Graphs showing:

11. Depth of uniform flow as a function of Reynolds number _______---___--------------------- 15

12. Darcy-Weisbach friction factor for uniform flow as a function of Reynolds number and average

depth -___.__________________________________--.__-_- _-- --_-- -------- 17

13. Chezy's C for uniform flow as a function of Reynolds number and average depth_________--___-- 19

14. Manning's n for uniform flow as a function of Reynolds number and average depth __________ 20

15. Ratio of mean velocity to surface velocity for uniform flow as a function of Reynolds number and

'average depth--_-___---_________________-_--_-_______------_--------------- - - 21

16. Downslope profiles of depth and surface velocity for sprinkled tests ________-_-___---------- 22

17. Depth and surface velocity as a function of Reynolds number for sprinkled tests.________-_-_--- 23

18. Summary curves of depth and surface velocity as a function of Reynolds number for sprinkled

tests _____________________________________________--._____.------ 24

19. Darcy-Weisbach friction factor as a function of Reynolds number for sprinkled tests _________ 25

in
IV CONTENTS

Page 

FIGURES 20. Summary curves of Darcy-Weisbach friction factor as a function of Reynolds number for sprinkled

tests.__________.___.___.___.__._____.._.________________________ A26

21. Chezy's C and Manning's n as a function of Reynolds number for sprinkled tests_____________ 27

22. Summary curves of Chezy's C and Manning's n as a function of Reynolds number for sprinkled

tests______________________________________________________________ 28

23. Froude number and velocity ratio as a function of Reynolds number for sprinkled tests-_________ 29

24. Summary curves of Froude number and velocity ratio as a function of Reynolds number for

sprinkled tests.____________________________________________________________________ 30

25-31. Maps showing topography and flow pattern at:

25. Pole Creek Site 1_........_________...__.__....___-...___________..________ 31

26. Pole Creek Site 2______________-.._______________________________________ 31

27. Pole Creek Site 3_-,__.______________ ____----- --__- - - _--__ _-_..-- 32

28. New Fork River Site 1_________._-_____-___---__-__________________________ 32

29. New Fork River Site 2_________________________________._-__-_.______________ 33

30. Boulder Lake Site 1__________________________________________________________ 33

31. Boulder Lake Site 2---____-_-_-_-_---_---------------------------------------_--_ _____ 34

32. Downslope profiles of depth and surface velocity for Pole Creek Site 3-__--_--_-__________-___________ 35

33. Downslope profiles of depth and surface velocity at field sites._.._____________________________________ 36

34-39. Graphs showing:

34. Depth and Darcy-Weisbach friction factor as a function of Reynolds number, Pole Creek Site T__ 37

35. Summary curves of depth and Darcy-Weisbach friction factor as a function of Reynolds numb er,

field sites____________________________________...___________________ 37

36. Chezy's Cand Manning's n as a function of Reynolds number, Pole Creek Site 3_______________ 38

37. Summary curves of Chezy's C and Manning's n as a function of Reynolds number, field sites_____ 38

38. Froude number and velocity ratio as a function of Reynolds number, Pole Creek Site 3__________ 39

39. Summary curves of Froude number and velocity ratio as a function of Reynolds number, field sites. _ 40

40. Hillslope profiles for various runoff rates.________-___-_---_-----_--__-_---____--____.__________-___ 40

41. Hillslope profiles for various initial gradients__-_-_--__---------___----__-____----_--______________ 41

TABLES

TABLE 1. Analytical results of surficial soil samples from overland flow field sites________-___-_______-__--_------ A9

2. Characteristics of overland flow field sites____________-___-------___-------------_-----_------------ 10

3. Rainfall and runoff rates at overland flow field sites.__________________________-_-__-____--_------___ 12

4. Summary and comparison of exponents in hydraulic geometry_____________________-____-------__--__- 22

5. Analytical results of sediment samples from overland flow field sites.._____-______--__-_-----_--------- 42

6. Average values of sediment sample analyses compared to ground slope and vegetation cover for overland flow

field sites__-_____-____-__-_____________-___-___-______--_-_____------_-----___------------- 43

SYMBOLS

A Area in acres

C Chezy coefficient, C=(8g/ff)^, in feet*- per second

D Average depth in feet

F Infiltration rate in inches per hour

I Rainfall intensity in inches per hour

K Coefficient of runoff

L Slope length in feet

M Exponent reflecting the degree of turbulence

F Froude number, F=F/(grZ>)^

R Reynolds number, R = 4;VD/v

Q Discharge in cubic feet per second

R Runoff rate in inches per hour

S Slope in feet per foot

T Temperature, °F and °C

V Mean velocity, V=q/D, in feet per second

V, Surface velocity in feet per second

W

b

c

f 

ff

g

i 

k 

m 

n

9

t

y

z

Width in feet

Exponent of width, WccQb

Constant

Exponent of depth, DCCQf

Darcy-Weisbach friction factor, ff=8gDS/V2

Acceleration of gravity in feet per second squared

Maximum intensity of rainfall in inches per hour

Proportion of impervious surface

Exponent of velocity, VccQm

Manning resistance coefficient, n = 1.5D^/C, in feet Ye

Unit discharge in cubic feet per second per foot

Time, in hours, minutes, and seconds

Exponent of friction, //ocQ»

Exponent of slope, /SocQ*

Kinematic viscosity in square feet per second
DYNAMIC AND DESCRIPTIVE STUDIES OF HILLSLOPES

THE HYDRAULICS OF OVERLAND FLOW ON HILLSLOPES

By WILLIAM W. EMMETT

ABSTRACT

Overland flow resulting from rainfall on natural hillslopes 

responds to the downslope increase in discharge by increasing 

its depth and velocity. Depth absorbs about two-thirds of the 

increase in discharge; velocity absorbs about one-third. For 

straight slope segments investigated in the field, resistance to 

flow remains nearly constant in the downslope direction. The 

comparison of field data to laboratory data shows general agreement, but it illustrates the extreme influence of vegetation and 

topographic irregularities on resistance to flow over natural 

hillslopes. Values of resistance to flow expressed as Manning's n 

were as high as 1.0 and averaged about 0.5; this roughly corresponded to a Darcy-Weisbach friction factor of 100.

A theoretical model of overland flow on slopes was developed 

based on most probable statistical concepts. Evaluation of the 

model for laminar and turbulent flow, and the interpolation of 

these two cases, corresponds to overland flow on hillslopes from 

laminar at the hilltop to fully turbulent at some distance down 

the slope. The model is in general agreement with measured 

data on the downslope increase of depth and velocity and further 

shows that when no constraint is placed on slope, the slope for 

laminar flow increases downslope, the slope for turbulent flow 

decreases downslope, and a mixed or disturbed flow has an 

intermediate value or generally constant downslope gradient. 

This requires that a hillslope must have a convex upper segment, 

a straight middle segment, and a concave lower segment. This 

is the slope profile more often than not found in nature. Slope 

steepness and the length of each segment are controlled by the 

runoff rate and the initial gradient at the top of the slope. Thus 

the shape of each slope profile is related to its climatic and geologic environments.

ACKNOWLEDGMENTS

This study was initiated in the fall of 1966 and fieldwork was conducted in the summer of 1967. Luna B. 

Leopold, U.S. Geological Survey, was instrumental in 

establishing the experimental program, assisted in the 

collection of data, and provided stimulating discussion 

and review of the manuscript. Others who assisted in 

the collection of field data include E. L. Howell, C. A. 

Weidowke, E. A. Daly, and J. T. O'Eourke who also 

identified the plant species. Their help is gratefully 

acknowledged. Thanks is due also for permission to 

work on the properties of Bill Bloom, the Christman 

Corporation, and the U.S. Forest Service.

The sediment concentration samples were analyzed

by V. W. Norman and the size distribution of the soil 

samples was determined by A. B. Commings, both of 

the U.S. Geological Survey. For their review, comments, 

and suggestions, the author is indebted to W. O. Eee, 

L. D. Meyer, M. G. Wolman, C. B. Hunt, G. E. Foster, 

and E. F. Hadley.

INTRODUCTION

DESCRIPTION OF THE PROBLEM

Overland flow is the initial phase of surface runcfL 

It is sometimes referred to as sheet flow because the 

water is envisioned as moving in a sheet downslope 

over a plane surface to the nearest concentration point 

or channel. Nearly all surface runoff starts as overland 

flow in the upper reaches of a watershed and travels 

at least a short distance in this manner before it reacl <^s 

a rill or channel. Once a known flow rate reaches a 

defined channel its action may usually be characterised 

adequately by standard hydraulic procedures.

In overland flow the variables are more difficult to 

define precisely and the use of a simple hydraulic p^ocedure for predicting overland flow is beset with many 

difficulties. Overland flow is both unsteady and spatially 

varied since it is supplied by rain and depleted by infiltration, neither of which is necessarily constant with 

respect to time and location. Flow may be either laminar 

or turbulent or a mixture of these two conditions. 

Flow depths may be either below or above critical, or 

the depths may change from subcritical to supercritical. 

Under certain conditions the flow may become unstable 

and may give rise to the formation of roll waves. The 

action of raindrop impact on the sheet of flowing water 

further complicates the overland flow problem.

Although the ground surface over most of the plot 

areas was covered by surface detention during overland 

flow, most runoff occurred in several laterally-spaced 

concentrations of flow. These concentrations of flow 

wove anastomosing paths downslope. Over the short 

lengths of the runoff plots, the Eeynolds number, a 

measure of fluid turbulence, remained in the regime 

normally considered laminar flow, but the flow was not 

truly laminar because of the disturbance by falling

Al
A2 DYNAMIC AND DESCRIPTIVE STUDIES OF HILLSLOPES

raindrops and the influence of topographic irregularities. Such a disturbed flow is capable of eroding and 

transporting sediments. Despite surface erosion by the 

runoff, no rilling was observed to have developed. It is 

suggested that the studied slopes are in dynamic equilibrium with other slopes in the drainage system. A complex interaction of vegetation, topography, and other 

friction terms provides a resistance to flow that maintains depths and velocities, and thus erosion is just 

sufficient to continue downcutting equilibrium with 

other slopes in the drainage system. Rilled slopes are in 

areas which require more rapid erosion to maintain 

equilibrium.

The need to accurately determine the hydraulic 

parameters characterizing overland flow and the role 

of overland flow as a landscaping agent led to the present 

experimental study directed toward quantitative evaluation of the variables associated with overland flow. 

The experimental study is still in progress, but sufficient 

data on the hydraulics of overland flow have been 

collected to enable the present analysis of that aspect.

REVIEW OF THE LITERATURE

In the course of the initial literature search it became 

apparent that many aspects of the hydraulics of overland flow have not been investigated. Early researchers 

tended to direct their studies toward individual aspects 

of overland flow. Little effort has been made to integrate 

various aspects into an attempt to quantify the hydraulics of overland flow. However, the individual 

aspects did serve to provide some of the important 

initial theories; for example, the behavior of laminar 

sheet flow and the theories of infiltration and detention 

were well documented. These writings were followed 

by a series of experiments in which investigators attempted to determine values for the constants in the 

earlier theories. Most of the more recent researchers 

have directed their attention to analytical and theoretical solutions to the hj'draulics of overland flow.

Although his studies are not directly related to the 

present study, Kuichling (1889) made the first attempt 

to rationalize computations of surface runoff. The formula which he proposed, popularly known as the 

rational method, is expressed as

Q=kiA (1)

in which Q is the discharge in cubic feet per second, 

k is the proportion of impervious surface, i is the maximum intensity of rainfall in inches per hour, and A 

is the area in acres. It is evident that the rational method 

contains many deficiencies; even Kuichling noted that 

it is "nothing more than a crude approximation * * *." 

During the next half century following Kuichling's 

work, few studies were conducted to increase the knowledge of surface runoff computations. Most of these 

investigations were confined to filling the deficiencies 

in the rational formula or in applying the rational 

formula to special shapes of watersheds.

The first of the works utilizing details of the surface 

phase of the hydrologic cycle began in 1933, when R. 

E. Horton described his theories of infiltration capacity 

and surface detention (Horton, 1933). This vork was 

closely followed by Horton, Leach, and Van Vliet (1934) 

in a study of the basic behavior of laminar si °-et flow. 

In this study, values of depth and velocity associated 

with the shallow flow of water over sloping surfaces were 

predicted. Horton (1936,1938) continued to be the pacesetter for a description of overland flow. His efforts 

resulted in a classical work on geomorphology (Horton 

1945) in which he postulated that a condition of mixed 

flow exists in nature; that is, areas of fully turbulent 

flow are interspersed with areas of laminar flow. For 

turbulent flow, depth can be estimated by the Manning 

equation. Horton expressed this as

in which q is the unit discharge in cubic feet per second, 

K is a coefficient of runoff reflecting among oth^r things, 

slope and bed roughness for turbulent flow and slope 

and viscosity for laminar flow, and D is the depth in feet. 

For laminar flow a form of the Poisseuillo formula 

may be used to estimate the depth. This is expressed as

n _ TTT& fo\ 2 xi.-L' . \o)

For either turbulent or laminar flow, depth can be 

expressed as

q=KDM (4)

in which M is an exponent reflecting in part the degree 

of turbulence. The value of M for fully turbulent flow 

is % and is 3 for fully laminar flow. Thus, with increases 

in discharge, depth increases more rapidly in turbulent 

flow than laminar flow. For mixed flow, as Horton postulates occurs in nature, values of M would range between these two extremes. Horton continued his analysis 

with expressions for the downslope profile of overland 

flow and surface erosion by overland flow. Among those 

who determined the values of the constants in Horton's 

(1938) equations were Ree (1939) and Izzard (1943).

Keulegan (1944) employed a mathematical analysis 

to obtain a complete solution to spatially varied discharge over a sloping surface. One of his conclusions 

was that the direct resistance effect of falling rain is 

small, but the perturbing effect will give an increased 

velocity close to the bed of the channel.

Verifications of the Horton, Leach, and T;ran Vliet 

(1934) investigation of uniform laminar flow were conducted by Parsons (1949), Straub (1939), Owe^is (1954),
THE HYDRAULICS OF OVERLAND FLOW ON HILLSLOPES

and others. These studies were conducted in fully established uniform flow and were analyzed to show the 

dependence of resistance terms on Reynolds number. 

They further showed the presence of a transition region 

between laminar and turbulent flow. The transition region was variously reported to lie between Reynolds 

numbers of 2,500 to 12,000. Parsons (1949) further 

investigated the surface runoff resulting from the simulation of rainfall. One interesting aspect of Parsons' 

work was his determination of the ratio of measured 

depth to a theoretical depth calculated from a form of 

the Poisseuille formula. For uniform flows, the ratio 

ranged from 1.00 for a smooth surface to 1.25 for a rough 

and pitted mortar surface. For runoff from artificial 

rainfall, this depth ratio ranged from 1.46 for the rough 

and pitted mortar surface, 1.5 to 2.8 for bare soil, and 

up to 10.2 for bluegrass. These data illustrate the tremendous effect of surface roughness on extremely shallow flows. The rough and pitted mortar surface was 

evaluated for both uniform flow and runoff from artificial rain. Thus, the separate effects on the depth ratio 

caused by bed roughness and raindrop impact can be 

isolated. These data, collected at differing channel slopes 

and spray intensities, showed that raindrop impact 

increased depths from 8 to 28 percent over the theoretical depth, with the average increase being 17 percent. 

No consistent variation in relative increase with slope 

or spray intensity was noted.

Keulegan's (1944) conservation of momentum concept provided the base for a new series of overland flow 

experiments. Among these investigators were Izzard 

(1944, 1946), Parsons (1949), Behlke (1957), and Woo and 

Brater (1962). Izzard experimented with artificial rainfall over paved and turfed areas. From his empirical 

data, a nomograph was prepared for the solution of 

overland flow detention on a unit strip. Woo and Brater 

determined water surface profiles for combinations of 

rainfall intensity, surface roughness, and slope. The 

effect of rainfall impact was clearly expressed in terms 

of uniform flow condition, slope, and Reynolds number.

Richey (1954) and Chen (1962) theoretically derived 

the surface profile of overland flow by the methods of 

finite integration. The surfaces for which profiles were 

developed were smooth planes.

The above summary of the literature is by no means 

complete. However, it is representative of the development of knowledge of overland flow. References pertaining to overland flow in the geologic literature are 

included in subsequent sections of this report.

SCOPE OF THE INVESTIGATION

Many of the early studies involving the simulation 

of rainfall over small plots were concerned only with

the bulk quantities of rainfall, infiltration, runoff, and 

the shape of the runoff hydrograph. Attention was 

seldom paid to a detailed characterization of the hydraulics of flow. Except with analytical models then, it 

has been impossible with the existing experimental data 

to completely describe the hydraulics of surface runoff 

from the moment a raindrop hits the ground until the 

time many drops collectively are established as channel 

flow in the nearest rill. The analytical models are also 

deficient in that there are insufficient field verifications 

to determine the constants in their equations.

Closely related to the hydraulic properties of overland 

flow is the ability of these extremely shallow flows to 

rework the ground surface over which they flow. Such 

reworking occurs in nature and is evidenced by the sheet 

erosion of hillslope sediments and the tranportation of 

these sediments, which are either deposited at some 

other location on the slope or are carried entirely out 

of the drainage system. Under certain conditions of flow 

and environment, more noticeable modifications of the 

ground surface appear. Included in this category is the 

formation of rills. Once a rill has been established, further modifications are controlled more by the laws governing concentrated channel flow than those by overland 

flow. Unfortunately, the present knowledge of overland 

flow as a landscaping agent is even more deficient than 

the knowledge of its hydraulic characteristics.

In an attempt to fill some of the gaps in the knowledge 

of overland flow, an experimental study was initiated 

to systematically evaluate the hydraulic parameters 

descriptive of overland flow. The study carried from the 

laboratory to the field.

In the laboratory, an impervious, smooth plane surface of adjustable slope was used to study uniform flow 

over a range of shallow depths from 0.0029 to 0.0435 

foot (0.9 to 13.3 millimeters) and of five slope values 

from 0.0033 to 0.0775 foot per foot. At each slope position, spatially varied flow resulting from the uniform 

application of artificial rainfall was studied at five intensities of rainfall. These intensities were about 3.5, 4.7, 

6.1, 8.5, and 11.5 inches per hour. After the completion 

of these smooth-surface tests, a uniform sand-grain 

roughness was applied to the flume floor and tests 

approximating those for the smooth surface were conducted as before. The principal measurements made 

include depth, surface velocity, discharge, and water 

temperature. Qualitative observations were also made 

by the diffusion of dye to determine whether the 

flow was laminar or turbulent and whether or not unsteady flow exemplified by roll waves was occurring. 

For the tests with artificial rainfall, depths and velocities were measured to determine the downslope 

changes and the total discharge measured was distributed over the runoff surface area to determine the average
A4 DYNAMIC AND DESCRIPTIVE STUDIES OF HILLSLOPES

intensity of rainfall. The data collected allow the 

computation of additional hydraulic parameters describing the characteristics of the flow.

Seven field sites in west central Wyoming were selected for verification of the laboratory data.The field 

sites were 7 feet wide, about 45 feet long, and approximately represented four slope angles. These slope angles 

were about 0.003, 0.10, 0.20, and 0.33 foot per foot. 

To adequately describe the field sites, detailed topographic maps were prepared, surficial soil samples were 

analyzed for particle-size distribution, the relative 

density of different vegetation types was measured, 

and an estimate was made of overall vegetation density 

and overstory cover. Each field site was sprinkled 

with artificial rain at an intensity of approximately 

8.5 inches per hour. About 10 percent of this amount 

was wind blown from the runoff area and, generally, 

runoff of 4 inches per hour was measured at the lower 

end of each plot. Beginning with the initial runoff, 

flow rate was recorded to determine the rising hydrograph and the infiltration characteristics. Periodic 

sampling of runoff water provided data on the sediment 

concentration of the flow. These data were analyzed 

for both the mineral and organic content. After the 

infiltration rate became constant, values of depth and 

surface velocity, and their downslope changes, were 

measured. Although the entire surface of the runoff 

plot generally glistened with standing water, most 

runoff occurred in concentrations of flow directed 

downslope. These flow concentrations, related mostly 

to the microrelief of the plot surface, were mapped by 

dye tracings to show the general pattern of flow. Finally, 

rain gages were placed over the plot area to check on 

the accuracy of the calibrated sprinkler system and 

to determine the uniformity of the rainfall distribution.

LABORATORY APPARATUS AND TECHNIQUES OF 

MEASUREMENT

LABORATORY EQUIPMENT

All laboratory tests reported in the present investigation were made in the Hydraulics Laboratory of the 

U.S. Geological Survey, Washington, D.C. A temporary 

flume was constructed to represent a segment of hillslope length. Water was supplied to the flume either 

from a 4-inch line from the laboratory's constant head 

system (uniform flow) or the city water supply (simulation of rainfall). Gate valves were used to regulate 

the discharge of water.

THE LABORATORY FLUME

The flume used in this investigation was constructed 

with a plywood bed supported by 2- by 4-inch timber 

beams. Flume walls were 3 inches high and made of

clear plastic. The width was 4 feet and the length was 

16 feet. Flume slope was adjustable by hydraulic jacks 

at the lower end and, to prevent sagging in the vertical, 

intermediate supports were placed under the 2- by 4- 

inch beams. The general arrangement of the equipment 

is shown in figure 1.

For a first series of tests, the plywood floor was 

sanded smooth and covered with two layers of enamel. 

In a second series of tests, a uniform sand roughness 

with a median grain diameter of 0.50 millimeter was 

glued to the flume floor by applying a heavy layer of 

varnish to the surface and then sprinkling the sand 

evenly onto the varnish after it had only partly dried. 

After the varnish had fully dried, the excess sand was 

swept from the surface leaving an applied roughness 

which was several grain diameters thick. This gave a 

firmly attached roughness without the surface of the

FIGURE 1. General arrangement of the laboratory equipment. 

Upper: Looking upslope. Lower: Looking downslope.
THE HYDRAULICS OF OVERLAND FLOW ON HILLSLOPES A5

top layer of grains being smoothed by excess varnish. 

The sand used as the roughness element was well 

sorted by sieving to give a uniform roughness; sorting 

characteristics were:

Grain size 

(mm)

0.44__ 

.50__ 

.60__ 

.71---

.84__

Percentage finer 

by weight than 

indicated size

4

45

92

99

100

For the study of uniform flows at shallow depths, 

water was discharged from the supply line into a stillingtype of forebay. Uniform flow entered the flume over 

a rounded brink on the flume floor. Because all depths 

of flows investigated were extremely shallow (less than 

0.05 ft.), there was no need for either upstream or downstream controls to promote uniform flow.

SIMULATION OF RAINFALL

Artificial rainfall was produced using a commercially 

available type of line sprinkler. This apparatus consisted 

of a 3^-inch copper pipe equal in length to the length of 

the flume. A series of specially punched holes at 1-foot 

intervals along the pipe allowed the sprinklers to spray 

a fan of water in a narrow width along the line of 

sprinklers. Water was centrally supplied to each sprinkler unit through a gate valve and pressure gage. Each 

sprinkler unit was calibrated and rainfall intensity could 

be determined by the pressure gage indication. The 

distribution of rainfall over the sprinkled area was 

checked by randomly placing collecting gages over the 

area. It was determined that rainfall distribution was 

evenly divided over the area; individual gages indicated 

more or less than the average, but no systematic pattern 

could be detected over the entire area. Most likely, 

excess readings were due to higher concentrations of 

water in the tailing ends of each fan of water spray; 

deficient readings were due to a central location within 

the spray. Some details of the sprinkling apparatus and 

the appearance of artificial rainfall over the flume area 

are shown in figure 2.

No attempt was made to determine the impact velocity or drop size of the falling rain droplets. Natural 

rainstorms at a given intensity include a wide range of 

drop sizes and the drop-size distribution varies with 

rainfall intensity. The size distribution by volume for 

different rainfall intensities shows mean drop sizes of 

1, 2, and 3 millimeters for intensities of 0.01, 1.0, and 

4.0 inches per hour, respectively (Laws and Parsons, 

1943). However, the percentage by volume contributed 

by drop sizes within J^ millimeter of the sizes listed 

above are, respectively, only 28, 12, and 9 percent of the 

total rain, the remainder being about equally contribFIGURE 2. Appearance of artificial rain over the flume area. 

Upper: Looking upslope. Lower: Looking downslope.

uted between larger and smaller drops. Water drops 

falling through the air approach a terminal velocity 

which varies with drop size. The relation of distance of 

fall to drop-fall velocity was studied by Laws (1941) 

and Gunn and Kinser (1949). For drop sizes of 1.25, 2.0, 

and 3.0 millimeters, a respective fall distance of about 

15, 30, and 40 feet was needed to obtain terminal 

velocity of 15.8, 21.6, and 26.5 feet per second, 

respectively.

In the laboratory, two sprinkler units were placed 

approximately 6 feet above the flume floor and pointed 

downward. Because of the initial acceleration in being 

sprayed downward, the impact velocity of the falling 

droplets was believed to be of reasonable acceptance. 

However, the average drop size in the present experiments was about 0.5 millimeter and varied little with 

the intensity of spray. This is considerably smaller than

368-391 O 7C
A6 DYNAMIC AND DESCRIPTIVE STUDIES OF HILLSLOPES

the reported size of drops occurring in natural rainstorms. At the time the laboratory equipment was 

designed, this deficiency in attempting to simulate 

natural rainstorms was not believed to be an extremely 

important factor in the hydraulics of overland flow. 

Thus, Keulegan (1944) has reported that the retarding 

effect of falling rain is small. Apparently, however, the 

geomorphic or erosional effects of falling raindrops are 

related in part to the depth of flow into which they fall. 

Palmer (1965) investigated the soil loss by waterdrop 

impact forces for three drop sizes and with various 

depths of a water layer over the soil surface. Water 

layer depths were varied from 0 to 30 millimeters 

(0.10 foot). Maximum soil losses for drop sizes of 2.9, 

4.7, and 5.9 millimeters occurred at a critical depth of 

the water layer of 2, 4, and 6 millimeters (0.007, 0.013, 

and 0.020 foot), respectively. Thus the critical depth 

occurs in a region where a 1:1 relationship exists between the drop diameter and the depth of the water 

layer.

DISCHARGE MEASUREMENTS

Total discharges below 0.10 cubic foot per second were 

measured volumetrically. All tests with artificial rainfall 

lie within this range. For discharges greater than 0.10 

cubic foot per second, a calibrated bend meter in the 4- 

inch supply line was used.

DEPTH MEASUREMENTS

Measurements of flow depth and determination of 

flume slope were obtained with a point gage mounted on 

a precision leveled carriage which is independent of 

the flume structure. The point gage could be positioned 

anywhere over the flume surface. Depth determinations were recorded as the difference between the elevation of the flume floor and the water surface. The point 

gage could be read directly to 0.001 foot, and with discretion given to the flume-floor and water-surface 

elevation readings, the accuracy of the depth measurements was believed to be within 0.0005 foot.

Depth readings were recorded for 3 transverse locations for each 1-foot downslope position between 1 foot 

to 15 feet. The three transverse locations were at the 

quarter points (1 and 3 ft) and midpoint (2 ft) across 

the flume width. For each run then, 45 observations 

of depth were recorded. In the uniform flow tests, the 

45 readings were averaged to give a mean depth, and 

for tests with artificial rain, each set of three transverse 

readings were averaged to give a mean depth for each 

downslope position.

For tests with the roughened surface, a mean flume 

floor elevation equal to the top of the roughness elements was used in depth determinations. The top of 

the roughness elements was measured by attaching a

blunt ^-inch-wide blade to the tip of the point gage. 

In all computations that follow, no correction that took 

into consideration the voids between sand particles 

was applied to depths as measured at the top of the 

roughness element.

Figure 2 also illustrates the point-gage arrangement 

and some of the problems involved with depth measurements in tests with artificial rain.

SURFACE-VELOCITY MEASUREMENTS

Surface velocity was measured by tracing the travel 

of dyes over specified downslope distances which had 

been marked out as a grid system on the flume floor. 

For most of the uniform flows, a liquid food coloring 

was used. As the dye advanced downslope, a dye streak 

was left behind as dye at the water surface moved downslope faster than dye settling downward in the flow. 

The leading edge of the dye streak was timed to assure 

that velocity at the water surface was being measured. 

The effect of impact from artificial rain was to hasten 

the diffusion of the liquid dye and it was difficult to 

trace the dye movement. Therefore, for tests with artificial rain, a nonwetting, brilliantly colored powder was 

sprinkled on the water surface and movement of the 

powder was timed over specified distances.

For uniform flow, the surface velocity was measured 

between downslope distances of 2 to 8 feet and 8 to 14 

feet and at the three transverse positions of the quarter 

points and midpoint. These six readings were averaged 

to determine the mean surface velocity for each run. 

No systematic difference in velocities was detected 

between the six measuring reaches.

For tests with artificial rain, surface velocity was 

measured at the transverse quarter points and midpoint and between the downslope distances of 1 to 3 

feet, 3 to 5 feet, 5 to 7 feet, 7 to 9 feet, 9 to 11 feet, 11 

to 13 feet, and 13 to 15 feet. Each set of three transverse 

readings were averaged to give the mean surface velocity for each of the seven downslope positions.

OTHER MEASUREMENTS

In addition to the above measurements, at the tjme 

velocity for uniform flow was being determined by the 

dye measurements, visual observations were made of 

the amount of dye diffusion to determine if the flow 

was laminar, turbulent, or a mixture of the two.

Observations were made as to whether or not unsteadiness of flow as characterized by roll waves was occurring. Data from tests with roll waves were compared 

to data from tests without waves to determine if significant discrepancies were being caused in the measurements of depth and surface velocity. Some free-surface
THE HYDRAULICS OF OVERLAND FLOW ON HILLSLOPES A7

instability can be detected for the flow illustrated in 

figure 1 (lower photograph).

Water temperature was recorded for each test to 

determine the appropriate value of viscosity used in 

subsequent computations.

FIELD SITES AND DESCRIPTION OF MEASUREMENTS 

GENERAL LOCATION

Seven sites were selected for field verification of the 

hydraulic characteristics of overland flow as determined 

in the laboratory investigation. All of the field sites were 

located in Sublette County, west-central Wyoming, near 

the town of Pinedale. This location was selected because 

it centers in the area where the author participates in 

other field research problems; the area has no particular 

advantages or disadvantages.

Individual sites were selected on the basis of several

FIGURE 3. Pole Creek Site 1. Upper: Looking upslope. Lower: 

Runoff and surface detention immediately after rainfall.

FIGURE 4. Pole Creek Site 2. Upper: Looking upslope. Lower: 

Looking across slope.

criteria including: the proximity to a source of water to 

facilitate the generation of artificial rain, a ground surface with a slope of essentially a smooth plane, and vegetation and surface features which have not been unduly 

influenced by man or animal.

The seven selected sites represented three geographical areas. Three sites were on slopes bordering Pole 

Creek at a reach about 2 miles downstream from Little 

Half Moon Lake, two sites were along the New Fork 

River about 1 % miles below the bridge crossing of State 

Highway 187, and two sites overlooked Boulder Lake 

near the upper end of the lake. The runoff plot established at each site was 7 feet wide and generally longer 

than 40 feet. The general appearance of the seven field 

sites is illustrated in figures 3 to 8. Some details of figures 

3 to 8 are discussed in the following sections.
A8 DYNAMIC AND DESCRIPTIVE STUDIES OF HILLSLOPES

?*., .'V l&e, ,

* ' "" ".. "*#- f'£ i~

sandstone, claystone, and shale. Bedrock is within several feet of the ground surface.

Samples of the surficial soil at each site were analyzed for their particle-size distribution. The samples 

were obtained from the top 2 inches of soil at several 

random locations over each site. The analytical results 

of the size distribution are listed in table 1. Because 

the samples were skimmed from the ground surface 

with a shovel, a considerable amount of organic material 

was present in each sample. To eliminate the organics 

from the samples, the samples were treated with hydrogen peroxide (H2O2) and baked for 2 days in an oven. 

Conventional sieve and pipette analyses were conducted 

for the sediment residue. These analyses indicate that 

all sites were composed of very poorly sorted sediments ranging in size from clay particles to small 

gravel. The influence of the soil-size distribution on the 

hydraulics of overland flow is discussed in a later secFIGUKE 5. Pole Creek Site 3. Upper: Looking upslope. Lower: 

Looking downslope.

GEOLOGY AND SOILS

The Pole Creek and Boulder Lake sites were on normally eroded morainal surfaces of sand, gravel, and 

boulders formed during the glaciation of the Wind Kiver 

Kange. Although boulders are common in the area, the 

sites selected included only a few small patches of exposed rock and no large protruding boulders. The 

ground surface at Pole Creek Sites 1 and 3 differed most 

from the general appearance of the morainal topography. These sites were located close to Pole Creek and 

infrequent high-water events in this creek have probably sent flowing water over these areas resulting in 

some smoothing of the surface and the deposition of 

fluvial sediments.

The two sites along the New Fork Kiver were on a 

soil mantle developed from the Wasatch Formation of

FIGURE 6. New Fork River Site 1. Upper: Looking downslope. 

Lower: Delta formed of sediments eroded upslope.
THE HYDRAULICS OF OVERLAND FLOW ON HILLSLOPES A9

TABLE 1. Analytical results of surficial soil samples from overland flow field sites

[Diameter in millimeters. Site number: PC, Pole Creek; NF, New Fork River; 

and BL, Boulder Lake]

Site number

PC-1 PC-2 PC-3 NF-1 NF-2 BL-1 BL-2

Percentage finer by weight than indicated size

Grain diameter:

0.002.. 

.004 

.008 

.016 

.031 

.062 

.125. 

.250 

.500 

1.00. ......

2.00 

4.00 

8.00..........

16.00. 

5

........... 1

........... 10

... 15

 22

 30

 ... 36

 44

... ..... 54

...... 64

 72

 ... 75

 ... . 75

 ... ..... 100

5

7

10

14

20

28

34

40

51

64

73

80

89

100

8

11

14

21

30

44

52

55

60

68

77

84 .

93 .

100

7

8

10

12

16

26

42

76

97

99

100

10

14

20

28

37

47

53

59

66

72

75

79

81 .

100

8

12

15

22

30

39

47

57

70

84

95

100

6

8

11

15

21

28

35

46

58

70

82

89

91

100

Diameter corresponding to particle class

Particle class:

D,6. ......

DM .....

1DM.. ........

 .... 0.018

... ..... .38

 .. 14.0

0.021

.48

5.4

0.010

.10

4.0

0.030

.15

0.005

.09

.30 11.0

0.009

.16

1.0

0.018

.32

2.3

tion. Pole Creek Site 1 and New Fork River Site 2 had 

the greatest number of coarse-sized particles as indicated 

by the large percentage of sediment weight in particles 

8 to 16 millimeters. New Fork River Site 1 was characterized by a near absence of particle sizes greater 

than % millimeter. New Fork River Site 1 had the highest 

percentage of fine-sized particles followed closely by 

Boulder Lake Site 1 and Pole Creek Site 3. The large 

number of fine particles at Pole Creek Site 3 may help 

confirm that this site has, at times, been flooded by 

Pole Creek.

VEGETATION

At each site, detailed studies were conducted to determine plant species and the relative density of cover 

of each species. To determine these vegetation parameters, a 1-foot square metal grid was randomly tossed 

on the ground at about every 5-foot downslope distance. 

Within the 1-foot grid, each plant species was identified 

and the density of each occurring plant, on a relative 

scale of one to five, was observed. Observed plant 

species and the value of their relative density are listed 

in table A of the "Summary of data." The usual assortment of western range grasses, herbs, and shrubs predominate. An estimate of overall vegetation density for 

each site, expressed as a percentage of the total area, is 

given below the table. The New Fork River sites, located 

on soils weathered from the Wasatch Formation, exhibit 

the fewest number of species and also the lowest overall 

density of cover.

At most sites, a measure of the overstory vegetation 

was made by summing in tenths of a foot the footage of 

overstory lying below a 100-foot tape. These measures 

of overstory, expressed as a percentage of the total

length of the transect, are also listed below table A in 

the "Summary of data." All but two sites had a characteristic overstory of sagebrush. One exception, Pole 

Creek Site 1, had no overstory on the site despite the 

general occurrence of sagebrush in the area. The other 

exception, Pole Creek Site 3, supported a sparse stand 

of young aspen in addition to sagebrush.

In order to observe and measure the hydraulic parameters of over land flow adequately, a clear and unobstructed view of the ground surface is necessary. To 

achieve this criterion, all overstory vegetation at the 

sites was cleared by cutting at the ground surface. 

Special care was taken not to disturb the ground surface 

during the clearing. Stems preferably were cut by clippers to minimize organic debris, but occasionally were 

cut with a saw. Figures 3 to 8 illustrate characteristics 

of the vegetation cover and the appearance of the sites 

after overstory vegetation was cleared.

FIGURE 7. New Fork River Site 2. Upper: Looking upslope. 

Lower: Runoff collector.
AID DYNAMIC AND DESCRIPTIVE STUDIES OF HILLSLOPES

FIGURE 8. Boulder Lake Site 2. Upper: Looking upslope. 

Lower: Details of vegetation cover.

TOPOGRAPHY

The initial topographic survey at each site was to 

determine the most direct downslope distance. The eye 

is deceiving in this judgment and it is important to lay 

out the runoff plot perpendicular to the slope. After this 

direction had been determined, the general area was 

cleared of overstory vegetation as described above. 

Within this general area, the 7-foot-wide test plot was 

delineated over a length dependent on the continuity 

of the slope.

The topography of each site was surveyed on a 1-by 

1-foot grid system. An exception was Pole Creek Site 1 

which was mapped on a 1-foot-transverse by a 2-footdownslope grid system. In lieu of presenting actual elevation data (all original data are on file with the U.S. 

Geological Survey), topographic maps of each site were 

prepared with contour intervals of either 0.05, 0.10, or

0.20 foot. These maps are presented in a later section 

of this report.

Eight surveyed elevations comprise transverse data 

at each downslope position. These eight readings were 

averaged to give a mean elevation. Mean elevations 

are plotted in figure 9 and show the hillslope profile at 

each site. The average ground slope was determined by 

visually fitting a straight line to the plotted data.

Figure 9 shows that the seven field sites represent 

only four different slope gradients of approximately 

0.03, 0.10, 0.20, and 0.33 foot per foot. Thus, data can 

be analyzed holding slope constant to show the 

influence of other factors on values of the hydraulic 

parameters.

Table 2 summarizes some of the physical characteristics of the field sites.

TABLE 2. Characteristics of overland flow field sites

Site name

Pole Creek Site 3. .

Avg 

elev 

(ft)

7,150

7,220

7,160

7,315

7,320

7,330

7,240

Slope 

aspect

S. 60° E. 

N.75°W. 

S. 50° E. 

N. 30° W. 

N. 40° W. 

N.30°W. 

N. 05° E.

Ground slope

(ft per 

ft)

0.0290 

.0960 

.1000 

.1880 

.2080 

.3315 

.3320

(degrees)

1°40' 

5°31' 

5°44' 

10°53' 

12°00' 

19°21' 

19°23'

Estimated

cover 

(percent)

8 

20 

10 

28 

35 

22 

28

ARTIFICIAL RAINFALL

The same type of line sprinkler used in the laboratory 

investigation was also used to simulate rainfall in the 

field. One major difference in the field arrangement of 

the sprinklers was the placing of the sprinklers on the 

ground rather than have them suspended above the plot. 

Within the 7-foot-wide plot, the sprinklers were placed 

6 inches inward from each side of the plot and ran continuously along the length of the plot, the total length 

being made up of 16-foot units placed end to end. Each 

unit was centrally supplied with water through a gate 

valve and pressure gage and was calibrated in the laboratory so that the total discharge from each unit was 

indicated by the pressure gage reading. With the sprinklers placed on the ground, the spray of water was 

pointed upward and reached a height of more than 10 

feet before falling downward over the plot. As in the 

laboratory, neither drop size distribution nor terminal 

fall velocity for the applied rainfall intensity was 

achieved. However, because of the collision and meshing 

of drops within the spray, more larger drops were produced in the field arrangement than in the laboratory. 

The distribution of rainfall was generally uniform over 

the plot area, but there was a slight tendency for the 

heaviest concentration of water to be along the centerline of the plot which received overlapping spray from 

the laterally spaced sprinklers. The sprinkler arrange-
THE HYDRAULICS OF OVERLAND FLOW ON HILLSLOPES /ll

CD

o

CD

EXPLANATION 

°-Plotted values represent an average 

of eight transverse elevations across 

the width of the plot. (Note change 

in elevation ordinate between upper 

Boulder Lake Site 1 and lower figures)

e slope=0.1880

Pole Creek Site 2 

Average slope=0.3320

Boulder Lake Site 2 

Average slope=0.33

Pole Creek Site 3 \/* 

Average slope=0.2080

- 102

106

105

=. 104

|jj 103

LJJ

102

101

100

99

98

New Fork River Site 1 

 Average slope=0.1000

Pole Creek Site 1- 

s Average slope=0.0960

New Fore River Site 2 

Average slope=0.0290

 ri*^^ I - s^

8 12 16 20 24 28 32 36 40 44 48 52 

DOWNSLOPE DISTANCE, IN FEET

FIGURE 9. Hillslope profiles of field sites.

ments and the general appearance of the artificial rainfall over the test plots can be seen in figures 3 to 8.

Water was pumped to the sprinkler units from a 

nearby stream or lake source. The pump had sufficient 

capacity to maintain a constant pressure gage reading 

at each sprinkler. Throttling of water was achieved 

with the gate valve at each pressure gage. The suction 

line of the pump was placed above the stream or lake

bed to eliminate pumping any sediments to the sprnklers. Sediments could clog the sprinkler openings r.nd 

also supply extraneous sediment to the runoff water 

and thus influence analyses of sediment concentrations 

in the runoff.

The first two plots (Pole Creek Sites 1 and 2) were 

sprinkled at a pressure gage reading of 25 pounds per 

square inch (7.80 in. per hr). The other five plots were
A12 DYNAMIC AND DESCRIPTIVE STUDIES OF HILLSLOPES

sprinkled at a gage reading of 30 pounds per square 

inch (8.50 in. per hr). Fourteen rain gages placed over 

the sprinkled area were used to check the uniformity of 

rainfall distribution and to compare the actual intensity 

with that indicated by the pressure gage reading. At 

most sites some of the artificial rain fell outside the 

boundaries of the plot, largely from wind. At four sites, 

this loss of water was severe enough to warrant the construction of 7-foot high windscreens on the windward 

side of the plots. The windscreens successfully minimized the windblown loss of water. At each site, an 

estimate was made of any water falling outside the 

plot. At four sites, sufficient water fell outside the plot 

boundaries to warrant a reduction in rainfall intensity 

from the calibrated intensity. The calibrated rainfall 

intensity and a weighted rainfall intensity for each site 

is listed in table 3. The maximum difference in the two 

intensities is for Pole Creek Site 1 where a 10 percent 

correction was made.

TABLE 3. Rainfall and runoff rates at overland flow field sites

Calculated Measured Weighted Weighted Runoff

Site name rainfall» runoff rainfall 2 runoff 2 rainfall

(in. per (in. per (in. per (in. per (perhr) hr) hr) hr) cent)

Pole Creek Site 1...... .......

New Fork River Site 1 .......

8.5

7.8

8.5

8.5

8.5

8.5

7.8

4.5

1.8

3.9

4.4

4.2

2.5

8.1

7.0

8.5

Q e

8.5

8.1

7.4

4.1

3.0

4.5

45

4.5

4.1

3.4

51

42

53

53

53

51

46

1 From laboratory calibration using pressure gage readings.

2 Weighted values used in all computations. Note that the weighted values indicate 

an infiltration rate of 4 in. per hr.

RUNOFF MEASUREMENTS

Runoff water was directed into a funnel-shaped collector at the lower end of each runoff plot. On the entering end, the funnel collector had a 1-inch lip which 

protruded into the ground and prevented flow losses 

under the collector. Depending on the topography 

of each site, 3-inch-high aluminum stripping of the 

type commonly used as flower garden borders was 

placed in a slit in the ground surface and further directed the flow to the runoff collector. (See, for example, 

figure 7 (lower photograph).) In a few instances, short 

lengths of the stripping were placed at locations along 

the sides of the plots. Care was taken not to divert any 

of the flow leaving the plot back onto the plot but rather 

to direct it downslope outside the plot and include it 

in the collection of total runoff. Without extensive sidewalls at each site, it was impossible to collect all of the 

runoff in the downslope collector. And, in some instances, runoff water was collected which fell as rain outside 

the plot. As in the determination of effective rainfall, 

a weighting of the measured runoff was made based on 

field observations of the effectiveness of collecting total

runoff. Although these observation are only estimates, 

they are considered more factual than the measured 

values. Measured values of runoff and the weighted values of runoff are listed in table 3. Weighted values of 

runoff are used in later computations of hydraulic 

parameters.

At the instant that artificial rainfall application began, a clock timer was started and all data are referenced to this as zero time. Beginning with the first 

runoff, the rate of runoff passing through the funnel 

collector was volumetrically measured. The successive 

collection of runoff rates allows the shape of the rising 

hydrograph and the eventual constancy of runoff to 

be determined. An example of runoff hydrographs for 

New Fork River Site 1 is illustrated in figure 10. Figure 

10 shows the rapid achievement of a constant runoff 

rate and the effects of sprinkling on a previously wetted 

surface and of increasing the rainfall intensity. Figure 

10 and table 3 show that the infiltration capacity of 

all sites was about 4 inches per hour. This T^alue of 

infiltration may seem high, but investigations by 

Smith and Leopold (1942) and Hadley, McQueen, 

and others (1961) report values of infiltration comparable to those found in the present investigatior. Smith 

and Leopold showed a correlation of infiltration rates 

with vegetation density, but the present data, with 

only a limited range in density of cover, failed to show 

any correlation. The data of Hadley were observed on 

surfaces of the Wasatch Formation, one of the geologic 

formations underlying the present sites.

All measurements of velocity and depth wer^ made 

after the runoff rate became constant.

SEDIMENT SAMPLES

Periodically, the containers used to measure runoff 

rate were put aside after filling for analysis of the 

sediment concentration. The samples wer?. later 

filtered through filter paper and the trapped sediments 

were analyzed. Total sediment and organic content, 

expressed as milligrams per liter by weight of the total 

sample weight was first measured and then the organic 

content of the total sample was removed by Jrrdrogen 

peroxide (H2O2). Thus, a separate measure of both the 

organic and sediment contents was obtainei. The 

data are presented in a later section of this report.

SURFACE-VELOCITY MEASUREMENTS

Surface velocity was measured for two trals at 

each site. One trial was essentially over the left half of 

slope and the other over the right half. A liquid dye 

(food coloring) was poured over the ground surface at 

the upper end of the runoff plot (0-foot dovoislope 

position). As the dye touched the ground, one observ-
THE HYDRAULICS OF OVERLAND FLOW ON HILLSLOPES A13

V

EXPLANATION 

Date Intensity 

7-29-67 8.50in.perhr 

7-30-67 8.50 in.perhr 

7-31-67 10.25 in.perhr

(Vaues of runoff shown are actual measurements 

and do not reflect a weighted value due to losses 

in runoff collection. Weighted runoff value used 

in data computations is 4.5 in. per hr. Note 

the break in time scale between 40 and 210 min 

I I I I I__

10 20 30 40 210 220 230

TIME a) IN MINUTES

FIGURE 10. Hydrographs of runoff for New Fork River Site 1.

er, watching the dye trace, called for a second observer, with stop watch and note pad, to start the watch. 

As the dye front passed each successive 1-foot downslope distance, the first observer notified the second 

who recorded the time. Increments of time provided 

the average velocity over each 1-foot reach of slope. 

As the dye trace became faded, it was reinforced with 

a new slug of dye. Always, the leading edge of the 

dye trace was used in timing its movement. Since 

the flow tends to accumulate in particular transverse 

concentrations, and in these concentrations velocity 

is highest, measurements of surface velocity were considerably higher than the actual average velocity.' 

An example of the actual velocity measurements for 

Pole Creek Site 3 is included in the "Summary of 

data," table B. For the other sites, velocity measurements are listed in the "Summary of data," table F.

FLOW PATTERN OF OVERLAND FLOW

As previously mentioned, surface runoff within the 

plot area tended to accumulate in several lateral 

concentrations. Dye tracings used to measure the 

surface velocity clearly demonstrated this tendency. 

On nearly flat slopes, microrelief features on the order

368-391 O 70 3

of only 0.10 foot appeared to dictate the paths of the 

flow concentrations. However, on steeper slopes, small 

microrelief features did not appreciably alter the downslope gradient and their influence on concentrations of 

flow was masked. Since detailed topography was 

surveyed for each site, a mapping of the pattern of 

flow concentrations was made to determine if any 

relation could be established between these concentrations and any of the other measured variables. Maps 

of the flow patterns are included in a later section. 

The food coloring dye was introduced as a line 

source at the upper end of the plot and the stringers 

of dye left behind as concentrated flow advanced 

downslope more rapidly than the general sheet of 

water were mapped. The dye was reinforced every 

several feet downslope with new line sources of dye 

to detect new concentrations as they formed downslope.

DEPTH MEASUREMENTS

Depths were measured with the same type of point 

gage used in the laboratory investigation. A carriage 

was constructed of %-inch steel pipe to accommodate 

the point gage. The carriage was constructed such 

that measurements at two slope stations could be made
A14 DYNAMIC AND DESCRIPTIVE STUDIES OF HILLSLOPES

with one positioning of the carriage and then the 

carriage was positioned at another upslope position. 

Depth measurements began at the downslope end of 

the plot and the observer worked from the downslope 

side of the carriage. In this manner, the area not yet 

measured had not been influenced by trampling.

The vertical-positioning mechanism of the point gage 

was loosened so that only slight resistance to lowering 

the point would cause slippage in the mechanism rather 

than to continue to lower the point. A blunt, %-inchwide tip was affixed to the lower end of the point to 

offer additional resistance as the point touched the 

ground surface. Along with this sensitivity in locating 

the position of the ground surface, close visual observation as the point was lowered assured accuracy in 

determining the elevation of the ground surface. A 

second point-gage reading at each location determined 

an elevation of the water surface. The difference in 

ground-surface and water-surface elevations was recorded as depth. Observations were read directly to 

the nearest 0.001 foot.

Depths were measured on a 1-foot-transverse by a 

2-foot-downslope grid system. Over the 7-foot-wide 

test plot, eight depths were thus recorded for each 

downslope position. These eight depths were averaged 

to give the mean depth as a function of downslope 

distance. Depth measurements at Pole Creek Site 3 

are included in the "Summary of data," table C. For 

the other sites, only the average depth for each downslope position is listed in the "Summary of data," 

table F.

ANALYSIS OF RESULTS AND DISCUSSION 

GENERAL

The presentation and analysis of hydraulic data 

follow a theme analogous to the hydraulic geometry 

of streams introduced by Leopold and Maddock (1953). 

The general technique in hydraulic geometry is to 

relate changes in the hydraulic parameters of flow to 

changes in discharge. This method of analysis is similar 

to the technique used by Horton (1945) except that 

Horton plotted discharge along the ordinate axis rather 

than the more conventional manner of plotting discharge along the abscissa axis. Thus data from the 

present investigation can be easily compared to both 

Horton's studies and the more voluminous collection 

of data for flow in river channels.

Because water temperature (and therefore values for 

the viscosity of water) varied in the present investigation, the Reynolds number, R, has generally been 

substituted for discharge in the analysis of data. The 

Reynolds number, here proportional to the discharge

per unit width, is a nondimensional paramete" relating 

the effect of viscosity to inertia and is defined as

4VD R=

in which V is the mean velocity in feet per second, D 

is the average depth in feet, and v is the Hnematic 

viscosity having dimensions of feet squared pev second. 

Depths of flow in the study were sufficiently small that 

depth rather than hydraulic radius could bo used in 

computations of the Reynolds number. Use of the Reynolds number does not influence the comparison of 

data with other studies of hydraulic geometry and the 

use of the Reynolds number is convenient in visualizing 

whether the flow is laminar or turbulent.

For uniform flows in the laboratory flume, the 

analysis is similar to at-a-station hydraulic geometry 

because for a given discharge, depths are constant 

downslope. Generally, data are also plotted against 

depth, as well as Reynolds number (discharge), to show 

the importance of geometric similarity on values of the 

hydraulic parameters.

For tests with artificial rainfall, and thus with increasing downslope discharge, the analysis is similar to 

the case of downstream hydraulic geometry. At-astation relations may also be developed by considering 

only data collected at the same downslope portion.

Because the mass of collected and computed data 

is so large, it has been placed in the "Summary of data." 

All data collected are included in these tables, but in 

some of the illustrations which follow, only examples 

are plotted and summary curves describe the remainder 

of data. Throughout this section of the report, the data 

are presented with limited discussions. A more complete 

discussion follows after all data have been introduced.

Some of the results reported herein are not always in 

agreement with previous experiments in hydraulics 

and seemingly violate some of the known lavrs of hydraulics. Rather than a violation of the laws the explanation is that the present investigation was 

conducted at an extreme end of the spectrum for which 

conventional hydraulic formulas are applicable. It is 

emphasized even before the data are introduced that 

many of the relationships indicated by the following 

analysis are unique to the flow of very shallow depths 

of water over sloping surfaces. Serious error could be 

incurred by the extrapolation of the present data to 

conditions beyond those investigated. It is as equally 

inapplicable to apply open channel hydraulics to the 

analysis of overland flow as it is to apply the present 

data to studies of river channels.
THE HYDRAULICS OF OVERLAND FLOW ON HILLSLOPES A 15

LABORATORY TESTS WITH UNIFORM PLOW

Detailed data from the laboratory tests with uniform 

flow are included in the "Summary of data," table D. 

Graphical representation of the data is illustrated with 

the next series of figures.

Figure 11 illustrates the relationship between the 

depth of uniform flow and the Keynolds number. The 

two most apparent observations are the break in the 

relationship at a certain critical value of Reynolds number between 1,500 and 6,000 and the increase in deoth 

with decreasing slope. The critical Reynolds number 

marks a change in regime from laminar flow at smaller 

Reynolds numbers to turbulent flow at greater ReyncMs 

numbers. For both smooth and roughened surfaces, 

the critical value of Reynolds number increases with 

increased slope. This indicates that the shallower flows 

on the steeper slopes are somewhat more stable against 

change to turbulent flow.

0.10

0.05

0.02

0.01

0.005

0.002

0.001

0.02

0.01

EXPLANATION 

Symbol Series Slope fvalue

Laminar Turbulent

0.0775 0.41 0.57

.0550 .43 .57

.0342 .37 .57

.0170 .36 .57

 1

6. Roughened surface

EXPLANATION 

Series Slope f value

0.0033

.0170

.0342

.0550

.0775,

0.005

0.002

100 200 500 1000 2000 500010,00020,00050,000 

REYNOLDS NUMBER

FIGUKE 11. Depth of uniform flow as a function of Reynolds number.
A16 DYNAMIC AND DESCRIPTIVE STUDIES OF HILLSLOPES

A similar expression for the present analysis is

In terms of hydraulic geometry, the depth may be 

expressed as

(5)

(6)

The values of / are the reciprocal of the M values 

(refer to=4) used by Horton (1945). Values of/ are 

tabulated in the explanation blocks in figure 11. For 

turbulent flows over the smooth surface, the value 

of / is 0.60 for all slopes. As well as the lines can be 

fitted to the data (all curves in this report were fitted 

by eye), this value is equal to the theoretical value of 

% or, in the Hortonian expression (see=2),M=% for 

fully turbulent flow. For laminar flow over the smooth 

surface, values of / range from 0.27 to 0.37. These 

values tend to center around the theoretical value of 

J^ (M=3; see eq 3). The scatter of values around a 

central value is attributed to the accuracy of data 

rather than any trend that might be suggested. Considering that errors of only a few ten-thousandths of a 

foot would appreciably alter the plotting position of the 

data, the plotted points appear to be satisfactory.

For the roughened surface, the value of /for turbulent 

flow is 0.57. Values of / less than % would indicate flow 

less than fully turbulent. The effect of a roughened 

surface is to retard the flow near the bed of the flume. 

In flows as shallow as those investigated, that which 

is considered to be flow near the bed actually may 

represent a considerable part of the entire depth. 

Thus, it is quite reasonable to expect extremely shallow 

flows over roughened surfaces to exhibit some tendencies of laminar flow.

The laminar flow regime for the roughened surface 

produces values of / ranging from 0.36 to 0.43. One 

explanation for the values slightly higher than the 

theoretical value of % is that no correction was applied 

to values of depth as measured from the top of the 

roughness element. At the extremely shallow depths 

for flows in the laminar region (generally less than 

0.007 foot), a correction that allows for the voids between bed roughness particles and is added to the 

measured depths would, percentagewise, increase 

the shallowest depths most; the effect would be to 

decrease the value of /. For depths as large as those 

in the turbulent flow region, the effect would be negligible.

The effect of roughness on values of depth is both 

general and complex. Because of the additional resistance to flow, roughness increases the depth of flow for 

a given discharge. The maximum influence of roughness 

appears near the transition from laminar to turbulent

flow. In this region, depths on the roughened surface 

are from 15 percent greater (for the less steep slopes) 

to 30 percent greater (for the steeper slopes) than 

depths on the smooth surface. In the turbulent region 

of flow for roughened surfaces, depth increases with 

increases in discharge less rapidly than for a smooth 

surface. Therefore, for flows at the highest Feynolds 

numbers investigated, increase in depth due to roughness is less pronounced. At a Keynolds number of 

20,000 this increase in depth ranges from zerc for the 

less steep slopes to about 25 percent for the steeper 

slopes. These data demonstrate that relative roughness 

for a given surface decreases as flow depths increase. 

At depths of flow somewhat greater than thore investigated, further increases in depth would only negligibly 

decrease relative roughness and the influence of roughness on depth would be minimal.

In the laminar flow region, / values are higher for 

roughened surfaces than for smooth surfaces rlthough 

as explained above, this is probably true only because 

no correction was made for measurements cf depth 

for the roughened surface. Using the data as plotted, 

as Reynolds number decreases, the percentage influence 

of roughness on depth decreases. At a Reynolds number 

of 200, there are actually smaller depths reported for 

the roughened surface than for the smooth surface. For 

a low Reynolds number, a certain finite depth must 

exist regardless of further decreases in the B.eynolds 

number. Thus for Reynolds numbers lower than those 

reported in this investigation, the relationship shown 

in figure 11 must begin to tail off to the left and the 

lines for all flume slopes would merge into a single 

curve at some small given value of depth. Likewise, 

as depths and Reynolds numbers increase above those 

reported in this investigation, the / value for the 

roughened slopes would approach a value of % a^ effects 

of roughness diminish.

The effect of flume slope on depth is to decrease 

depth for increasing slopes. The relationship is hyperbolic; that is, as slope approaches zero, depth approaches 

infinity and as slope approaches high gradients, depths 

approach some minimum value. A roughened surface 

tends to dampen this effect. That is, the approach to 

some minimum depth regardless of further increases 

in slope occurs at a smaller gradient for the roughened 

surface. Thus, for flume slopes of 0.0775 and 0.0550 

foot per foot, data on the roughened surface nearly 

describe a single curve while for the smooth surface, 

the data are still separate by a small distance.

A measure of the resistance to flow, the DarcyWeisbach friction factor, is plotted in figure 12 as a 

function of Reynolds number and average depth.
THE HYDRAULICS OF OVERLAND FLOW ON HILLSLOPES A17

The Darcy-Weisbach friction factor is defined as 

,_8gDS

Jf T/2 V2

in which g is the acceleration of gravity in feet per 

second squared and S is the flume slope in feet of 

drop per foot of slope length.

The expression for velocity in terms of hydraulic 

geometry is

(8)

or

(9)

The friction factor, in terms of hydraulic geometry, 

may be written as

(10)

or

(H)

When slope, S, is constant, equation 7 may also be 

written

D

or

(12)

(13)

Thus for a constant gradient, the slope, y, of the Met'on 

line as a function of the Reynolds number is / 2m. 

Also, since VD=q, then /+m=l or m=l /. For 

turbulent flow, the slope of the line is 0.60 2 (0.40)= 

0.20 and for laminar flow it is 0.33 2 (0.67)=-1.0. 

Negative values of y indicate a decrease in resistance 

to flow with increasing Reynolds number. For laminar 

flow in smooth rectangular channels, the equation of 

the line with a slope of 1.0 is

96 (14)

For rough channels, values of the friction factor would 

be higher and would plot above the lower limits defined 

in equation 14.

<

CD 

UO

IU

5.0

2.0 

1.0 

0.5

0.2 

0.1 

)05

.02 

.01

\* * °H P

^

',-'

D

T 

O

O

\. o

T^

Symb

o

X

A

T

D

H

0

a h- 

 i

T

1-

\>

EXPLANATION 

ol Series Slope Su

1 0.0033 Smi 

2 .0170 Sm 

3 .0342 Sm 

4 .0550 Sm 

5 .0775 Sm 

6 .0775 Rou 

7 .0550 Rou 

8 .0342 Rot 

9 .0170 Rot

-ID 

<> h* <

tX

A

\* 0»

> -1 n

1 "

c$* T

M

rface

50th

ooth 

ooth 

ooth 

joth

ghened 

ghened

ghened 

ghened

^^

From Tracy and Lester (1961) 

(Smooth rectangular channel)

o| 

« 1

-*-T-

* V*

100 200 500 1000 2000 5000 20,000 

REYNOLDS NUMBER (R =^~

FIGURE 12. Darcy-Weisbach friction factor for uniform flow as a function of Reynolds number and average depth.

0.001 0.002 0.005 0.01 0.02 05 0.10 

AVERAGE DEPTH (D), IN FEET
A18 DYNAMIC AND DESCRIPTIVE STUDIES OF HILLSLOPES

For turbulent flows, the friction factor-Reynolds 

number relation has a slope of 0.20. For a smooth 

surface flume, this value is indicated in figure 12 with 

a line representing data from experiments by Tracy 

andLester (1961).

The data of figure 12 plot higher than the limits indicated by the equations applicable to a smooth surface. 

This illustrates the pronounced effect of channel roughness on the friction factor. The smooth flume in the 

present investigation was in fact not completely smooth 

as indicated by the data plotting higher than the equations for a smooth surface.

Using the average value of the friction factor at a 

Reynolds number of 20,000, reference to a Stanton or 

Moody diagram gives a relative roughness of 0.03 for 

the roughened surface and 0.002 for the smooth(er) 

surface. At an average depth of 0.03 foot for a Reynolds 

number of 20,000, a computed absolute roughness is 

0.0009 foot for the roughened surface and 0.00006 foot 

for the smooth surface. One-half the diameter of the 0.5 

millimeter grain roughness used on the flume is 0.00082 

foot. This is very close to the computed roughness for 

the roughened surface. The computed value for the 

smooth surface is not unreasonable for sanded plywood with a paint finish.

Only two roughnesses are involved with the two 

surfaces but because each plotted point in figure 12 

has a different depth, the data include many values of 

relative roughnesses. For a Reynolds number of 300, 

depths are approximately 0.003 foot and the relative 

roughness is 0.3 for the roughened surface. This is 10 

times rougher than at a Reynolds number of 20,000. 

If points representing equal depths were connected, 

one would find the beginnings of a family of curves, 

each representing a given relative roughness. The curves 

are not drawn in figure 12 because the data are too 

sparse. However, it is interesting to note that most of 

the data lie in a range of friction factors and relative 

roughnesses much greater than those included on conventional Moody diagrams. This again illustrates the 

tremendous influence of even small surface roughnesses 

on flows as shallow as those investigated and that 

occur in overland flow.

The right half of figure 12 again illustrates that plotted points represent differing depths. To maintain geometric similarity between the depth of flow and scale 

of roughness, friction factors are plotted against depth. 

The tendency to converge into a single curve for laminar 

flow and into two curves, one for each roughness, at 

higher Reynolds numbers is apparent. The remaining 

scatter in data is most likely within the accuracy of the 

experiment. From equation 7 and the relation V=y/D,

the friction factor may be expressed as

, _8gD*S 

- (15)

from which it can be seen that the percent error in 

friction factor is three times the percent error in depth. 

Using a nominal depth of 0.005 foot (typical of depths 

at low Reynolds numbers), an error of only 0.0005 foot 

(one-half the direct reading accuracy of the point gage) 

in the measurement of depth yields a 30 percent error 

in friction factor.

A commonly used uniform flow formula is the 

Chezy formula,

where C is a factor of flow resistance called Chezy's C. 

Normally, hydraulic radius would be used rather than 

depth, but in the present investigation, depth and 

hydraulic radius are practically identical. Substitution 

of equation 7 into equation 16 gives a solution for 

Chezy's C in terms of the Darcy-Weisbach friction 

factor:

(17)

Figure 13 illustrates values of Chezy's C as a function 

of Reynolds number and of average depth. T" e slope 

of the Chezy C'-Reynolds number relation is equal to 

m (}0/ or 0.5 for laminar flow and 0.1 for turbulent 

flow. Upper limits for values of C are shown in the same 

manner as for friction factor in figure 12. The influence 

of laminar, transitional, and turbulent flow, a? well as 

roughness and geometric similarity, are analogous to 

those in the previous discussion of the Darcy-Y^eisbach 

friction factor.

Another popular open channel formula is tl e Manning equation:

n

(18)

in which n is a coefficient of roughness known as Manning's n. In terms of Chezy's C:

n=-1.5D*

C

(19)

Computed values of Manning's n are plotted in figure 

14 as a function of Reynolds number and average depth. 

In terms of hydraulic geometry, Manning's r, can be 

expressed by

(20)
THE HYDRAULICS OF OVERLAND FLOW ON HILLSLOPES A19

o> 

oo

>-

fvl

IUUU

500

200 

100 

50

20 

10 

5

2 

1

o(8gR/96)'/2 ^ 

^ °

y^* o

,-<+ A

A° A"1 n

D

T

'V fc"* 1 -

D

* S

» H 

< T

a

Symbo

+

o

X

A

T 

D

O

1-

Dot 

re

<P ? *

T2> r

X

H

4) ^ *

H D

a

a from 

ctangu

smooth 

lar channels

\j

^A T 1 T T 

f- h H

K>n ,0^0 a<*

EXPLANATION 

1 Series Slope S 

1 0.0033 Sm 

2 .0170 Sm 

3 .0342 Sm 

4 .0550 Sm 

5 .0775 Sm 

6 .0775 Ro 

7 .0550 Ro 

8 .0342 Ro 

9 .0170 Roi

\

urface

ooth 

ooth 

ooth 

ooth 

ooth 

ughened 

ughened. 

ughened 

jghened

100 200 500 1000 2000 5000 10,00020,000 50,000 0.002 0.005 0.01 0.02 0.05 0.10

REYNOLDS NUMBER AVERAGE DEPTH (D), IN FEET

FIGURE 13. Chezy's C for uniform flow as a function of Reynolds number and average depth.

Thus the slope of the Manning's relation as a function 

of the Reynolds number is (%)/ m or 0.45 for laminar 

flow and 0.0 for turbulent flow. The data closely follow 

these values. The previous discussion concerning the 

Darcy-Weisbach friction factor is again applicable to 

both plots of figure 14.

Figure 15 is a plot of the ratio of mean velocity to 

surface velocity, V/VS, as a function of Reynolds number and average depth. In the turbulent region of flow, 

the velocity ratio is very close to the theoretical value 

of 0.8. In the laminar flow region, the theoretical velocity ratio of 0.67 tends to define an upper limit to the 

measured data. Most likely, the explanation, for the 

lower measured values is the extreme retardance of flow 

of shallow depths by surface friction. This argument is 

supported by the plot of velocity ratio as a function of 

average depth. The close grouping of the plotted data 

and the variation with depth suggest that depth of flow 

is an influencing factor.

LABORATORY TESTS WITH ARTIFICIAL RAIN

All of the measured and computed data for the laboratory experiments with artificial rainfall are included

in the "Summary of data," table E. As will be shown, 

the maximum Reynolds numbers which occurred with 

flows from artificial rain were less than 1,500. The df.ta 

from uniform flow tests indicate this is entirely witlin 

the region of laminar flow. The effect of falling rain sufficiently disturbed the flow of water that injections of 

dye were rapidly dispersed. Although this flow has some 

characteristics of turbulent flow, it exhibits most of the 

properties of laminar flow. This type of flow does rot 

belong to any of the classifications of laminar, transitional, or turbulent flow. In this report, runoff from 

artificial rain will be called disturbed flow.

The downslope change in depth of nonuniform flows 

resulting from a uniform increase in discharge is illustrated in the lower half of figure 16 by two exampT es 

of the tests with artificial rain. The data are for five 

intensities of rainfall on both the smooth and roughened surface. The same depth data are plotted on the 

lower half of figure 17 as a function of Reynolds number. 

The effect of plotting against Reynolds number is to 

eliminate the influence of increasing rainfall intensities. 

The single line drawn through the data of figure 17 

represents the average downslope increase in depth 

due to increasing discharge. The single line relationship
A20 DYNAMIC AND DESCRIPTIVE STUDIES OF HILLSLOPES

o

I.U

0.5

0.2' 

0.1 

0.05

0.02 

0.01 

0.005

0.002 

n ftm

Symbol

+

o

X

JL

T

a

O

X T

a 

*°S« o

~* A

1

EXPLANATION 

Series Slope Su 

1 00033 Smo 

2 .0170 Smo 

3 .0342 Smo 

4 .0550 Smo 

5 .0775 Smo 

6 .0775 Rout 

7 .0550 Roucj 

8 .0342 Roue 

9 .0170 Roue

a

r a 

I?, -AK. -- - - -

V o * o V T < 

\ fi

o

H a 

4 HO >*

\-

& *z

rface

oth 

3th 

oth

oth 

oth 

|hened_

hened 

hened

hened

>H hcP;?

+ 

-0x4, 

*«? °<p j'r^u-

_ !. <* +

100 200 500 1000 2000 5000 10,00020,000 50,000 0.002 0.005 0.01 0.02 0.05 0.10

REYNOLDS NUMBER (^~-^r) AVERAGE DEPTH (D), IN FEET 

FIGURE 14. Manning's n for uniform flow as a function of Reynolds number and average depth.

from figure 17 is shown on figure 16 as the downslope 

profiles for each intensity of rainfall.

One effect of the falling rain is to increase the variability in depths and possibly to decrease the accuracy 

in measurement. The irregularities in the downslope 

profiles of figure 16 are not consistent and indicate 

that the variability in depth is random and not related 

to the experimental apparatus. The downslope profiles 

in figure 16 suggested by the single line relation of 

figure 17 are not unreasonable representations of the 

measured profiles. This indicates that for increasing 

discharge, the at-a-station changes in hydraulic parameters are identical or close to the downslope changes 

in parameters.

An at-a-station type of analysis may be conducted 

by connecting points from equal downslope distance 

from the depth profile plot in figure 17. That is, if each 

of the first plotted various symbols were connected, 

followed by the second, third, fourth, and so on, the 

slope of these short line segments would describe the 

at-a-station relations of hydraulic geometry. The variability of the data is such that no distinction can be 

made between the at-a-station and downslope hydraulic 

geometries. Thus for the analysis of laboratory data 

with increasing discharge, at-a-station and downslope

changes in the hydraulics of flow are considered 

analogous.

The most important effect of the falling raindrops 

is to retard the flow and increase the depth for a given 

discharge. Consideration of the momentum exchange 

between the mass of falling water and the mass of 

water as surface flow would predict this increase in 

depth. The momentum of the falling rain has little 

downslope component compared to the surface runoff. 

One would expect that the increase in depth would be 

least for the lowest intensities of rainfall and the highest rates of surface runoff. The present data do not 

entirely confirm this hypothesis. The effects of rainfall 

intensities are masked because lowest intensities are 

accompanied by lowest runoff rates, highest intensities 

by the highest runoff rates, and the overall eFect is a 

balancing of the momentum exchange so that the 

percentage effect is roughly equal to all intensities of 

rainfall. For a constant intensity of rainfall, greater 

depths downslope should be less effected by raindrop 

impact than shallower upslope depths. The depth 

profile for the smooth surface in figure 17 illustrates 

this by a convergence of the plotted data to the line 

representing depths from the uniform flow teft. That 

is, the / value for the runoff from rainfall is loss than
THE HYDRAULICS OF OVERLAND FLOW ON HILLSLOPES A21

10

5.0

2.0 

1.0 

0.5

o

0.1

0.05

0.02

0.01

La minar flc

°^ x o

A ^ *

a a

T

>w, y= 2/3 vs

 V 

 *o jj ^o . 

*> £H _f.. " n>

T

T

Symbol

0

A

T

a

H

O

HTurbu

l_ h

o^^k

X T

ent fl(

> #&S

w, y=

fcp-^V

EXPLANATION 

Series Slope Su 

1 0.0033 Sm 

2 .0170 Sm 

3 .0342 Sm 

4 .0550 Sm 

5 .0775 Sm 

6 .0775 Roi 

7 .0550 Roi 

8 .0342 Roi 

9 .0170 Roi

0.8 V5

\

5<

rface

joth 

ooth 

ooth

ooth 

ooth 

ghened 

jghened 

jghened 

jghened^

V=0.8VS

100 200 500 1000 2000 5000 10,000 50,000 0.002 0.005 0.01 0.02 0.05 0.10

REYNOLDS NUMBER (R=^) AVERAGE DEPTH (bj, IN FEET 

FIGURE 15. Ratio of mean velocity to surface velocity for uniform flow as a function of Reynolds number and average deptb.

the / value for uniform flow. The data for test series 3 

(smooth surface) plotted in figure 17 indicate that the 

percentage increase in depth over uniform flow depth 

is about 60 percent at a Reynolds number of 100 and 

decreases to about 35 percent at a Reynolds number 

of 1,000. This increase in depth due to rainfallim pact 

is considerably greater than the average of 17 percent 

reported by Parsons (1949).

The data for test series 8 plotted in figure 17 does 

not show a reduction in the increase of depth with an 

increase in Reynolds number. However, if a correction 

in depth to allow for the voids between grains in the 

roughness was added to the measured depths, the data 

would more closely conform to that from the smooth 

surface. For the uncorrected data from the rough surface plotted in figure 17, the increase in depth is about 

50 percent at a Reynolds number of 200 and about 65 

percent at a Reynolds number of 1,000.

Summary curves describing the relation between 

average depth and Reynolds number for all tests are 

shown on the lower graphs of figure 18. For all tests, 

the depth profiles with artificial rain showed greater 

depths than for uniform flow. No test data differed 

greatly from the examples plotted in figure 17. For

368-391 O 70 ' 1

smooth surface tests, the / values with artificial rain 

are slightly less than the / values for uniform laminar 

flow. Conversely, the / values for artificial rain on the 

roughened surface are slightly greater than the/ vaHes 

for uniform laminar flow.

Unlike the present study of shallow flows in a constant width flume, most rivers are also free to change 

their width with changes in discharge. This change in 

width may be expressed as

W oc Qb ocR6 (21)

Since VDW=Q, then m+/+6 = l. It is of interest to 

briefly summarize and compare values of the exponents 

m,/, and 6 from the present laboratory data with values 

from rivers and a constant width flume with grer.ter 

depths than those in the present study. This summary 

is shown in table 4; river and flume data are after 

Langbein (1965).

It is apparent from the data of table 4 that the constraint of constant width for overland flow imposes 

additional requirements for depth and velocity to absorb 

changes in discharge. The nearly comparable cases are 

the roughened surface sprinkled tests and the
A22 DYNAMIC AND DESCRIPTIVE STUDIES OF HILLSLOPES

2.0

1.0

>- o

» <~» ,. _

is °-5

 i as:

LLJ UU

> QO LLJ Q 2

<; LLJ J 'i

uZ "-

0.1

0.05

0.05

0.02

Downslope profiles suggested 

by graph of surface velocity 

versus Reynolds number

Downslope profiles suggested-)

by graph of surface velocity 

versus Reynolds number _

O

z 

o

0.01

1*0.005

Q_

0.002

EXPLANATION 

(Series 3; slope=0.0342; plotted points are 

average of three transverse readings) 

~~ Symbol Test

Downslope profiles suggested 

by graph of average depth 

versus Reynolds number

EXPLANATION 

(Series 8; slope=0.0342; plotted points are

average of three transverse readings) 

 Symbol Test

Downslope profiles suggested 

by graph of average depth 

versus Reynolds numbe0.5 1.0 2.0 5.0 10 20 50 0.5 1.0 2.0 5.0 10

DOWNSLOPE DISTANCE, IN FEET 

A. SMOOTH SURFACE 8. ROUGHENED SURFACE

FIGURE 16. Downslope profiles of depth and surface velocity for sprinkled tests.

20 50

stream river channel. The river channel absorbs half 

of the increase in discharge by an increase in width, but 

for the constant width, roughened surface, overland 

flow in the laboratory, the increase in discharge is about 

equally absorbed between increase in depth and velocity. The constant width flume data for uniform 

sediment concentration compare with reasonable agreement to the present data for uniform turbulent flow.

Measurements of the downslope changes in surface 

velocity are shown in the upper parts of figures 16 and 

17 by two examples from the nine-test series. The actual 

downslope profiles are illustrated in figure 16 and the 

same data are plotted as a function of Reynolds number 

in figure 17. A straight line relation of surface velocity 

to Reynolds number was determined for the data in 

figure 17 and this relation is used in figure 16 to suggest 

the downslope surface velocity profiles for each rainfall intensity. For all laboratory tests, there appears to 

be some reduction in surface velocity, when compared

TABLE 4. Summary and comparison of exponents in hydraulic

geometry

Values of exponents in hydraulic geometry

Type of channel Depth (/) Velocity (m) V'idth (6)

Theory Data Theory Data Theory Data

Laboratory Shallow Flows: 

Uniform Flow:

Smooth, turbulent___. 0.60 0.60 0.40 0.40 0 

Smooth, laminar_...... .33 .33 .67 .67 0

Roughened, turbulent.__-.-.-._ .57. . .43 .....--

Roughened, laminar___..___ .39 .......... .61. 

Sprinkled Tests: 

Smooth, disturbed......--.----.--.. .26 ....... .74 .......

Roughened, disturbed.._-.-..._ .48 ...-... .52 .......

Rivers, at-a-station:

Cohesive . - .43 .40 .32 .34 

Noncohesive......___.... .27 . .. .23 ........

Rivers, downstream. _____ .37 .40 .13 .10 

Flume, constant width, uniform sediment concentra-

.25 .26

.50 .... -

.50 .50

tion. .67 .67 .33 .33
THE HYDRAULICS OF OVERLAND FLOW ON HILLSLOPES A23

From data of tests 3 -1 

to 3-9; uniform flow

From data of tests 8-1 

to 8-12; uniform flow

o

UJ

O

0.02

0.01

0.005

0.002

0.001

I EXPLANATION 

(Series 3; slope=0.0342; plotted points are 

average of three transverse readmes)

data of tests 3-1 

3-9; uniform flow

EXPLANATION | | 

(Series 8; slope=0.0342; plotted points are 

_average of three transverse readings) 

Symbol Test

From data of tests 8-1 

to 8-12 ; uniform flow

20 50 100 200 500 1000 2000 5000 20 50 100 200 500 1000 2000 5000

REYNOLDS NUMBER R= 

A. SMOOTH SURFACE B. ROUGHENED SURFACE

FIGURE 17. Depth and surface velocity as a function of Reynolds number for sprinkled tests.

to the suggested profiles, in the upstream reaches of 

the flume and especially for the flows at higher rainfall intensities. In figure 16, this gives the appearance 

of the radial family of curves rather than the suggested 

parallel profiles. The apparent upslope reduction in 

velocity is attributed to the greater retarding effects of 

high rainfall intensities in the region where surface 

velocities and momentum of flow is initially small. This 

influence is not as noticeable in figure 17 where surface 

velocities are plotted against Reynolds number.

As partly supported by figure 17, surface velocities 

in flows from artificial rain are generally lower than 

surface velocities in uniform flow. Summary curves 

for all tests are shown on the upper part of figure 18. 

The slope, or ra value, for the downslope profiles of 

surface velocity is approximately the same for smooth 

and roughened surfaces and it averages about 0.60. 

The range in values about this average is not systematic with flume slope and apparently is related to 

measurement accuracy in timing surface velocities 

over 2-foot reaches. The m values for surface velocity 

as shown in figure 18 do not have to be identical to the

m value for mean velocity. By the law of continuity 

for constant-width channels, the m value for mean 

velocity is 1.0 minus the/value.

The Darcy-Weisbach friction factor for two of the 

test series is plotted in figure 19 as a function of Reynolds number. Summary curves for all tests are shown 

in figure 20. The same discussion of the friction factor 

for uniform flow is applicable to the friction factors 

plotted in figure 19. Thus, much of the scatter in data 

is related to the effects of relative roughness.

The lines of best fit to the data of figure 19 average 

a value of resistance to flow about four times greater 

than the theoretical value of//=96/R for uniform flow 

on a smooth surface. However, in the present exT>eriment, friction factors for uniform flow tests (see figure 

12) were also greater than the theoretical value 

(/y=96/R) by about a factor of 2. Therefore, the isolated effect of the type of artificial rainfall used in the 

present investigation is to about double the friction 

factor over that for flows without rainfall.

The line of best fit to the data in figure 19 is a computed line from the relation established between
A24 DYNAMIC AND DESCRIPTIVE STUDIES OF HILLSLOPES

	EXPLANATION 

Series f value m value

1 0.21 0.70

2 .18 .51

3 .29 .57

4 .31 .68

5 .31 .62

EXPLANATION 

Series f value m value

6 0.53 0.67

7 .53 .67

8 .43 49

9 .41 .55

50 100 200 500 1000 2000 5000 20 

REYNOLDS NUMBER

100 200 500 1000 2000 5000

A. SMOOTH SURFACE B. ROUGHENED SURFACE 

FIGURE 18. Summary curves of depth and velocity as a function of Reynolds number for sprinkled tests.

depth and Reynolds number in figure 17. Computed 

lines of best fit are used in the analysis because any 

percentage errors in the original depth measurements 

are multiplied in the computations of hydraulic parameters. This enlarges the scatter of points on plots of 

computed data and increases the difficulty of curve 

fitting. The relation of depth to Reynolds number can 

be accurately determined from graphs with little 

scatter to the data and computed lines of best fit to 

other graphs are equally good fits. The computed 

lines of best fit are used for the summary curves in 

figure 20.

The resistance terms in the Chezy and Manning 

formulas are plotted for the same two examples in 

figure 21 and summary curves for all tests are shown 

in figure 22. Because these terms are related to the 

Darcy-Weisbach friction factor, they follow the same 

pattern as figures 19 and 20. The inclusion of graphs 

for all three resistance terms is to facilitate the visualization of the behavior of these terms. Each of the 

three most common resistance terms is presented

inasmuch as individual hydrologists are more familiar 

and have customarily preferred to use one expression 

rather than another.

The examples of data in figure 23 and the summary 

curves in figure 24 show the relation of the Froude 

number and the ratio of mean velocity to surface 

velocity as functions of the Reynolds number. The 

Froude number is defined as the ratio of inertirl forces 

to gravitational forces; flows with a Froude number 

greater than 1 are supercritical, flows with a Froude 

number less than 1 are subcritical. Within the range 

of conditions investigated, most of the flows observed 

in the smooth channel and all of those observed in the 

roughened surface channel were in subcritical flow. 

Over longer slopes, however, supercritical flovs could 

be expected. Theoretically, the slope of the line relating 

the Froude number to Reynolds number is 0.5 for 

laminar flow. The present data for the smooth surface 

tests indicate a value slightly higher than 0.5 and the 

roughened surface tests have a value somewhat less 

than 0.5. This difference is related to the difference in
THE HYDRAULICS OF OVERLAND FLOW ON HILLSLOPES A25

to I Qok

00 I

100

50

20

10

5.0

2.0 

1.0 

0.5

0.2 

0.1

\

T

\

ff =96,

A

\

1 

0

\

«-

Syn

H

)

i

A

XT

N^o

r

\-

EXPLANATION 

(Series 3; slope=0.034 

ibol Test Rainfall 

* 10 11.35 in 

11 8.51 in 

12 6.35 ir 

i 13 4.86 ir 

14 3.12 ir

Compu

A

K- ,

A\ 

EfX

>:>

i

\

ted line 

graph o 

versus

 y

*X

00

\

of best 

f avera 

?eynol(

/

/

k

+

2)

ntensity 

. per hr 

. per hr. 

i. per hr 

i. per hr 

i. per hr

fit from 

ge depth 

s number

X

\

ff =96

T

N>

x

X

T

\

/R -

Sym

1 1

EXPLANATION 

(Series 8; s|0pe=0.034 

bol Test Rainfall 1 

y 13 11.95 in. 

14 8.78 in.

15

A 16

x

o

x^A £-

T A

iX\

17 

 Comp

+

A 

0* *

X. o +

6.11 in. 

4.78 in.

2)

ntensity 

per hr 

per hr _ 

per hr 

per hr

3.61 in. per hr

jted line of best fit fromgraph of average depth

versus Reynolds number

+

.^M '

L-T, V <"Hi^J ,'-£> *

* T 4

X

\

**sX 

0 °X.

°

A

\

/t 

X

+

20 50 100 200 500 1000 2000 5000 20 50 100 200 500 1000 2000 5COO

REYNOLDS NUMBER (R = ^r)

A. SMOOTH SURFACE B. ROUGHENED SURFACE

FIGURE 19. Darcy-Weisbach friction factor as a function of Reynolds number for sprinkled tests.

/ values shown in figure 18. (Lest the reader jump to 

early conclusions, it will be shown in the next section 

that the Froude number for natural slopes is nearly 

constant with increasing discharge and generally stays 

below a value of 0.2.)

The upper parts of figures 23 and 24 show values of 

the ratio of mean velocity to surface velocity. Nearly 

all values of the ratio are smaller than 0.67, the theoretical value for uniform laminar flow. This indicates 

that mean velocity is retarded more than surface velocity and this influence is greatest at the lower Reynolds numbers. For seven of the nine test series, the 

slope of the line relating the velocity ratio to Reynolds 

number is positive. The slope of this line is determine^ 

by the ratio of the computed m value for mean velocity 

(m 1 f) to the m value for measured surf ace velocity. 

The actual slope is this ratio minus 1.0. From the information in figure 18, the value of 1 / is greater than the 

surface velocity m value in all test series except numbers 

6 and 7.

FIELD INVESTIGATION OF OVERLAND FLOW

The results of the field verification studies are illustrated by an example of data from one site, Pole Creek 

Site 3, and summary curves representing the data from

all sites. All of the measured and computed data 

from the field sites are included in the "Summary of 

data," table F.

Topographic maps were prepared from the detailed 

surveying at each site. These maps are shown as part 

A of figures 25 to 31. All of the maps show the ger^ral 

downslope orientation of the runoff plots and because 

of the close contour interval, many details of the 

microrelief on the slopes are apparent. Supplemerting 

each topographic map is a grid layout covering the area 

of the runoff plot. At each field site, physical features 

influencing the runoff of water were observed and 

located on the grid layout. These layouts are shown as 

part B in figures 25 to 31. The mapped features influencing flow include vegetation mounds, exposed rock 

surfaces, the aluminum stripping used as a barrier to 

direct runoff, and the position of the collecting trough. 

The vegetation mounds were generally less than 0.1 

foot high and normally occurred at places where sagebrush overstory was removed. Most likely, the eagebrush had protected mound areas from erosion by 

wind, rain, and the trampling of livestock.

As explained earlier, the flow rarely occurred as a 

uniform sheet of water and the majority of vater 

travelled downslope in several lateral concentrations of
A26 DYNAMIC AND DESCRIPTIVE STUDIES OF HILLSLOPES

i i

EXPLANATION 

Series Slope0.0033 

.0170 

.0342

EXPLANATION 

Series Slope _ 

0.0775 

.0550 

.0342 

.0170 ~

50 100 200 500 1000 2000 5000 20 50 100 200 500 1000 2000 5000

REYNOLDS NUMBER (R=^) 

A. SMOOTH SURFACE B. ROUGHENED SURFACE

FIGURE 20. Summary curves of Darcy-Weisbach friction factor as a function of Reynolds number for sprinkled tests.

flow; however, these concentrations were not considered 

rill flow. Dye tracings were mapped to determine the 

patterns of flow illustrated in part B of figures 25 to 31. 

Each site exhibited a unique flow pattern dependent 

mostly on the physical characteristics of the slope.

It is emphasized that not all the runoff occurs in the 

concentrations of flow shown in figures 25 to 31. The 

general appearance of runoff at most field sites was one 

of omnipresent surface detention, easily detected by 

the glistening of the sheet of water in sunlight. Dye 

tracings showed that this sheet of water moved slowly 

downslope and often it moved laterally to join the 

concentrated areas of flow. Few areas approached 

stagnation because continuing rainfall forced runoff. 

Therefore, the flow patterns shown represent only the 

concentrations of flow and not all the flow. A number 

of flow lines uniformly spaced, as in the lower fourth 

of the plot shown in figure 27B, indicate depths of flow 

great enough that runoff is uniform over the entire 

width.

Pole Creek Site 1 is shown in figure 25. This site was 

relatively free of topographic irregularities and surface 

runoff was essentially downslope. Note in figure 25 the 

trending of the flow pattern in the lower half of the plot

in response to the curvature of the contour lines. 

Runoff from this site and some of the other sites was 

also characterized by surface detention in a series of 

puddles formed by barrier dams of organic debris. 

These miniature lakes are illustrated in figure 3 (lower 

photograph). Surface runoff occurs, in part, by a succession of failures of these barriers.

The slope of Pole Creek Site 2 was great enough to 

override the influence of minor topographic irregularities. As shown in figure 26, the general pattern of flow 

is directly downslope with little anastomosing of the 

flow concentrations. A similar flow pattern is noted in 

figure 27B for Pole Creek Site 3. However, the less steep 

slope of Pole Creek Site 3 begins to show the influence 

of small topographic features and the curve of flow lines 

around topographic highs. In the lower fourth of the 

runoff plot at Pole Creek Site 3, depths of flow are sufficiently great and are evenly enough distributed so that 

flow was nearly uniform across the plot. Note also the 

shift in direction of the flow pattern in this are0, in response to a curvature in slope direction.

The ground slope at New Fork River Site 1 is flat 

enough that small topographic features are obvious in 

the topographic map in figure 28 and are visible in the
THE HYDRAULICS OF OVERLAND FLOW ON HILLSLOPES A27

c 

o

0.2

0.1

0.05

0.02

\

A

>"<

r

/ 

Computed line o 

fit from graph 

"average depth

Reynolds numl

I

^T

T

f best 

of

versus 

icr

A

$*<: x

^

*

V^H" + >*,

^^^^ 

+

Computed line of best fit from graph of 

average depth versus Reynolds numbe

EXPLANATION 

Symbol Test 

+ 10

(Series 3; slope=0.0342)

Compute 

fit from

average 

Reynolc

T

^

J line o 

graph 

depth 

Is numt

0

V---T0

T A

1

f best 

of

versus 

er

+ 

A *

<Cx ^XM 

r A A ^^ 

TT ^ 

TT A X

+ 

, ** « 

L! * 

^*

x 00 

A

+

Computed line of best fit from graph of 

average depth versus Reynolds numta

EXPLANATION 

Symbol Test I

13

14 

15-1

16

17 

(Series 8; slope=0.0342)

20 50 100 200 500 1000 2000 5000 20 50 100 200 500 1000 2000 5000

REYNOLDS NUMBER /R=^7^| 

A. SMOOTH SURFACE B. ROUGHENED SURFACE

FIGURE 21. Chezy's C and Manning's n as a function of Reynolds number for sprinkled tests.

upper photograph of figure 6. The flow pattern responding to this topography is shown in figure 285. The 

gradient at the lower end of the plot was such that water 

ponded in the lower 2 feet of slope. In this ponded area, 

sediment was deposited as a delta. The size of the delta, 

shown in the lower photograph of figure 6, indicates the 

effectiveness of overland flow to erode and transport 

sediments. The eroded sediments apparently were derived as sheet wash since no rilling was observed. The 

ponding had no effects on the upslope hydraulics of flow 

and affected only the analysis of sediment concentrations.

The flattest slope of the sites investigated was for 

New Fork River Site 2. Irregular surface features are 

unmistakeable in the topographic map in figure 29A 

although they stand out only slightly in the photographs 

of figure 7. The pattern of flow over this topography 

is shown in figure 29.B. The flow is definitely directed 

around the topographic highs and follows the microvalleys indicated by the contour map. Water in the 

lower 8 feet of this site was also ponded and there was 

some deposition of sediment in this area. The deposition 

was distributed over the area and did not form a delta 

as at New Fork River Site 1.

Figures 30 and 31 illustrate the topography end 

flow patterns for the two Boulder Lake sites. The 

appearance and behavior of flow at these sites are 

similar to those just described for the other sites.

Examples of downslope profiles of depth and surface 

velocity are shown in figure 32 for Pole Creek Site 3. 

This site was chosen as an example because it represented an intermediate slope in the range of slopes 

investigated. Measurements listed in the "Summary 

of data," table C, were used to construct the downslope 

profile of depth. With little variation, the data can 

be described with a straight line having a slope of 

0.80 on the log-log plot. Surface-velocity measurements are plotted as the downslope profile in the right 

half of figure 32. Part B of this figure is a plot of the 

actual individual measurements and part A is an 

attempt to smooth the data by using a running 3-foot 

average of the measured velocities. The data can be 

adequately expressed with a straight line of slope 0.25.

Summary curves of downslope profiles of depth *vnd 

surface velocity are shown in figure 33 for all field sites. 

Values of/for the exponent of depth range from 0.4C to 

1.00 and m values of velocity range from 0.25 to 1.00. 

More will be said about these values of / and m later.
A28 DYNAMIC AND DESCRIPTIVE STUDIES OF HILLSLOPES

EXPLANATION 

Series Slope 

1 0.0033 

.0170 

.0342

EXPLANATION 

Series Slope

6 0.0775

7 .0550

8 .0342

9 .0170

20 50 100 200 500 1000 2000 5000 20 50 100 200 500 1000 2000 5000

REYNOLDS NUMBER (R=~) 

A.SMOOTH SURFACE B. ROUGHENED SURFACE

FIGURE 22. Summary curves of Chezy's C and Manning's n as a function of Reynolds number for sprinkled tests-.

Depth data are also plotted as a function of Reynolds 

number on the left of figure 34. The same line of fit for 

figure 32 is also shown in figure 34. Summary curves of 

depth as a function of Reynolds number are shown in 

the left graph in figure 35.

Values of the Darcy-Weisbach friction factor for Pole 

Creek Site 3 are plotted in the right graph of figure 34. 

The scatter of data shows the tremendous effect of 

small depth discrepancies in the computation of friction 

factors. The suggested straight line relationship is a 

computed line of best fit taken from the opposite graph 

in the figure. The slope of the straight line relationship, 

as determined from equation 13, is equal to / 2m or 

/ 2(1 /). For a value of/ equal to 0.67, the slope of 

the friction factor relationship is 0; smaller values of / 

yield negative slopes, and greater values of/give positive slopes. Since /=0.80 for Pole Creek Site 3, the 

slope of the friction factor relationship is 0.40 and this 

indicates the friction factor increases in the downslope 

direction. Summary curves of the friction factorReynolds number relation are shown in the right half 

of figure 35 for all field sites. The wide range in values 

of slope for the friction factor relation are due to the 

range in values of/ for the depth relations.

Values of Chezy's C and Manning's n for Pole Creek 

Site 3 are plotted as a function of Reynolds number in 

figure 36. Summary curves for all plots are si own in 

figure 37. The appearance of these curves is similar to 

those for the Darcy-Weisbach friction factor.

The relation of the Froude number to Reynolds number is shown in the left graph of figure 38 for the data 

of Pole Creek Site 3. Positive or negative slopes for the 

straight line relation depend on whether the / value is 

greater or less than 0.67. The summary curves for 

Froude number as a function of Reynolds number are 

shown in the left graph in figure 39.

The ratio of mean velocity to surface velocity for 

Pole Creek Site 3 is shown as a function of Reynolds 

number in the right graph of figure 38 and summary 

curves are shown in the right graph of figure 39. The 

near horizontal to negative range in slopes of tl^ lines 

in figure 39 indicate a relatively more rapid downslope 

increase in surface velocity than mean velocity.

COMPARISON OF FIELD RESULTS TO LABORATORY

DATA

The most apparent difference in field and laboratory 

data is the greater depths occurring in the fieM run-
THE HYDRAULICS OF OVERLAND FLOW ON HILLSLOPES A29

< 

oe.

I.U

0.2 

n i

 

T

_Comput< 

versus 

of surf

o

T

id line 

Reynol 

ace ve!(

+ T } TA/f*°

 ~ "" 0

if best 

Js numl 

>city vei

 ^" « A

Fit from g 

>er and li 

sus down

x_*"

raph of 

ie from 

slope d

_____ -

averae 

graph 

stance.

e depth _

. 

_ Com put 

versus 

of sur

ed line 

Reyno

ace vel

+

of best 

ds num 

ocity v<

-2 fc-T^f 

°x """o 

A

fit from e 

ber and 1 

srsus dow

raph o 

ne fronr 

nslope

averai 

i graph 

distant*

|e depth_

i

5.0

ce.

LLJ 

CD

0.5

0.2 

0.1

0.(

EXF 

(Series 

Symb

o

A

T

-^

'LANA' 

3; slop< 

»l Te 

1( 

1 

1 

1 

1

o

^

ION 

J =0.0342) 

st

D 

11 

J 

\

A

+j$

On

 *

r

^ ^^

Computed line of best fit from graph of 

average depth versus Reynolds number

EXPLANATION 

(Series 8;slope =0.0342) 

Symbol Test

0

A

T

T

1 

1 

1 

1 

1

TV

T

3 

4

5 

6 

7

*3-£ 0 ^

-I"-.*

J^»V

% Qfl

A *

0,

'* + +

f t + 1-

 f^

Computed line of best fit from graph of 

average depth versus Reynolds number

20 50 100 200 500 1000 2000 5000 20 50 100 200 500 1000 2000 5000

REYNOLDS NUMBER (R = VPJ

A. SMOOTH SURFACE * B. ROUGHENED SURFACE

FIGURE 23. Froude number and velocity ratio as a function of Reynolds number for sprinkled tests.

off. This was not an unexpected observation. The 

laboratory data indicated that the effect of roughness is to retard the flow and increase the depth; the 

sand grain roughness in the laboratory increased the 

depths up to 30 percent over those on a smooth surface. 

Surface roughness of the field sites is difficult to estimate. The roughness of field sites consists of both particle roughness (sand grain roughness in bare areas and 

plant sprouts in vegetated areas) and form roughness 

(topographic irregularities). Mean grain sizes of the soil 

particles at the field sites are smaller than those in the 

laboratory roughness so that the increase in depths is 

due primarily to vegetation and topographic characteristics of the field sites. Depths at the upslope end of the 

field plots were comparable to depths at the upstream 

end of the flume in the laboratory. Thus the downslope 

rate of increase in depths is greater for the field sites. 

Figure 33 shows/ values for field sites range from 0.40 

to 1.00, average 0.69, and compare to an average/value 

of 0.48 for the rough surface tests in the laboratory.

Higher/values are related both to the magnitude of 

relative roughness (degree of overall retardance) and 

the character of the runoff (for example, ponding as at 

Pole Creek Site 1, lower photograph in figure 3). The

368-391 O 7C

/ values for the field sites show no correlation rath 

ground slope, or, at least, the data indicate that other 

characteristics of the field plots override the influence 

of slope. Since no correlation could be established between vegetation cover in percent (or type of vegetation) and/ value, the increase in/values at field fHes 

is attributed to topographic form and, dependent on 

form, the character of runoff. No two field sites are 

identical in form and no two depth profiles are the same.

Values of / in the relation D <x.qf are related to downslope changes in resistance to flow. Resistance to flow, 

expressed in this report as the Darcy-Weisbach friction 

factor ff, Chezy's C, and Manning's n, describe 1 nlk 

resistance to flow rather than resistance attributable to 

grain roughness alone. With increasing downslope discharge, one would expect resistance to flow to decrease 

downslope as relative roughness decreased (as in all 

laboratory cases). Overriding influences, such as ponding, are analogous to tremendous retarding forces. T" us, 

depending on topographic form, relatively smoother 

surfaces may show higher resistance to flow and different 

rates in downslope changes in roughness.

The average of the downslope changes in roughness 

at the field sites is approximately zero, this indicates a
A30 DYNAMIC AND DESCRIPTIVE STUDIES OF HILLSLOPES

EXPLANATION 

Series Slope 

0.0033 

.0170 

.0342 

.0550

EXPLANATION 

Series Slope

6 0.0775

7 .0550

8 .0342

9 .0170

0.05

20 50 100 200 500 1000 2000 5000 20 50 100 200 500 1000 2000 5000

REYNOLDS NUMBER /R= ^p) 

A. SMOOTH SURFACE B. ROUGHENED SURFACE

FIGURE 24. Summary curves of Froude number and velocity ratio as a function of Reynolds number for sprinkled tests.

downslope increase in relative roughness. Absolute 

roughness is probably not increasing, so the apparent 

increase in roughness is clue to a decrease in runoff efficiency and is related to the micro topography of the site. 

As a first approximation to overland flow on natural 

ground surfaces, an / value of 0.67 and no downslope 

change in roughness may be used to estimate the hydraulic parameters. Absolute values of depth and the 

resistance term may be approximated from figures 35 

and 37. Values of relative roughness corresponding to 

values of the Darcy-Weisbach friction factor are beyond 

those shown on conventional Moody diagrams, but they 

would appear in some instances to have a value greater 

than 1. This is not unreasonable comparing the shallow 

depths of flow to the magnitude of vegetation and topographic barriers.

It is difficult to compare values of the friction factor 

at field sites to values from the laboratory tests. However, in general, the field data indicate a tenfold increase 

in resistance on the natural field plots compared to the 

laboratory surfaces.

Values of m for surface velocity are generally less for 

the field sites than for the laboratory flume (compare

figure 33 to figure 18). As depth enlarges its role in 

absorbing downslope increases in discharge, mean 

velocity must absorb less of the change. Graphs of the 

velocity ratio in figure 24 indicate that the velocity 

ratio is nearly constant. This is approximately true for 

the field data. (See figure 40.) Thus,- m values for 

surface velocity in the field must be lower than laboratory values. An average value of the ratio of mean 

velocity to surface velocity is about 0.4 to 0.5. One 

reason for this low value of the velocity ratio is that a 

maximum surface velocity was measured in the field. 

The leading edge of the dye trace was measured and 

as the dye merged into concentrated areas of flow, the 

velocity timed was greater than an average surface 

velocity over the width of the plot. Still, values of the 

velocity ratio from field data were not substantially 

lower than values from laboratory data.

The downslope change in Froude number for field 

data varied, but on the average it was nearly constant 

down the slope and was considerably lower than values 

from laboratory data. This behavior is related to the 

differences in depths of field runoff compared to labora-
THE HYDRAULICS OF OVERLAND FLOW ON HILLSLOPES A31

o 

o

o 

<

z 

o

> 

o

z 

o

105.20

TRANSVERSE

STATIONING,

IN FEET

6 4 2

TRANSVERSE 

STATIONING,

IN FEET 

6420-2

A. TOPOGRAPHIC MAP

^Collecting trough 

B. FLOW PATTERN

FIGURE 25. Topography and flow pattern at Pole Creek Site 1.

tory tests. An average value of the Froude number is 

0.1, which is well within the regime of subcritical flow.

PROBABILISTIC APPROACH TO OVERLAND FLOW AND 

THE SHAPE OF HILLSLOPES

In accommodating the downslope increase in discharge from rainfall, overland flow on hillslopes can 

change velocity, depth, and slope. These are the factors 

which describe the hydraulic geometry. The exponents 

of hydraulic geometry are indices of the deviations of 

the dependent factors for any change in the independent 

factor, discharge. The variability of the dependent 

factor is minimized when the variance of the factor is 

minimized. Such minimization of the variability of the 

dependent factors provides the most probable relations 

among the factors. When variability of dependent

factors are jointly minimized, the sum of the variance 

of the factors is minimized.

HYDRAULIC CHANGES DOWNSLOPE

In the presentation of data in earlier sections of this 

report, hydraulic geometry was used to describe the 

downslope changes in depth, velocity, and resistance 

to flow. Exponents in the hydraulic geometry equations, 

summarized here,

and

o 

o

oI 

z 

o

>- 

oc

<

o

I 

> 

(5, 6)

(10, 11)

TRANSVERSE

STATIONING,

IN FEET

TRANSVERSE 

STATIONING,

IN FEET 

86420-2

115.20

A. TOPOGRAPHIC MAP B. FLOW PATTERN

FIGURE 26. Topography and flow pattern at Pole Creek 

Site 2.
A32 DYNAMIC AND DESCRIPTIVE STUDIES OF HILLSLOPES

were computed for the condition of constant slope. 

More generally, slope can also be expected to vary with 

discharge :

#cc#*ccR*. (22)

Thus, it can be seen that quantification of four variables, 

/, m, y, and z is needed to describe the hydraulics of 

flow with increasing discharge.

The known laws of hydraulics do not provide sufficient physical relations to offer a solution to the above 

equations. However, in a clever reasoning of the most 

probable energy distribution and expenditure within 

a river system, Leopold and Langbein (1962) were 

able to supply additional equations needed for a solution to flow in river channels. Namely, they postulated that energy expenditure per unit of surface area

TRANSVERSE

STATIONING,

IN FEET

6 4

TRANSVERSE

STATIONING,

IN FEET

6420-2

o 

o

o

 < / Barrier

jf" Vegetation 

mound

Z

O

z 

o

A. TOPOGRAPHIC MAP

Collecting trougrr 

B. FLOW PATTERN

o 

o

o

I 

z 

o

Z

o

TRANSVERSE

STATIONING,

IN FEET

6 4

TRANSVERSE

STATIONING,

IN FEET

104.00

102.40

102.20

102.00

101.80

100.20

100.00

99.80

99.60

99.40

A. TOPOGRAPHIC MAP

Barrier

Deposition

B FLOW PATTERN

FJGTTBE 27. Topography and flow pattern at Pole Creek Site 3.

FIGURE 28. Topography and flow pattern at New Fork River

Site 1.

is equal throughout the river system and that total 

energy expenditure in the system is a mirimum. 

Langbein (1964) elaborated on this pioneering work; 

Emmett and Leopold (1964) presented graphical solutions for Langbein's equations, and Langbein (1965), 

in a closure to his 1964 paper, demonstrated the validity 

of this new concept through the agreement between 

theory and data for many examples of flow in rivers, 

canals, and flumes. Although controversy still exists 

about the applicability of "most probable" statistical 

concepts to hydraulics, there is increasing accentance 

and elaboration of the basic ideas. For example, Mad-* 

dock (1969) has applied these concepts to sediment 

transport in alluvial channels. It would be interesting
THE HYDRAULICS OF OVERLAND FLOW ON HILLSLOPES

to apply these statistical techniques to an analysis of 

overland flow.

For overland flow, width may be considered constant, 

6=0, and increase in discharge is absorbed through the 

interaction of depth and velocity and in turn is reflected 

in shear and friction. The variability of each of these 

dependent factors is its exponent in hydraulic geometry 

and the variance of each of these terms is the square 

of the exponent relating that variable to discharge. 

Thus the variance of depth may be expressed as f2 , 

velocity as m2 , shear as (J+z) 2 , and friction as 

(j+z 2m) 2 . The most probable way that an increase 

in discharge can be met is given by the condition that 

the sum of these variances is minimized:

(23)

o 

o

o 

o

oI 

z 

o

<

LU

>

O

TRANSVERSF

STATIONING,

IN FEET

TRANSVERSE

STATIONING,

IN FEET

99.60

99.55

99.50

99.45

0 -2

Vegetatior 

mound

Vegetation 

/ mound

 ' Barrier

A. TOPOGRAPHIC MAP

c ,. - j - ... /Barrier Sediment deposition^ 

BarrieNJ =t

Collecting trough 

B. FLOW PATTERN

Minimization of equation 23 will be considered for two 

cases: (1) turbulent flow and (2) laminar flow.

The theoretical value of/ for turbulent flow is 0.60; 

the theoretical value of/ for laminar flow is 0.33. Th ese 

are the same values illustrated in figure 11 for relation 

between depth and Reynolds number for uniform flow. 

For constant widths, m \ j. Thus, for turbulent 

flow,/= 0.60 and m=0.40, and for laminar flow,/=C,33 

and m=0.67. With these values of/ and m for equation 

23, minimization of equation 23 gives a value of 

z~ 0.20 for turbulent flow and s=+0.33 for laminar 

flow. Thus for turbulent flow, slope decreases doTTislope and for laminar flow, slope increases downslcpe. 

It may be supposed that flows intermediate between 

laminar and turbulent (as those in the transition region 

or, in the present investigation, a disturbed type of

o 

o

o 

<:

oc

=3

o

ae. 

ce.

Hca 

oc

<:

LU

>

O 

as

Z

o

h- 

> 

TRANSVERSE

STATIONING,

IN FEET

642

TRANSVERSE

STATIONING,

IN FEET

6 4 20-2

108.40

108.00

107.60

107.20

- 106.80 VegetatioT 

mound

106.40

106.00

105.60

105.20

104.80

104.40

104.00

Exposed rock

Barrier

A. TOPOGRAPHIC MAP 8. FLOW PATTERN

FIGURE 29. Topography and flow pattern at New Fork River

Site 2.

FIGURE 30. Topography and flow pattern at Boulder Lake

Site 1.
A34 DYNAMIC AND DESCRIPTIVE STUDIES OF HILLSLOPES

flow caused by raindrop impact and the anastomosing 

of flow concentrations) would show intermediate values 

of downslope changes in slope. In the present probablistic approach to overland flow, an intermediate value 

(or value for flows somewhere between laminar, 

s=+0.33, and turbulent, 2= 0.20) is approximated 

by a zero downslope change in slope, s=0.0.

From the computed values of z above, values of the 

roughness exponent, y, can be computed from the DarcyWeisbach formula (eq 7): y j-{-z 2m or y= 0.40 

for turbulent flow, and y= 0.67 for laminar flow. 

From figure 12 and its discussion, it has been shown 

that for uniform flow on a constant slope, the exponent 

y should have a value of 1.0 for laminar flow. The less 

negative value ( 0.67) in the present analysis indicates

o 

o

o

I 

 z. 

o

TRANSVERSE

STATIONING,

IN FEET

TRANSVERSE

STATIONING,

IN FEET

109.20

108.80

108.40

108.00

107.20

106.80

106.40

106.00

105.60

105.20

104.80

104.40

104.00

103.60

102.80

102.40

102.00

101.60

101.20

100.80

100.40

100.00

99.60

99.20

0-2

Exposed rock

A. TOPOGRAPHIC MAP B. FLOW PATTERN

a relative increasing downslope resistance to flow. 

That is, when slope is relaxed and allowed to change 

in the downslope direction, the resistance to laminar 

flow decreases downslope less rapidly than for a fixed 

slope. Conversely, for turbulent flow, the data of figure 

12 indicate that y should have a value of 0.20 for 

fully turbulent flow. The more negative value ( 0.40) 

in this analysis indicates decreasing resistance to turbulent flow in the downslope direction.

APPLICATION TO THE SHAPE OF HILL SLOPE 

PROFILES

It is of interest to apply the results of this analysis 

to flow over a long length of hillslope. Without any 

external factors affecting the downslope runoff of unconcentrated sheet flow resulting from rainfall, Eeynolds 

number increases in the downslope direction. For 

uniformity of rainfall and infiltration, Reynolds number 

increases uniformly downslope from a value of zero at 

the hilltop to a maximum at the base of the slope. 

For sufficiently long slopes, overland flow at the foot of 

the hill could be expected to be fully turbulent. It 

should be noted, however, that the Reynolds number 

is dependent on the runoff rate. The Reynolds number, 

R=4VD/v, may also be expressed as

(24)

where c is a coefficient including the value of kinematic 

viscosity of water, R is the runoff rate in inches per 

hour, and L is the length of slope in feet. For an average value of viscosity of 1X10"5 feet squared per 

second, the following tabulation shows for several 

intensities of runoff the length of slope required to 

obtain the given Reynolds number:

Reynolds number

Length of slope, L, in feet

0.5 in. per hr 1.0 in. per hr 2.0 in. per hr

500 _________

2*000

s'ooo

4*000

_______ _ 108

_________ 216

__ ____ 432

_________ 648

_________ 864

54

108

216

324

432

27

54

108

162

216

FIGURE 31. Topography and flow pattern at Boulder Lake

Site 2.

Doubling the runoff rate would halve the length of 

slope needed to obtain the same Reynolds number. 

The preceding analysis would indicate that an upper 

reach of slope, characterized by laminar overland flow, 

should be convex (z is positive). A middle reach of slope 

with mixed flow should be nearly straight (z is approximately zero) and a lower reach of slope with turbulent 

overland flow should be concave (z is negative). From 

the tabulated slope lengths above for one inch per hour 

of runoff, such a slope profile may be convex for about
THE HYDRAULICS OF OVERLAND FLOW ON HILLSLOPES A35

U.I

0.05

i 

£ 0.02

z

a* 0.01

3= i 

S 0.005

LU 

O

> 0.002 

0.001 

0.0005

0.0002

0.0001 

1

^

X

^7

S

^f=0.8

Dep

Veloc

/4/

D

h^r A/\l

EXPLANATI 

\\\ o, Average 

transverse

ty +Trial 1, left 

x,Trial 2, rig

 ^k Jr? frif

u

ON 

of eight -

9

readings 

half of sic 

ht half of

/

>pe

slope

0 2.0 5.0 10 20 50 1C

A. RUNNING 3-FOOT AVERAGE

B. INDIVIDUAL MEASUREMENT

0.5 1.0 2.0 5.0 10 20 

DOWNSLOPE DISTANCEJN FEET 

FIGURE 32. Downslope profiles of depth and surface velocity for Pole Creek Site 3.

50 100

the first 100 feet, straight for the next 200 feet, and 

concave for the remainder of the profile. Such convex, 

straight, concave hillslope profiles are schematically 

shown in figure 40 for three intensities of runoff on 

slopes with the same initial gradient. The steepening 

of the straight segment of slope with decreasing runoff 

rates may not be significant because the slope of the 

straight segment depends primarily on the initial gradient at the top of the hill. The influence of initial gradient is schematically shown in figure 41 for a constant 

runoff intensity.

White (1966) has shown that many hillslopes are 

indeed characterized by a convex, straight, and concave 

profile. The length of each of the three slope segments 

is dependent on the runoff rate which in turn relates to 

rainfall intensity and infiltration, and short slopes may 

not be long enough to develop all of the three segments. 

The steepness of the straight segment is dependent on 

a number of possible combinations of initial gradient 

and runoff intensity. As one possibility, the initial gradient might be associated with a runoff intensity (a 

combination of figs. 40 and 41) in such away that slope 

steepness is constant and only the length of each slope 

segment is different for differing rates of runoff. But

regardless of the slope steepness, the rate of downslope 

change of gradient in the convex and concave segments 

should be similar between most slopes, an observation 

verified by measurements of hillslopes by White (19f *>). 

It appears likely that the overall hillslope profile 

(lengths of each of the three slope segments) is dependent on the climate which defines the rainfall intensity 

and the geologic structure, especially rock type, which 

controls the infiltration rate. Differing rainfall intensities sculpture the ground surface in proportions different 

than those of the observed profile, but the general shape 

of the hillslope is that profile determined by a dominant 

runoff rate. Slopes with different infiltration rates (differing geologic structure and rock type) in the same 

climatic environment may have different lengths of each 

slope segment as may slopes of the same geologic structure and rock type in different climatic environments. 

But all slopes subject to overland flow would tend towards a characteristic convex, straight, and concave 

profile.

It is emphasized that the profile suggested by the 

above analysis is not characteristic of any given slope, 

but it is a most probable profile toward which all hillslopes tend to develop. And, of course, an impl'cit
A36 DYNAMIC AND DESCRIPTIVE STUDIES OF HILLSLOPES

0.1

0.05

0.02

0.01

5: 0.005

0.002

0.001

0.0005

0.0002

0.0001

EXPLANATION 

Symbol Site name

NF-2 New Fork River Site 2

PC-1 Pole Creek Site 1

NF-1 New Fork River Site 1

BL-1 Boulder Lake Site 1

PC-3 Pole Creek Site 3

BL-2 Boulder Lake Site 2

PC-2 Pole Creek Site 2

Slope

0.0290 

.0960 H 

.1000 

.1880 

.2080 

.3315 ~] 

.3320

1

0.01

5 10 20 50 100 ''0.5 1.0 2.0 

DOWNSLOPE DISTANCE, IN FEET

FIGURE 33. Downslope profiles of depth and surface velocity at field sites.

50 100

assumption is that overland flow is the only operative 

process developing the profile. Other processes, for 

example mass movement, might serve to alter a profile 

developed only from the flow of unconcentrated runoff.

EROSION AND SEDIMENT TRANSPORT

BILLS AND DYNAMIC EQUILIBRIUM

One of the most ubiquitous processes occurring on 

hillslopes is the erosion, transportation, and deposition 

of debris by running water. The formation of rills is one 

consequence of the flow of water. However, some slopes 

may show no rills and may be undergoing uniform degradation by sheet erosion. The question may be logically asked why some slopes develop rills and others 

do not? Since the development of rills is widespread, 

the question extends beyond the field sites of this study 

and is pertinent to the general science of geomorphology.

Both rills and sheet erosion are the products of overland flow. However widespread overland flow may be, 

it is one of the most elusive processes to observe and 

measure. This fact has made difficult the collection of 

quantitative data to help resolve the questions of why 

and how rills develop. In fact, little is known of the 

general mechanics of slope erosion by overland flow.

The author and others (Leopold and others, 1966) 

have measured hillslope erosion for nearly 10 years in 

a semiarid area of New Mexico. Despite efforts to observe overland flow from thunderstorms occurring 

during the several weeks of residence at the project 

area each year, overland flow was never observe! in the 

field. Yet, during the period of measurement, surface 

erosion on unrilled slopes yielded 13,600 tons per square 

mile per year or 98 percent of the sediment production 

from all sources. Obviously, surface erosion on. these 

unrilled slopes must be the work of unconcentrated 

overland flow, but without the detailed measurements 

of hillslope erosion, the full importance of overland flow 

was not apparent in the field. Still, the question remains; 

why did the slopes degrade by sheet erosion rath er than 

develop rills?

The presence of rills was not observed at any of the 

field sites of the present investigation and rilling is not 

common in the general area. Flow concentrations occurring at the sites were dictated by microtopo^raphic 

features, but the paths followed by concentrations of 

flow were not in discernible rills. Nor, during the course 

of sprinkling at each site (generally about 6 hours or 

longer), were rills observed to be formed by flow concen-
0.1 

0.05

,_ 0.02

LU 

LU 

LL.

E 0.01

g

£ 0.005

LU 

O

LU

CD

^ 0.002

LU

3> 

<

0.001

0.0005

0.0002

THE HYDRAULICS OF OVERLAND FLOW ON HILLSLOPES

1000

500

QU 200 

roK 

col

II

,*£ 100

AB7

x Taken from line of average 

depth versus downslope distance

CD 

OO

>-

oc

<

50

20

10

Computed line of best fit 

from graph of average 

depth versus Reynolds number

20 50 100 200 500 1000 2000 20

REYNOLDS NUMBER

50 100 200 500 1000 20CO

FIGURE 34. Depth and Darcy-Weisbach friction factor as a function of Reynolds number, Pole Creek Site 3. 

O.lOi i i i i i i 1000

EXPLANATION

Site name

New Fork River Site 2 

Pole Creek Site 1 

New Fork River Site 1 

Boulder Lake Site 1 

Pole Creek Site 3 

Boulder Lake Site 2 

PC-2 Pole Creek Site 2_ 

500

Symbol 

NF-2 

PC-1 

NF-1 

BL-1 

PC-3 

BL-2

0.0002

20 50 100 200

Slope . 

0.0290 

.0960 

.1000 

.1880 

.2080 

.3315 

.3320

1000 2000 50 100 200 500 1000 2000

REYNOLDS NUMBER 

FIGURE 35. Summary curves of depth and Darcy-Weisbach friction factor as a function of Reynolds number, field sites.
A38

50

20

10

5.0

o>

00 '

O.I

DYNAMIC AND DESCRIPTIVE STUDIES OF HILLSLOPES

5.0

Computed line of best fit 

from graph of average

depth versus Reynolds number

Z 

<

2.0 

1.0 

0.5

0.2

0.1

0.05

0.02

0.01

Computed line of best fit 

from graph of average 

depth versus Reynolds number

50 100 200 500 1000 2000

n 

JJ

50 100 200 500 1000 2000 20

REYNOLDS NUMBER (R=- 

FIGURE 36. Chezy's C and Manning's n as a function of Reynolds number, Pole Creek Site 3.

5.0 I I I I 

	EXPLANATION

Symbol Site name Slope

NF-2 New Fork River Site 2 0.0290

>C-1 Pole Creek Site 1 .0960

NF-1 New Fork River Site 1 .1000

BL-1 Boulder Lake Site 1 .1880

PC-3 Pole Creek SiteS .2080

BL-2 Boulder Lake Site 2 .3315

PC-2 Pole Creek Site 2 .3320

50

20

10

5.0

'2.0 

1.0 

0.5

0.2

0.1 I_____I I I_____I I I 0.01

20 50 100 200 500 1000 2000 20

REYNOLDS NUMBER

50 100 200 500 1000 2000

FIGURE 37. Summary curves of Chezy's C and Manning's n as a function of Reynolds number, field sites.
THE HYDRAULICS OF OVERLAND FLOW ON HILLSLOPES A39

5.0

2.0

1.0

0.5

S 0.2

o 

ct:

0.1

0.05

0.02

0.01

20

Computed line of best 

fit from graph of 

average depth versus 

Reynolds number

50 100 200

10

5.0

2.0

r 

. 1.0

0.5

0.2

0.1

0.05

0.02

500 1000 2000 20 

REYNOLDS NUMBER

Computed line of best fit 

from graph of average

-depth versus Reynolds__ 

number and line from 

graph of surface velocity 

versusdownslope distance

50 100 200 500 1000 2000

FIGURE 38. Froude number and velocity ratio as a function of Reynolds number, Pole Creek Site 3.

trations. Rilling is generally considered to be evidence 

of more accelerated erosion than sheet erosion. Sediment 

concentrations at New Fork River Site 1 were the highest observed at that time in the investigation and rilling 

was considered most likely to occur at this site. However, after nearly 10 hours of sprinkling at an intensity 

of 8.5 inches per hour, no observable rills had been 

formed. The sprinkling intensity was raised to 10.5 

inches per hour and continued for over 6 hours. Still 

no rills were formed by the increased runoff.

The appearance of rills on a soil surface during overland flow as influenced by slope steepness, runoff rate, 

and presence or absence of rainfall was reported by 

Meyer and Monke (1964) for a laboratory investigation using glass spheres as a noncohesive bed material. 

They reported erosion occurs predominately by rilling 

and the intensity of erosion increases with increasing 

slope steepness and runoff rates. Rainfall tended to 

level the bed surface, thereby smoothing its rill-roughened surface. For a 10 percent slope, the same as the slope 

steepness at New Fork River Site 1, Meyer and Monke 

report that erosion was rapid and rilling was pronounced. Rills were long narrow chutes and were directed predominately downslope. As erosion rates 

increased with increased runoff rates, they report that

erosion tended to be uniform since potential rills we^e 

filled by the great rates of soil movement before they 

could fully develop.

Using the reasoning of Meyer and Monke, it corld 

be argued in the present investigation that rilling should 

be the predominate erosion process but that rills were 

obliterated by deposition of sediments from intemll 

areas. However, the lack of rilling on both the less 

steep and more steep field sites and the lack of rilling 

in the general field area indicate that rilling need rot 

occur where there is erosion and may be related to some 

broader aspect of geomorphology. Such an aspect 

might be the "equilibrium concept of landscape" elaborated by Hack (1960). Briefly, Hack postulates that 

for landforms in dynamic equilibrium, all topograplic 

elements are eroding vertically at an equal rate with 

no change in time of slope form or areal arrangement 

of the topography. Such equilibrium landforms would 

be completely adjusted to the processes presently acting on them. The concept of dynamic equilibrium is 

supported by the most probable model analysis in the 

preceding section which suggests that hillslopes tend to 

adjust to and to maintain certain highly regular, 

geometric forms.

Utilizing Hack's thesis, it can be argued that the gen-
A40

=3 

O

0.02

DYNAMIC AND DESCRIPTIVE STUDIES OF HILLSLOPES

10

5.0

2.0

<> 1.0

0.5

0.2

0.1

0.05

0.01 0.02

Symbol 

NF-2 

PC-1 

NF-1 

BL-1 

PC-3 

BL-2 

PC-2

Site name

New Fork River Site 2 

Pole Creek Site 1 

New Fork River Site 1 

Boulder Lake Site 1 

Pole Creek Site 3 

Boulder Lake Site 2 

Pole Creek Site 2

Slope 

0.0290 

.0960 

.1000 

.1880 

.2080 

.3315 

.3320

20 50 100 200 500 1000 2000 20 50 100 200 500 1000 2000

REYNOLDS NUMBER /R=

FIGURE 39. Summary curves of Froude number and velocity ratio as a function of Reynolds number, field sites.

CQ

Runoff = 2.0 in. per hr

\

0 80 160 240 320 400 480

DOWNSLOPE DISTANCE, IN FEET

FIGURE 40. Hillslope profiles for various runoff rates; downslope distance shown is approximate for values of runoff shown.
THE HYDRAULICS OF OVERLAND FLOW ON HILLSLOPES

CD

I I

Low initial gradient

High initial 

gradient

Turbulent flow 

(Concave profile)

Laminar flow 

(Convex profile)

Mixed or disturbed flow 

(Straight profile)

40 80 120 160 

DOWNSLOPE DISTANCE, IN FEET

200 240

FIGUEE 41. Hillslope profiles for various initial gradients; downslope distance shown is approximate for a runoff rate of 2.0

inches per hour.

eral absence of rilling in the field area is related to the 

erosion rate necessary on the reach of slope investigated 

to keep in downcutting equilibrium with other slopes 

within the drainage system. Under conditions of dynamic equilibrium, the behavior of individual hydraulic 

parameters need not be elaborated. The requirement 

is that there is an interaction among all of the variables 

to promote those flow conditions of depth and velocity to maintain equilibrium. Data for the present 

investigation indicate that velocities sufficient to cause 

rilling never occurred, and figure 33 illustrates well 

that velocities in overland flow are indeed low. But the 

principle involved is that velocities were low because 

depths were relatively great; the increase in depth is 

related to its role in the interaction of all variables.

Rills may or may not develop on unrilled surfaces if 

some threshold is exceeded which causes a change in the 

degradation rate. Such a threshold may be exceeded, 

for example, because of climatic change, but equilibrium 

could be maintained by equally altering the erosion rate 

throughout the drainage system. It is interesting to note 

that even at the high intensity of rainfall applied to the 

test plots, a threshold was not exceeded with an external 

variable (rainfall intensity and duration) which was 

sufficient to cause rilling. This would imply that the

potential for increased erosion (supplied by greater rainfall intensities and durations than are probably nature!) 

was absorbed by increased depths of flow rather than 

by higher velocities and accelerated erosion by rillir'?. 

To maintain this equilibrium, each slope had developed 

both a form and a resistance to flow, manifested in a 

complex interaction of vegetation and microtopograpHc 

form, to which the depth and velocity components of 

overland flow must adjust.

Schumm (1962) discussed the development of resistance to flow to maintain equilibrium between pediments 

and hillslopes in an analysis of miniature pedimerts 

developed on badland topography in South Dakota. 

Using the Manning formula (eq 16) to estimate velocity, 

Schumm applied a value of Manning's n to the rougher 

but more steep hillslopes which was three times greater 

than the value of n for the smoother pediment surfaces. 

(The actual values of n used by Schumm were probal^y 

low, but the relative order of magnitude appears reasonable.) The pediment slopes were about eight times less 

steep than the hillslopes. Assuming that the depth of 

the sheet of water moving over the hillslope was the 

same as that over the pediment, the computed value of 

velocity was the same for the hillslopes as for the pediments. Thus, in the case of the pediment, the decrease
A42 DYNAMIC AND DESCRIPTIVE STUDIES OF HILLSLOPES

in roughness apparently compensates for the decrease 

in slope angle. Such mutual adjustment of the component variables is the key to equilibrium.

This example by Schumm and the data from figure 

39 of this report showing values of the Froude number 

and its downslope change should serve to discredit the 

existance of a hydraulic jump as overland flow on natural hillslopes passes from a steep slope to a moderate 

or flat slope. A hydraulic jump occurs as flow goes from 

supercritical to subcritical, but Schumm's example 

shows no decrease in velocity at the base of the steep slope 

because changes in resistance to flow compensate for the 

smaller value of slope. And the data of figure 39 show 

that the value of the Froude number for natural slopes, 

even steep slopes, is on the order of 0.1 and is essentially 

constant over the length of the slope. Although it is 

possible to have supercritical flow in river channels, 

especially with flash flooding in ephemeral channels, it 

is unlikely that overland flow is ever supercritical and 

thus never offers the opportunity for a hydraulic jump.

EROSION AND LAMINAR FLOW

The sediment concentrations observed in the samples 

taken during this study illustrate the ability of overland flow to erode and transport sediments. The analytical results of the several sediment samples from each 

site are included in table 5 and are summarized as averages for each site in table 6. The average values of 

sediment and organic content from table 6 show no

TABLE 5. Analytical results of sediment samples from overland 

flow field sites

Site No.i

PC-1-.-..

9

3... 

NF-1......

2......

BL-1......

9

t

Time = se 

Date (min- 

(1967) utes) o 

a 

C

... 6-27

6-27 

6-27 

6-28 

6-28 

... 7-14

7-14 

7-15 

... 7-19 ..

7-19 ..

7-19 ..

... 7-29

7-29 

7-29 

7-29 

7-30 

7-31 

... 8-18

8-18 

8-18 

8-18 

... 9-27

9-27 

9-27 

9-27 

... 9-28

9-28 9-28

35 

65 

129 

25 

85 

80 

85 

25

24 

34.7 

82 

119 

15 

150 

48 

79 

176 

270 

56 

80 

128.5 

232 

30 

45 

87

Total 

diment Sediment content 

and of total sample 

rganic

mg/1) 3 (percent)

31 

113 

68 

43 

83 

35 

24 

75 

25 

24 

29 

288 

184 

41 

36 

160 

49 

24 

10 

45 

9 

10 

14 

7 

4 

81 

87 

93

33

38 

20 

23 

38 

86 

79 

88 

12 

8 

24 

90 

92 

94 

89 

94 

90 

82 

70 

96 

75 

68 

69 

62 

50 

88 

83 

89

Organic content 

of total sample

(mgA) 3 (percent) (mg/1)3

10 

42 

14 

9.7 

31 

30 

19 

66 

3.0 

2.0 

6.9 

260 

170 

39 

32 

150 

44 

20 

7 

43 

7 

7 

10 

4 

2 

71 

72 

83

67 

62 

80 

77 

62 

14 

21 

12 

88 

92 

76 

9.9 

7.6 

5.8 

11 

6.4 

9.6 

18 

30 

4 

25 

32 

31 

38 

50 

12 

17 

11

21 

71 

54 

33 

52 

4.8 

5.0 

9.3 

22 

22 

22 

28 

14 

2 

4 

10 

5 

4 

3 

2 

2 

3 

4 

3 

2 

10 

15 

10

1 Site numbers: PC, Pole Creek, NF, New Fork River, and BL, Boulder Lake.

2 Time is from beginning of rainfall application.

3 Milligrams per liter by weight.

apparent correlation with the ground slope at the site 

(table 6) or with the rainfall and runoff rates (table 3). 

The range of runoff rates in the present study is perhaps 

too limited to show a correlation. However, it has been 

shown (for a summary of investigations, see Smith and 

Wischmeier, 1962) that a few high intensity storms 

cause a high proportion of total soil erosion. That is, 

erosion is caused more by the number of high intensity 

storms than by the total volume of runoff. Although 

the present data show no apparent correlatior of sediment concentration with slope, other investigators (see 

Smith and Wischmeier, 1962) have shown soil erosion 

to increase with increasing slope. The upper limit of 

slopes reported by Smith and Wischmeier was 18 percent (about 10 degrees).

In the present investigation, resistance to f ow was 

such that downslope profiles of depth and velocity 

were only negligibly influenced by slope. The similarity between field plots in the downslope profiles of 

depth and velocity is responsible in part for the lack 

of correlation of erosion rates to slope. Also responsible 

is the differences in vegetation density between sites. 

The average values of sediment concentration from 

table 6 correlate well with the density of vegetation 

except for the data of New Fork River Site 2. Ponding 

occurred in the lower 8 feet of this site and much of the 

sediment load of the runoff settled out as velocities 

were lowered. The correlation of sediment concentrations with vegetation density at the other six sites, 

however, illustrates the importance of grourd cover 

for prevention of erosion. Smith and Wischmeier (1962) 

summarize some earlier investigations on the relation 

of plant cover to erodibility and generally report 

decreasing soil losses for increasing densities of vegetation. It becomes apparent that the interaction of 

variables may mask the effects of any one variable. 

For example, a nearly flat bare surface may contribute 

as much sediment as a steeper, more vegetated slope. 

For the present data, if vegetation is held constant, 

ground slope does appear related to sediment concentrations. Comparison of Boulder Lake Site 1 to Pole 

Creek Site 2 and Pole Creek Site 2 to Boulder Lake Site 2 

illustrates that for the same vegetation density, sediment concentrations in the runoff increase vdth increased slope angle.

One important observation is the higher concentrations of sediment in the initial runoff and the relatively rapid decrease in concentrations during the 

remainder of the runoff. Unfortunately, the data of 

table 5 do not entirely confirm this observation because 

of a deficient number of samples collected during the 

early stages of runoff. Within the limitations of the 

present investigation, this observation is best illustrated by the data of New Fork River Site 1 included
THE HYDRAULICS OF OVERLAND FLOW ON HILLSLOPES

TABLE 6. Average values of sediment sample analyses compared 

to ground slope and vegetation cover at overland flow field sites

[Content in milligrams per liter by weight]

Site name

New Fork River Site 2.... 

Pole Creek Site 1.. ...... .

New Fork River Site ! .. 

Boulder Lake Site 1 _ ....

Pole Creek Site 3 _ ...

Boulder Lake Site 2__ _ ..

Pole Creek Site 2.. ........

Ground 

slope 

(ft per ft)

0.0290 

.0960

.1000 

.1880

.2080

.3315

.3320

Estimated 

vegetation 

covej 

(percent)

8 

20

10 

28

35

22

28

Total 

sediment 

and 

organic 

content 

(mg/1)

22.1 

67.6

126.3

8.8

26.0

87.3

44.7

Sediment 

content 

of sarrple 

(mg/1)

19.3 

21.3

115.8 

5.8

4.0

75.3

38.3

Organic 

content 

of sample 

(mgA)

2.8 

46.2

10.5 

3.0

22.0

11.7

6.4

in table 5. From a sediment concentration of 228 

milligrams per liter after 24 minutes of runoff, the 

concentration decreases to 184 milligrams per liter at

35 minutes, 41 milligrams per liter at 82 minutes, and

36 milligrams per liter at 119 minutes. Similar results 

were found by Lowdermilk and Bundling (1950). 

Their studies indicate that the erosion rate decreases 

throughout a simulated rainstorm as the finest particles were removed in surficial flow. Their removal led 

to the domination of the soil surface by larger particles 

until ultimately an erosion pavement was formed. 

Similar results were also found by Swanson, Dedrick, 

and Weakly (1965). However, the present data do not 

strictly support the pavement theory. Using the data 

of Pole Creek Site 2 and New Fork Kiver Site 1 from 

table 5, comparison of sediment concentrations observed early in the runoff from a second day of sprinkling to the concentrations at the end of the previous 

day's sprinkling shows the second day's initial concentration to be considerably higher than the preceding 

day's final concentration. Since a new number of 

fine-grained particles could not be produced in the 

short interval between sprinklings, higher initial sediment concentrations appear to be related to some 

process making soil particles ready for transport. Over 

a single night, as in the present investigation, the 

responsible process is most likely a wetting-drying 

effect on the soil. Between natural storms, processes 

making soil ready for transport would include wettingdrying, wind, frost action, churning by animals, and 

even weathering where intervals are long.

Splash erosion by raindrop impact before a protecting layer of surface detention is built up is also important in the initial high sediment concentrations (Borst 

and Woodburn, 1942). However, the present data do 

not fully confirm the conclusion of Borst and Woodburn 

that raindrop splash, not runoff, is responsible for soil 

loss. A number of other investigators have shown the 

importance of raindrop impact on erosion (for a summary, see Smith and Wischmeier, 1962). However, 

raindrop impact with very little transporting medium

by runoff is not likely to be an effective agent of eros'on. 

As surface detention builds up everywhere and depths 

increase downslope, the effect of waterdrop impact 

lessens. The data of Palmer (1965) indicate that for 

the size of waterdrops and depths of flow in the present 

investigation, there was probably little splash erosion 

due to raindrop impact.

The values of sediment concentration in table 5 

are adequate proof that overland flow can be effective 

as an eroding and transporting agent. It is interesting 

to note that the values of Reynolds numbers from all 

field tests were well within the regime of laminar f ow 

as defined in figure 11. As previously mentioned, overland flow is disturbed by rainfall and flow in the concentrations of water have higher Reynolds numbers 

than the average Reynolds number for a given downslope distance. The actual characteristics of flow are 

somewhere between laminar and turbulent and as indicated earlier in this report; the flow is primarily laminar in upslope reaches and becomes more turbulent as 

slope length increases. Regardless of the exact characteristics of overland flow, sediment was being eroded 

and transported.

Sediment transport occurring at the low value? of 

Reynolds number are in agreement with Bagnold's 

(1955) observation that turbulence is not an essential 

requisite of sediment transport. The present data tend 

to invalidate King's (1953) canon 27 of landscape evolution that laminar flow is nonerosive. That a large volume of material is indeed eroded and transported by 

overland flow is strikingly illustrated by the lower 

photograph in figure 6 of the delta formed by deposition of sediments eroded upslope in the plot at New 

Fork River Site 1. The photograph, taken after about 6 

hours of simulated rainfall at an intensity of 8.5 inches 

per hour, does not show all of the eroded and transported sediment as sediment concentration data of 

table 5 show high concentrations in the runoff water.

The average values of sediment content in tabta 6 

show great variability between different field sites. 

Although the values shown are valid only for the observed conditions of plot size and the hydrologic, geologic, and vegetation characteristics of the sites, a 

sediment production corresponding to the observed 

sediment concentrations of runoff can be computed. 

Using an average value of 55 milligrams per liter s?-diment content, runoff of 1 inch per hour for 1 hour would 

yield 4 tons of sediment per square mile. The extrapolation of plot data to watersheds is questionable and 

the above computation should be considered only illustrative of the large amount of sediment production 

from overland flow with small sediment concentrations.
A44 DYNAMIC AND DESCRIPTIVE STUDIES OF HILLSLOPES

SUMMARY OF FINDINGS

Extremely shallow uniform flows over sloping planes 

are characterized by laminar flow at Reynolds numbers 

less than 1,500 (or somewhat greater) and turbulent 

flow at Eeynolds numbers higher than 6,000 (or somewhat less). For constant widths and smooth surfaces, 

increases in depth absorb about one-third of increases 

in discharge for laminar flows, two-thirds for turbulent 

flows, and velocity absorbs the remainder. Transitional 

flow exists between laminar and turbulent flow; the 

range in Eeynolds number accompanying transitional 

flows is dependent on depth of flow and nature of surface roughness. Surface roughness tends to increase 

depth and, for the shallow flows investigated, even 

apparently smooth surfaces impart an element of 

roughness. For laminar flow on constant slopes, resistance to flow (expressed by the Darcy-Weisbach friction factor) decreases exponentially by a factor of 1 

with increases in discharge, but for turbulent flows, 

resistance to flow decreases only slightly with increases 

in discharge. Transitional flows show values of resistance to flow intermediate between laminar and turbulent flow. Absolute values of resistance to flow are 

dependent on the magnitude of the relative roughness 

of the flume surface. The ratio of the mean velocity 

to surface velocity is equal to the theoretical values of 

0.8 for turbulent flow and 0.67 (or somewhat less) for 

laminar flow.

For shallow flows with increasing downslope discharge due to uniform simulated rainfall over the flume 

area, depths of flow are increased because of the retarding influence of falling raindrops. The amount of the 

increase in depth varies, but for the laboratory conditions investigated the depths of flow due to simulated 

rainfall averaged about a 50 percent increase over 

depths of uniform flow. For the short lengths of slopes 

investigated in the laboratory, all sprinkled tests are 

in the laminar regime of flow as defined by the Eeynolds 

number criterion established by uniform flow tests. 

However, the flows are not truly laminar because of the 

disturbing effect of falling raindrops. For this disturbed 

type of flow, data indicate that depth absorbs somewhat 

less of the increase in discharge for smooth surfaces and 

somewhat more for roughened surfaces when compared 

with uniform flows hi the same channel. For disturbed 

flow compared to uniform flow, falling raindrops roughly 

doubles the resistance to flow. For these same disturbed 

(but nearly laminar) flows, the Froude number increases 

exponentially as the square of the increase in downslope 

discharge. Generally, the ratio of the mean velocity to 

surface velocity is about 0.5, which is less than the theoretical value of 0.67 for laminar flow. Thus, mean velocity is retarded more than surface velocity, but this 

effect decreases as depths increase.

Overland flow resulting from rainfall on natural slopes 

is characterized by several lateral downslope concentrations of flow rather than uniform sheet flow. These 

concentrations of flow are dictated by the resistance to 

flow (obstacles) developed on each slope. The dcwnslope 

increases in depth that resulted with increasing discharge varied between field sites, but they averaged an 

exponential value of about %. Increases in velocity 

absorbed the remainder of the increases in discharge, 

Values of resistance to flow for the several field sites 

ranged from positive to negative downslope changes in 

downslope frictional resistance, but the average value 

indicates no change in downslope resistance to flow. 

Values of resistance to flow are of a magnitude approximated by a Darcy-Weisbach friction factor cf 100, a 

Manning n of 0.5, or a Chezy C equal to 2.0. Actual 

values of resistance vary between sites and between 

downslope distances, but the average values listed above 

for the field experiments are of a magnitude 10 times 

greater than the laboratory data for sprinkled tests. 

On the average, Froude numbers in overland flow were 

less than 0.2 and averaged close to 0.1. From these 

values of Froude number, it appears unlikely that 

supercritical flow ever occurs as overland flow on natural hillslopes. The ratio of the mean velocity to surface 

velocity is somewhat suppressed below laboratory data 

and generally remains below a value of 0.5.

A theoretical model of overland flow, based on most 

probable statistical concepts of minimizing the variance 

in depth, velocity, shear, and friction, was evaluated 

for the condition of no constraint on slope and yielded 

(1) a downslope decrease in slope gradient for turbulent 

flow and (2) a downslope increase in slope gradient for 

laminar flow. The application of these two cases to overland flow on natural hillslopes, and the interpo^tion of 

intermediate conditions of flow, indicate that hillslope 

profiles should be convex at the top, straight in a middle 

segment of slope, and concave in lower reaches of slope. 

The length of the convex, straight, and concave segments of slope, and the steepness of slope, arc related 

to the runoff rate and the initial slope gradient. Thus 

the shape of hillslope profiles is controlled by their climatic and geologic environments.

It is suggested that each slope within a drairage system is in dynamic equilibrium with other slopes within 

the system. Downcutting of slopes hi equilibrium maintain erosion rates which are comparable with other 

slopes in the system. On unrilled slopes, the resistance 

to flow develops such that depths absorb most of the 

downslope increase in discharge and velocities1 remain 

small enough to prevent rilling. Although no rilling 

occurred on the field test plots, analysis of sediment
THE HYDRAULICS OF OVERLAND FLOW ON HILLSLOPES A45

samples shows that overland flow at low Reynolds numbers is capable of eroding and transporting sediment.

In summary, it appears that overland flow may be 

described by a downslope increase in depth which is 

proportional to about the two-thirds power of downslope increase in discharge. Increase in downslope velocity absorbs the remainder of the increase in discharge. 

When the variance of the parameters of hydraulic 

geometry are jointly minimized, the slope profile of 

overland flow should be convex at the hilltop, straight 

in a middle reach of slope, and concave for the remainder of the slope length. The dimensions (relief and 

length) of each slope segment are related to the climatic 

and geologic environvent of the drainage system. It is 

suggested that all slopes in a drainage system are in 

dynamic equilibrium; that is, all slopes are vertically 

downcutting at the same rate. This too is controlled 

by the climatic and geologic environments of the slope.

REFERENCES

Bagnold, R. A., 1955, Some flume experiments on large grains 

but a little denser than the transporting fluid, and their 

implications: London, England, Inst. Civil Engineers Proc., 

Paper 6041, p. 174-205.

Behlke, C. E., 1957, The mechanics of overland flow: Stanford, 

Calif., Stanford Univ. Ph.D. dissert., 49 p.

Borst, H. L., and Woodburn, Russell, 1942, The effect of mulching and methods of cultivation of runoff and erosion from 

Muskingum silt loam: St. Joseph, Mich., Agr. Eng., v. 23, 

p. 19-22.

Chen, Cheng-lung, 1962, An analysis of overland flow: East 

Lansing, Michigan State Univ. Ph. D. dissert.

Emmett, W. W., and Leopold, L. B., 1964, Discussion of geometry of river channels: Am. Soc. Civil Engineers Proc. v. 90, 

no. HY5, p. 277-285.

Gunn, Ross, and Kinser, G. D., 1949, Terminal velocity of water 

droplets in stagnant air: Jour. Meteorology, v. 6, p. 243-248.

Hack, J. T., 1960, Interpretation of erosional topography in 

humid temperate regions: Am. Jour. Sci., v. 258-A, p. 80-97.

Hadley, R. F., McQueen, I. S., and others, 1961, Hydrologic 

effects of water spreading in Box Creek basin, Wyoming: 

U.S. Geol. Survey Water-Supply Paper 1532-A, p. 1-48.

Horton, R. E., 1933, The role of infiltration in the hydrologic 

cycle: Am Geophys. Union Trans., v. 14, p. 446-460.

Horton, R. E., 1936, Hydrologic interrelations of water and soils: 

Soil Sci. Soc. America Proc., v. 1, p. 401-437.

Horton, R. E., 1938, The interpretation and application of runoff plot experiments with reference to soil erosion problems: 

Soil Sci. Soc. America Proc., v. 3, p. 340-349.

Horton, R. E., 1945, Erosional development of streams and their 

drainage basins; hydrophysical approach to quantitative 

morphology: Geol. Soc. America Bull., v. 56, p. 275-370.

Horton, R. E., Leach, H. R., and Van Vliet, R., 1934, Laminar 

sheet flow: Am. Geophys. Union Trans., pt. 2, p. 393-404.

Izzard, C. F., 1944, The surface profile of overland flow: Am. 

Geophys. Union Trans., v. 25, p. 959-968.

Izzard, C. F., 1946, Hydraulics of runoff from developed surfaces: 

Washington, D.C., Highway Research Board, Nat'1. Research Council, Nat'1. Acad. Sci., 26th Ann. Mtg., Pr^c.,

17 p. (repr.). 

Izzard, C. F., and Augustine, M. T., 1943, Preliminary report

on analysis of runoff resulting from simulated rainfall on a

paved plot: Am. Geophys. Union Trans., v. 24, p. 500-509. 

Keulegan, G. H., 1944, Spatially variable discharge over a sfoping plane: Am. Geophys. Union Trans., v. 25, p. 956-95?. 

King, L. C., 1953, Canons of landscape evolution: Geol. Soc.

America Bull., v. 64, p. 721-752. 

Kuichling, Emil, 1889, The relation between the rainfall and the

discharge of sewers in populous districts: Am. Soc. Civil

Engineers Trans., v. 20, p. 1-60. 

Langbein, W. B., 1964, Geometry of river channels: Am. Foe.

Civil Engineers Proc., v. 90, No. HY2, p. 301-312. 

Langbein, W. B., 1965, Closure to Geometry of river channels:

Am. Soc. Civil Engineers Proc., v. 91, No. HY3, p. 297-ri3. 

Laws, J. O., 1941, Measurements of fall velocity of water droplets and raindrops: Am. Geophys. Union Trans., v. 22, p.

709-721. 

Laws, J. O., and Parsons, D. A., 1943, Relation of raindrop size

to intensity: Am. Geophys. Union Trans., v. 24, p. 452-4<50. 

Leopold, L. B., Emmett, W. W., and Myrick, R. M., 1966, Channel and hillslope processes in a semiarid area, New Mexico:

U.S. Geol. Survey Prof. Paper 352-G, p. 193-253. 

Leopold, L. B., and Langbein, W. B., 1962, The concept of

entropy in landscape evolution: U.S. Geol. Survey P^of.

Paper 500-A, 20 p. 

Leopold, L. B., and Maddock, Thomas, Jr., 1953, The hydraulic

geometry of stream channels and some physiographic implications: U.S. Geol. Survey Prof. Paper 252, 57 p. 

Lowdermilk, W. C., and Sundling, H. L., 1950, Erosion pavement

formation and significance: Am. Geophys. Union Trans., v.

31, p. 96-100. 

Maddock, Thomas, Jr., 1969, The behavior of straight o-ien

channels with movable beds: U.S. Geol. Survey Prof. Ps.per

622-A, 70 p. 

Meyer, L. D., and Monke, E. J., 1965, Mechanics of soil erosion

by rainfall and overland flow: Am. Soc. Agr. Engineers

Trans., v. 8, p. 572-577, 580. 

Owens, W. M., 1954, Laminar to turbulent flow in a wide ooen

channel: Am. Soc. Civil Engineers Trans., v. 119, p. 1157-

1175. 

Palmer, R. S., 1965, Waterdrop impact forces: Am. Soc. Agr.

Engineers Trans., v. 8, no. 1, p. 70-72. 

Parsons, D. A., 1949, Depths of overland flow: Soil Conserv.

Serv. Tech. Paper 82, 33 p. 

Ree, W. O., 1939, Some experiments on shallow flows over a

grassed slope: Am. Geophys. Union Trans., v. 20, p. 653-f 56. 

Richey, E. P., 1954, The fundamental hydraulics of overland

flow: Stanford, Calif., Stanford Univ. Ph. D. Dissert., 62 p. 

Schumm, S. A., 1962, Erosion on miniature pediments in Badlands National Monument, South Dakota: Geol. Foe.

America Bull., v. 73, p. 719-724. 

Smith, D. D., and Wischmeier, W. H., 1962, Rainfall ersoion:

Advances in agronomy, v. 14, p. 109-148. 

Smith, H. L., and Leopold, L. B., 1942, Infiltration studies in

the Pecos River watershed, New Mexico and Texas: Soil

Sci., v. 53, p. 195-204. 

Straub, L. G., 1939, Studies of the transition region between

laminar and turbulent flow in open channels: Am. Geopl ys.

Union Trans., v. 20, p. 649-653.
A46 DYNAMIC AND DESCRIPTIVE STUDIES OF HILLSLOPES

Swanson, N. P., Dedrick, A. R., and Weakly, H. E., 1965, Soil White, J. F., 1966, Convex-concave landscapes: A geometrical

particles and aggregates transported in runoff from simulated study: Ohio Jour. Sci., v. 66, no. 6, p. 592-608.

rainfall: Am. Soc. Agr. Engineers, v. 8, p. 437-440. Woo, Dah-Cheng, and Brater, E. F., 1962, Spatially varied flow 

Tracy, H. J., and Lester, C. M., 1961, Resistance coefficients from controlled rainfall: Am. Soc. Civil Engineers Proc., v.

and velocity distribution smooth rectangular channel: U.S. 88, HY6, p. 31-56.

Geol. Survey Water-Supply Paper 1592-A, 18 p.
SUMMARY OF DATA
A48 DYNAMIC AND DESCRIPTIVE STUDIES OF HILLSLOPES

A. Vegetation type and relative density of cover at field sites 

[Values of density shown are based on a relative scale of 1 to 5 for each quadrat. T represents trace and is scored as 0.5]

Plant

1 2 3

Quadrat No.

4 5 6 7 8 9 10

Pole Creek Site 1 '

Antennaria.. .... ______ 

Eriogonum,-- _ ______ 

Poa secunda . ___ ____ _ __ 

Stipa comato 

Taraxacum officinale ___ 

Artemisia tridentata _ _ _ 

Agropyron dasystachum _ _ _ _ _ _ _ 

Agoseris - _ _______ __ _ __ 

Sitanion hystrix...-. . _ _ ___

Astragalus _ ____ ____ _ Misc. annuals _______

Unknown forb_____.__ _ ______

_ -__ _ Buckwheat 

__ ____ Bluegrass__. 

_ ______ Needlegrass 

_______ Dandelion.. 

___ ____ Sagebrush.. 

___ ____ Wheatgrass. 

___ ____ Agoseris___. 

_ _____ Bottlebrush.

____ ___ Pea. ______

._---___- 2 2 _

_________ 1 __.. 

_ ______ 2 T 

._-___-_. 1 ___ 

.-__-_-__ 1 T _

.____ _ _ 1 1

1 

1 

1 

T

1

1

1

T

. 2 .

1

3

1 

T

1

1

1 

2 

1

1

1

1 . 

1

1

. 1 _

1

T

. 2

1 

1

. T

7 

7 

6 

5. 5 

3 

2.5 

2 

1 

1

. 5

8

1

15.7 

15.7 

13.4 

12.3 

6.7 

5. 6 

4.5 

2. 2 

2.2

1. 1

17.9

2.2

Pole Creek Site 2 2

Antennaria... _ ________________

Sestuca idahoensis.... . ________

Stipa lettermani.

Agropyron spicatum _____ ____

Poa secunda. __ _ _ _

Taraxacum officinale.. . _ _ _

Artemisia tridentata _ _ _____

Achillea lanulosa.... _________

Agoseris ____ _____ ______ __

Stipa comata ______ _ _____

Bidens cernua ____ _ _ ___ ___

Kosa spp___ __ _________

Lupinus _ _______ __

Misc. annuals --_____-______ _

_ _____ Festuca __.

____ Needlegrass

____ _ _ Wheatgrass.

_______ Bluegrass__.

__ _ __ Dandelion..

_ __ ___ Sagebrush..

___ ____ Agoseris _ _.

_ _ _ _ _ _ _ Needlegrass.

__ _ ___ Lupine _ _.

_____________ 2

________ __ 2

_____________ 2 _

____________ 1 _

.___---_.-___ 1

_________ T _____

_ _ _ _ T _

1

3

1

T

2

2

1

T

T

T

1

. 1

1

1

1

1

1

T

T

3

2

2

1

T

3

2

1

T

.___

1

2

2

1

1

1

2

1

1

. 1

_.__

T

. T

. T

T

15. 5

15

8

3

3

3

1. 5

1. 5

1. 5

1.5

1

1

. 5

3

26. 3

25.4

13.6

5. 1

5. 1

5. 1

2. 5

2. 5

2. 5

2.5

1.7

1.7

.8

5. 1

Pole Creek Site 3 "

Carex. __ _ ______ _____ _

Taraxacum officinale. ____

Stipa lettermani. ___ ___ _____ _

Festuca idahoensis.... ________

Poa canbyi. _________ _ ____ _

Stipa comata _________ _ ___

Antennaria. . ... _ _________

Astragalus __ ________

Lupinus _ ____________

Achillea lanulosa....... _____

Agropyron spicatum ___________

Artemisia tridentata . ....... .

Misc. annuals _ ___ ______

______ . Sedge____ _

_______ Dandelion. .

_ Needlegrass.

________ Festuca. _.

_ ____ Bluegrass...

_ _ _ _ Needlegrass.

. ______ Pea _ _ _ .

_ _ Lupine. ___

________ Wheatgrass.

________ Sagebrush .

.---_--._____ 1

_____________ 2 _

. ____ __ 1 _

________ 1 1 _

._____-_____. 1 _

________ 1 _____

2

1

1

?,

T

1

2

2

1

T

1

3

2

?,

. 1 .

T

T

1

1

T

1

1

T

1

2

T

2

T

1

T

1

1

T

T

1

1

T

2

1

T

T

T

1

1

1

1

T

. 1

. 1

1

11

10.5

9

5. 5

4

4

3

3

2

1

1

. 5

6.5

18. 0

17.2

14. 8

9. 0

6. 6

6. 6

4.9

4.9

3. 3

1. 6

1. 6

.8

10.7

New Fork Hirer Site 1 4

Artemisia tridentata _ _________

Agropyron dasystachum ________

Carex __ ________________ ____

Castilleja __ _____ _ _ _

Blitum capitatum _ _____ _____

Chrysanthemum. . ____________

_ ______ Sagebrush .

__ _____ Wheatgrass.

________ Sedge____ .

___ _ _ Paintbrush

_________ 2 3

.--_-_-__ 2 3

____________ 1 _

__-_--. 1 _____

_ ___ 1 __ __

3

3

2

1

1

T

2

1

1

1

1

T

T

1

1

T

4

2

T

2

1

?,

T

T

1

____

20.5

16

5. 5

1

2.5

1

44. 1

34.4

11.8

2.2

5.4

2. 2

New Fork Rirer Site 2 !

Carex ___ ____ .. ___________

Sitanion hystrix...... . . . ___

Poa _____ _ _ ___ _ _ _

______ Sedge. __ _

_ _ _ Bottlebrush.

-__ __ Bluegrass __

_________ 3 1

_ ___ ___ 1 _

1

1

1

1

1

1

T

?, ?,

1

1 1

1 2

13

3

3.5

2

60. 5

13.9

16. 3

9. 3

See footnotes at end of table.
THE HYDRAULICS OF OVERLAND FLOW ON HILLSLOPES 

A. Vegetation type and relative density of cover at field sites Continued

A49

Plant Common name - 

1 2

Quadrat No.

3 4 5 6 7 8 9 10

Total Percent

Boulder Lake Site 1 6

Antennaria- __ _ ______ __ -

._ _____ Bluegrass.-.

._ __ __ _ Sedge...--.

._ ______ 2 2

_________ 2 .___

T

_-______-._- T .

3 

1 

1

1

2 

1 

2 _

2

1 

1

"f"

1

2 

1 

1

1

T 

1 

1 

1

T

4

""f" 

T

T

4 1 

3 3 

1 1 

1 ___. 

_ 1

21. 5 

13 

7 

3.5 

2 

6

40. 6 

24. 5 

13.2 

6.6 

3.8 

11.3

Boulder Lake Site 2 '

Poa -__ -______---_---__-__-

Paranychia depressis~ _ _.

Misc. annuals- __ _ ____.__.

.__ _ _ _ Bluegrass.-.

__ _ ____ Buckwheat.

.__ _ -_ _ Rushes. __.

._-__.___ 2 3

.___._______- 1

________ T 1 .

2

_ T -__.

3 

1

1

2

. 1 _

T

2 

1

T

1 

2

T

T

1 

2 

1

T

2 

3

T

1 _

2 3 

1 _ _

___ 1

21 

11 

2. 5 

2 

1 

1 

. 5 

5

47. 8 

25. 0 

5.7 

4. 6 

2.3 

2. 3 

1. 1 

11.3

1 Estimate of overall average density, 20 percent. No overstory cover on site.

2 Estimate of overall average density, 28 percent. Overstory of Artemisia Mdentata 

(sagebrush), 42.6 percent.

s Estimate of overall average density, 35 percent. Overstory of Artemisia Mdentata 

(sagebrush) and Populus tremuloides (aspen), 23.6 percent.

4 Estimate of overall average density, 10 percent. Overstory of Artemisia Mdentata 

(sagebrush), 49.9 percent.

s Estimate of overall average density, 8 percent. Overstory of Artemisia Mdentata 

(sagebrush) not measured.

6 Estimate of overall average density, 28 percent. Overstory of Artemisia Mdentata 

(sagebrush) not measured.

7 Estimate of overall average density, 22 percent. Overstory of Artemisia Mdentata 

(sagebrush) not measured.
A50 DYNAMIC AND DESCRIPTIVE STUDIES OF HILLSLOPES

B. Example of data from measurements of surface velocity, 

Pole Creek Site 3

Velocity (fps)

Downslope stationing (ft)

0

1__

2_ ________________________________

3__ _______________________________

4__ _ _

5. ________________________________

6_ ______________________________

7__ _______________________________

8_ ________________________________

9_ ________________________________

10_ __________-_-___-___---_-__-_..

12

13__ ______________________________

14_ ______________________________

15. _______________________________

16_ __________---___--__-_____---_.

17_ _______________________________

18_ -_-_________-___-_-____--_-___.

19. _-__-___-___-_-___-_-_____---..

20_ _______________________________

21_ _______________________________

22_ ______________________________

23_ _______________________________

24. _______________________________

25- ________-_-____--_______._-_-_.

26_ __-____-__-.-___-___-_-__--_-_

27

28_ _______________________________

29_. ______----_____-_-_-_---_--_.

30- -_-_-___-_-_____-___-_-_-_-.-_.

31_ ______________________________

32_ _______________________________

33_ _______________________________

34_ ______________________________

35_ __.___-___________-___-_-__.-_.

36---________ _ _--__ -.

37- --____-_-__-__ _-__ _-_-_ .

38_ ___________________ _______-_-.

39__ ______________________________

40_ ________-_-_____-___._____-_-_.

41__ ______________________________

42_ ______________________________

43__ _____________________________

44_ ______________________________

45__ ______________________________

46_ _____________-_.________-_-_--.

47

48. ______________________________

Trial 1

0.071

. 053

. 125

.200

.200

.091

. 083

. 500

.250

.250

.250

.200

.333

.250

.167

.111

.250

. 167

.250

. 143

.167

.250

. 200

. 143

.200

.250

.143

.250

.200

.250

.167

.333

.333

.333

.333

.333

.333

.333

.333

.250

.333

.333

.250

. 200

. 200

. 200

.333

. 250

Trial 2

0. 200

. 100

. 072

. 250

. 148

. 167

. 100

. 091

. 200

.250

. 148

. 091

. 125

.250

. 100

. 125

. 250

. 250

. 167

. 167

. 167

. 250

. 143

. 143

. 200

. 500

. 333

.200

. 125

. Ill

. 125

. 250

. 200

. 167

.200

. 250

. 143

. 143

.250

. 167

. 143

. 250

.500

.500

. 500

. 250

. 143

. 250
THE HYDRAULICS OF OVERLAND FLOW ON HILLSLOPES A51

C. Example of data from depth measurements, in feet, Pole Creek Site 3

Transverse 

stationing 

(ft)

0.---- ._ ....

!-__.. --_ -._-

2--___ -_-_.

3_- _____-__ -.

4_ _.__.__.__..

5---- -_~-~.

6-. __.__.__.. .

7_-_. .._ -.....

Avo*

0. _-.__.-__.__

1_

2

3__ _ _-

4_-_._-__. -___..

5--__ -__- ..

6__

7

Ave______.

Downslope stationing

1

._._ 0. 000

___- .000

._._ .000

.- .000

._._ .014

._ .010

.___ .012

.___ .005

..._ .0051

25

.___ 0. 022

._._ .075

.___ .028

._-_ .018

.___ .034

.-_. .013

._._ .031

.-__ .029

.___ .0313

3

0. 000 

. 010 

. 000 

. 013 

. 021 

. 010 

.020 

. 000 

.0093

27

0. 038 

. 021 

. 034 

. 028 

. 026 

.020 

. 013 

. 008 

. 0235

5

0. 000 

. 010 

. 010 

. 000 

. 000 

. 015 

.025 

. 006 

. 0083

29

0.047 

. 062 

.008 

. 046 

. 037 

.026 

. 035 

. 004 

. 0356

7

0.010 

. 014 

. 004 

.011 

.000 

. 004 

.017 

.042 

. 0128

31

0. 012 

. 094 

. 042 

. 026 

. 017 

.055 

. 012 

.012 

. 0338

9

0. 013 

. 000 

. 003 

. 009 

.042 

. OOC 

.000 

. 015 

. 0103

33

0. 000 

. 047 

.057 

.058 

. 030 

. 005 

. 033 

. 009 

. 0299

11

0. 055 

. 061 

. 000 

. 000 

. 014 

. 021 

.000 

. 035 

. 0243

35

0 069 

. 054 

. 056 

. 052 

. 022 

. 033 

. 043 

. 013 

. 0428

13

0. 023 

. 040 

. 012 

. 000 

. 034 

. 009 

. 047 

. 036 

. 0151

37

0. 029 

. 084 

. 023 

. 054 

. 042 

.053 

. 036 

.025 

. 0433

(ft),

15

0. 002 

.095 

. 019 

. 000 

. 008 

.017 

. 004 

. 015 

. 0200

39

0.073 

. 065 

. 041 

.051 

. 040 

. 044 

. 023 

. 012 

. 0436

17

0. 004 

. 013 

.003 

. 006 

. 043 

. 010 

. 012 

. 018 

. 0142

41

0. 037 

. 061 

.059 

.027 

. 045 

. 037 

. 049 

. 005 

. 0400

19

0.026 

.024 

.028 

. 019 

.066 

. 042 

. 034 

. 024 

. 0329

43

0.044 

.056 

. 067 

. 102 

.067 

. 026 

.050 

. 033 

. 0556

21

0. 014 

. 020 

. 013 

. 000 

.030 

. 020 

. 024 

. 033 

. 0193

45

0. 027 

.034 

.055 

.078 

. 045 

. 065 

.038 

. 038 

. 0475

23

0.014 

. 040 

. 020 

. Ill 

. Oil 

. 024 

. 014 

. 046 

. 0350

47

0.092 

.057 

. 064 

. 012 

. Oil 

. 032 

. 058 

. 027 

. 0441
A52 DYNAMIC AND DESCRIPTIVE STUDIES OF HILLSLOPES

D. Summary of laboratory data for uniform flow 

[Flow: T, turbulent; L, laminar; r, roll waves (R, more pronounced)]

Kine- DarcyAverage Mean Surface Velocity matic Reynolds Froude WeisOach Chezy Manning 

Series and test Discharge depth, D velocity, velocity, ratio, Temp, T viscosity number, number, Slope, S friction coeffi- resistance Flow 

g(cfs/ft) (ft) F(fps) V. (fps) VIV, (° C) XltH.M R F (ft per ft) factor,// cient, C coeffl- 

(sq ft cient, n

per sec)

1-1.........

2..........

3.... ......

4

5... .......

6_. . ------

7.. .........

S... ........

2-1... 

2...........

3.. ........

4...... ....

5 

6.....-.--.

7

8 . 9 ... 

10... .......

3-1 

2.. ........

3...... .

I.. .........

5.. .....

6...... .

7 

8 .......

9.... .

4-1 

2... ........

3 ...... .

4... .

5 .

6 .

7 .......

8 ... ..

9... ... .

10 .

6-1... ........

2 ..... .

3... ...... ..

4 ..

5...... .... .

6 ... ....

7... ....... .

8..... ..... .

6-1 .......

2.. .

3 

4 .... ...

5 ...

6 .... ...

7 .......

8...... .... .

9... ...

7-1. .

2._ 

3 .

4.. ... .

5.. .....

6.. .

7.. .....

8...... ..

9.. .........

10 .

11 

12 ..

8-1..... ......

2.... .......

3 .... .

4 .......

5.. .....

6.. ...

7 .....

8.... ...

9...........

10 

11... .......

12 

9-1 

2.. ...

3.. .... ..

4 ..... .

6... ........

6.. 

1.. .........

8...... .... .

9 ...

10 

11 . 

12... .......

.... . 0.0460

 . .0310

...... .0208

..... . .0133

...... .0078

...... .0046

..... . .0023

...... .0013

...... .0493

...... .0366

...... .0264

...... .0209

...... .0131

...... .0091

...... .0049

.. .0026

...... .0016

..... . .0010

...... .0508

...... .0361

...... .0255

...... .0130

.. .0082

...... .0043

.0023

...... .0013

...... .0007

...... .0508

...... .0354

...... .0231

...... .0138

...... .0092

...... .0050

...... .0035

...... .0025

...... .0014

...... .0008

...... .0492

...... .0354

.... .. .0258

...... .0139

..... . .0088

...... .0040

...... .0022

...... .0012

...... .0505

...... .0367

...... .0243

. . .0126

...... .0087

...... .0044

...... .0023

..... . .0012

.... . .0011

...... .0510

..... . .0303

...... .0251

...... .0166

...... .0103

...... .0067

...... .0042

...... .0028

..... .0022

...... .0018

..... .0011

..... .0009

...... .0505

...... .0383

...... .0288

..... . .0207

..... .0138

 . .0098

...... .0066

...... .0044

-. .0031

. .0022

..... .0015

.... . .0009

..... .0524

..... .0388

..... .0287

.... . .0192

-. .0135

.... . .0095

..... .0069

.... . .0042

..... .0029

..... .0022

..... .0014

..... .0009

0.0435

.0357

.0286

.0205

.0146

.0130

.0104

.0089

.0279

.0227

.0186

.0164

.0115

.0092

.0076

.0065

.0053

.0044

.0223

.0186

.0140

.0095

.0080

.0064

.0049

.0036

.0031

.0193

.0156

.0122

.0081

.0069

.0061

.0055

.0050

.0035

.0029

.0179

.0146

.0115

.0079

.0069

.0057

.0049

.0042

.0225

.0186

.0144

.0105

.0091

.0071

.0058

.0034

.0036

.0240

.0180

.0162

.0129

.0104

.0073

.0062

.0053

.0045

.0039

.0036

.0029

.0275

.0235

.0197

.0168

.0134

.0107

.0082

.0065

.0057

.0050

.0044

.0039

.0340

.0277

.0230

.0194

.0159

.0131

.0095

.0076

.0069

.0063

.0050

.0043

1.057

.868

.727

.650

.531

.366

.219

.140

1.768

1.610

1.419

1.273

1.141

.984

.646

.409

.297

.226

2.281

1.947

1.643

1.378

1.025

.669

.463

.341

.224

2.629

2.266

1.893

1.698

1.334

.805

.640

.487

.386

.259

2.753

2.435

2.247

1.766

1.284

.705

.456

.282

2.244

1.969

1.681

1.198

.956

.616

.398

.353

.285

2.125

1.681

1.551

1.289

.997

.914

.667

.530

.488

.451

.301 ..

.317

1.835

1.629

1.459

1.337

1.034

.913

.800

.629

.534

.437

.340

.239

1.541

1.398

1.248

1.003

.849

.725

.723

.551

.413

.344

.281

.197

1.235

1.093

1.007

1.033

.820

.527

.330

.215

2.118

1.923

1.770

1.653

1.765

1.439

.977

.628

.421

.302

2.756

2.466

2.222

2.273

1.794

1.149

.719

.439

.269

3.125

2.913

2.586

2.740

2.230

1.449

1.345

1.005

.660

.481

3.750

3.209

3.061

3.226

2.620

1.635

1.111

.770

2.913

2.532

2.166

1.796

1.571

1.215

.808

.775

.619

2.727

2.206

2.041

1.729

1.478

1.345

1.149

.896

.946

.748

.404

2.390

2.135

1.875

1.700

1.463

1.330

1.268

1.271

1.003

.844

.661

.436

1.935

1.695

1.463

1.302

1.117

.998

1.113

.988

.843

.704

.509

.347

0.86

.79

.72

.63

.65

.68

.66

.65

.84

.84

.80

.77

.65

.68

.66

.65

.71

.75

.83

.79

.74

.61

.57

.58

.65

.78

.83

.84

.78

.73

.62

.60

.56

.48

.49

.59

.54

.73

.76

.73

.55

.49

.43

.41

.37

.77

.78

.78

.67

.61

.51

.49

.46

.46

.78

.76

.76

.75

.68

.68

.58

.59

.51

.60

.78

.77

.76

.78

.79

.71

.69

.63

.53

.53

.52

.51

.55

.80

.83

.85

.77

.76

.73

.65

.56

.49

.49

.55

.57

13.5

14.0

15.0

16.0

17.0

11.0

11.5

12.5

10.0

10.0

11.0

12.0

12.0

12.0

12.5

11.0

11.0

11.0

11.0

11.0

11.0

11.0

11.0

11.0

12.0

12.0

12.0

12.0

15.0

15.0

15.5

16.0

16.5

14.5

14.0

16.0

16.0

16.0

16.0

16.0

16.0

16.0

16.0

16.0

16.0

15.0

15.0

15.0

16.0

16.0

16.5

17.0

21.5

17.5

21.0

20.5

20.5

19.0

19.5

20.0

20.0

20.0

19.0

19.0

19.0

18.5

18.0

18.0

18.5

18.5

19.0

19.5

19.5

20.0

20.0

19.0

19.0

19.5

17.0

17.0

17.0

17.5

17.5

18.0

22.5

21.5

21.5

22.0

20.0

19.5

1.29

1.28

1.23

1.20

1.17

1.38

1.36

1.32

1.41

1.41

1.38

1.34

1.34

1.34

1.32

1.38

1.38

1.38

1.38

1.38

1.38

1.38

1.38

1.38

1.34

1.34

1.34

1.34

1.23

1.23

1.22

1.20

1.19

1.25

1.27

1.20

1.20

1.20

1.20

1.20

1.20

1.20

1.20

1.20

1.20

1.23

1.23

1.23

1.20

1.20

1.19

1.17

1.03

1.15

1.04

1.06

1.06

1.11

1.10

1.08

1.08

1.08

1.11

1.11

1.11

1.12

1.14

1.14

1.12

1.12

1.11

1.10

1.10

1.08

1.08

1.11

1.11

1.10

1.17

1.17

1.17

1.15

1.15

1.14

1.03

1.05

1.05

1.04

1.08

1.10

14257

9760

6762

4442

2650

1341

670

378

13968

10362

7650

6232

3917

2702

1492

765

453

290

14710

10471

6659

3776

2378

1237

654

370

205

15149

11496

7504

4506

3050

1663

1131

770

453

253

16392

11783

8600

4625

2945

1337

738

396

16423

11935

7886

4192

2884

1475

784

470

361

19615

11415

9481

5992

3755

2469

1535

1043

775

631

395

332

17719

13421

10268

7376

4986

3556

2377

1641

1125

786

542

339

17906

13248

9812

6753

4690

3318

2674

1588

1083

837

519

307

0.89

.83

.76

.80

.78

.55

.38

.26

1.87

1.88

1.84

1.75

1.88

1.81

1.30

.90

.72

.60

2.70

2.52

2.45

2.50

2.02

1.48

1.17

.99

.71

3.34

3.20

3.02

3.33

2.84

1.81

1.52

1.21

1.15

.84

3.63

3.56

3.70

3.50

2.73

1.65

1.16

.77

2.64

2.56

2.46

2.06

1.60

1.29

.91

1.05

.83

2.42

2.19

2.15

2.00

1.73

1.89

1.48

1.28

1.28

1.28

.80

1.03

1.95

1.87

1.83

1.82

1.58

1.55

1.56

1.48

1.25

1.09

.90

.67

1.47

1.48

1.45

1.27

1.19

1.12

1.31

.85

.88

.73

.70

.53

0.0033

.0033

.0033

.0033

.0033

.0033

.0033

.0033

.0170

.0170

.0170

.0170

.0170

.0170

.0170

.0170

.0170

.0170

.0342

.0342

.0342

.0342

.0342

.0342

.0342

.0342

.0342

.0550

.0550

.0550

.0550

.0550

.0550

.0550

.0550

.0550

.0550

.0775

.0775

.0775

.0775

.0775

.0775

.0775

.0775

.0775

.0775

.0775

.0775

.0775

.0775

.0775

.0775

.0775

.0550

.0550

.0550

.0550

.0550

.0550

.0550

.0550

.0550

.0550

.0550

.0550

.0342

.0342

.0342

.0342

.0342

.0342

.0342

.0342

.0342

.0342

.0342

.0342

.0170

.0170

.0170

.0170

.0170

.0170

.0170

.0170

.0170

.0170

.0170

.0170

0.0330

.0402

' .0460

.0413

.0439

.0870

.1840

.3860

.0390

.0384

.0405

.0443

.0387

.0417

.0728

.1685

.2610

.3795

.0376

.0431

.0456

.0438

.0662

.1253

.2000

.2760

.5390

.0395

.0428

.0479

.0399

.0546

.1341

.1920

.2990

.3350

.6197

.0470

.0492

.0455

.0503

.0503

.2290

.4650

1. 0570

.0893

.0950

.1020

.1461

.1975

.3750

.7250

.5480

.8950

.0753

.0902

.0954

.1100

.1471

.1233

.1977

.2680

.2900

.2708

.5680

.4150

.0719

.0780

.0815

.0826

.1100

.1132

.1125

.1246

.1760

.2305

.3365

.6030

.0627

.0621

.0648

.0843

.0965

.1086

.0797

.1091

.1760

.2555

.2710

.4850

88.3

80.0

74.6

79.0

76.5

54.5

37.4

25.8

81.2

81.9

79.7

75.7

81.5

79.5

59.7

39.1

31.4

21.6

82.7

77.3

75.2

76.6

62.3

45.3

35.9

30.6

15.1

80.2

77.5

73.2

80.4

68.6

43.7

36.6

29.4

27.7

20.4

74.0

72.4

75.2

71.5

71.5

33.5

23.7

15.6

53.7

52.0

50.2

42.0

36.1

26.2

18.8

21.6

17.0

58.4

52.8

51.9

48.3

41.8

45.7

36.1

31.4

29.8

30.8

21.3

24.9

59.8

57.5

56.3

55.8

48.3

47.6

47.8

45.5

38.3

33.4

27.6

20.7

64.0

64.5

63.0

55.4

51.6

48.7

56.9

48.5

38.2

31.7

30.8

23.0

0.0101 T

.0108 T

.0110 T

.0099 L,T

.0097 L

.0133 L

.0187 L

.0264 L

. 0102 T

.0098 T

.0097 T

.0100 T

.0087 T, L

.008B L, T

.0111 L,r

.0166 L,r

.0199 L

.0282 L

.0098 T

.010C T

.0098 T

.0090 T

. 0108 T, R

.0152 L, T, R

.0170 L, R

.0192 L, r

.0379 L

.0096 T.r

.0097 T, r

.0098 T,R

.0084 T, r

.0098 T, L, r

.0147 L, r

.0172 L, R

. 0211 L, R

. 0211 L, R

.0278 L, R

.0104 T

. 0102 T, r

. 009S T, R

.0094 T,r

.0092 T, L

. 0195 L, R

.0260 L, R

. 0388 L, R

.0148 T

.0148 T, r

.0147 T, r

.0167 T

.0192 T, L

.0251 L, T

.0340 L, T, r

.0270 L, T, R

.0346 L, R

.0139 T

.0145 T

.0146 T

.0150 T

.0168 T

.0144 T

.0178 L, T, r

.0199 L, T, r

.0204 L, T, R

.0193 L, r

.0276 L, r

.0228 L

.0138 T

.0139 T

.0139 T

.0136 T

.0150 T

.0147 T

.0141 T

.0142 T, L, r

.0166 L, T, r

.0186 L, r

.0220 L, r

.0288 L

.0133 T

.0128 T

.0127 T

.0140 T

.0146 T

.0150 T

.0121 T, r

.0137 L, T, r

.0172 L, T, r

.0204 L,r

.0201 L

.0263 L
THE HYDRAULICS OF OVERLAND FLOW ON HILLSLOPES 

E. Summary of laboratory data for artificial rainfall

Downslope distance

(ft)

Discharge, q

(cfs per ft)

Average

depth, D (ft)

Mean

velocity,

V (fps)

Surface Velocity

velocity, ratio

V. (fps) V

V,

Test 1-9

[7=11.61 in. per hr; S=0.0033 ft per ft; T=9.5° C;

l

2

4

5 _-__ __- _

7

g

9

11 _ _ ________

13

14 _ __________

0. 00027

. 00054

. 00081

. 00108

. 00134

. 00161

. 00188

. 00215

. 00242

. 00269

. 00296

. 00323

. 00349

. 00376

. 00403

0. 0170

. 0117

. 0110

. 0113

. 0133

.0143

.0133

. 0153

. 0153

.0173

.0177

.0153

.0163

.0150

. 0113

0.016

. 046

. 074

.096

. 102

.113

. 142

. 141

. 158

. 155

.167

.211

.214

. 251

. 357

0. 10 0.

. 16

. 32

.42

Test 2-11

46

70

49

60

[ 7=11.56 in. per hr; S=0.170 ft per ft; T=12.0° C;

1 _

3

4_ ____________

Q

7

8

9

11 ____________

12 ____________

13

15

0. 00027

. 00054

. 00080

. 00107

. 00134

. 00161

. 00187

. 00214

. 00241

. 00268

. 00294

. 00321

. 00348

. 00375

. 00401

0. 0060

. 0063

.0070

.0073

.0070

. 0067

.0073

.0070

.0077

.0067

.0087

.0073

. 0087

. 0067

.0077

0.045

. 085

. 115

. 147

. 191

.240

.257

.306

. 313

.399

. 338

.440

.400

. 559

. 521

[/=8.60in. perhr;

l

2

3

^

5--. ... --------

7__ ..__--

g

10

11 ______ ___

13

14

15

0. 00020

. 00040

. 00060

. 00080

. 00100

. 00119

. 00139

. 00159

. 00179

. 00199

. 00219

. 00239

. 00259

. 00279

. 00299

0. 0053

. 0073

.0060

.0070

. 0067

.0073

.0060

. 0070

. 0077

.0067

. 0087

. 0067

. 0090

. 0077

. 0070

0.038

.055

. 100

. 114

. 149

. 164

.232

.227

.233

.297

.252

. 356

.287

.361

.426

0. 246 0.

. 339

.372

. 387

.442

. 531

.625

Test 2-12

35

43

65

79

Qfl

83

89

S=0.0170 ft per ft; r=11.0° C;

0. 128 0.

.293

.316

.349

. 359

.444

.444

43

39

52

65

83

80

81

Reynolds

number, R

Froude

number, F

DarcyWeisbach

friction

factor, //

Chezy

coefficient,

C

Manning

resistance

coefficient ,

n

p=1.43X10-5 sq ft per sec]

76

150

225

301

376

451

526

601

676

752

827

902

977

1052

1127

0.017

. 075

. 124

. 159

. 156

. 167

. 217

.201

.225

. 208

.221

. 301

.295

. 361

. 592

56.45

4.70

1.707

1.042

1.087

.952

.561

.654

.521

. 612

.610

.292

. 303

. 202

.075

2.14

7.40

12. 28

15.72

15. 39

16.45

21.43

19. 85

22.24

20.52

20. 55

29. 70

29. 16

35.71

58. 61

0. 3554

.0966

. 0576

.0495

.0474

. 0438

.0341

.0377

.03^6

. 0348

. 0373

. 0252

. 0259

. 0210

. 0121

p=1.34X10-5 sq ft per sec]

80

160

240

31 Q

399

479

559

639

719

799

878

958

1038

1118

1198

0. 102

. 189

.242

. 303

.402

.517

.530

. 644

. 629

. 860

.733

.907

. 756

1. 205

1.260

12.97

3.82

2.32

1.480

.840

. 510

.484

.327

. 344

. 184

.334

. 165

.238

. 094

. 124

4.46

8. 21

10. 54

13. 19

17. 51

22.49

23.07

28. 05

27. 35

37. 39

27.79

39.49

32. 89

52. 38

45.54

0. 1435

.07^5

.06?2

.0501

.0375

.02^0

.02°6

.02*4

. 02 < 4

.0174

.0245

.0167

.0217

.0124

. 0146

p=1.38X10-s sq ft per sec]

58

115

173

231

288

346

404

461

519

577

634

692

750

808

865

0. 092

. 113

. 227

.240

.321

.338

.527

.478

.468

. 640

.476

.767

.533

.725

. 897

16. 08

10. 57

2. 63

2. 36

1.322

1. 189

.488

.595

.621

. 333

. 600

. 232

.479

.259

. 169

4. 00

4.94

9.90

10.45

13.96

15. 17

22.98

20. 81

20. 37

27.91

20. 72

33. 32

23. 19

31. 54

39.04

0. 15**5

. 13^8

. 0646

. 06^8

.0467

.0435

.0278

. 0315

.0327

.0234

.03^8

.0195

.02^5

.0211

. 0168
A54 DYNAMIC AND DESCRIPTIVE STUDIES OF HILLSLOPES

E. Summary of laboratory data for artificial rainfall Continued

Downslope distance

(ft)

Discharge, g

(cfs per ft)

Average

depth, D (ft)

Mean

velocity,

V (fps)

Surface Velocity

velocity,

V, (fps)

ratio,

r

V,

Reynolds

number, R

Froude

number, F

DarcyWeisbach

friction

factor, //

Chezy

coefficient,

C

Manning

resistance

coefficient,

n

Test 2-13

[ 7=6.09 ia. per hr;

1 _ _ ___ __ __

2

4 _ __-___.___-

6 _ ___-__-_--

g

g

10

jj

12

14

15

0. 00014

. 00028

. 00042

. 00056

. 00070

. 00085

. 00099

. 00113

. 00127

. 00141

. 00155

. 00169

. 00183

. 00197

. 00211

0. 0047

. 0053

. 0053

. 0060

. 0067

. 0073

. 0060

. 0060

.0057

. 0053

. 0073

.0080

. 0083

. 0070

. 0067

0. 030

.053

.080

. 094

. 105

. 116

. 164

. 188

. 222

. 266

. 212

.211

. 221

. 282

. 315

S=0.0170 ft per ft;

0. 115

. 230

. 268

. 295

. 323

. 292

. 444

r=io.5° c

0.46

.41

. 43

. 64

.82

.72

. 64

; v= 1.40X10-5 sq ft per sec]

40

81

121

161

201

242

282

322

362

403

443

483

523

564

604

0. 077

. 128

. 194

.214

. 226

.239

.373

.427

. 518

. 644

.437

. 416

.427

. 594

. 679

22. 87

8. 26

3. 63

2.97

2. 66

2.38

.977

. 744

. 507

. 328

.711

. 787

. 744

. 386

.296

3.

5.

8.

9.

9.

36

58

43

31

84-

10.41

16.

18.

22.

28.

19.

18.

18.

25.

29.

24

61

54

0?,

03

09

61

83

50

0. 1829

. 1122

. 0743

.0687

.0662

.0635

. 0394

. 0344

. 0281

. 0223

. 0347

. 0371

. 0363

. 0254

. 0221

Test 2-14

[7=4.63 in. per hr; S=0.0170 ft per ft;

1

2

4_ _____ __ ___

g

1

8

9 _____-__-_--_

j j

12

13 _ __ _____

15

0. 00011

. 00021

. 00032

. 00043

. 00054

. 00064

. 00075

. 00086

. 00096

. 00107

. 00118

. 00129

. 00139

. 00150

. 00161

0. 0053

. 0053

. 0057

. 0060

. 0060

. 0067

. 0057

. 0050

. 0053

.0057

. 0077

. 0067

. 0087

. 0070

. 0067

0. 020

. 040

. 056

. 071

. 089

. 096

. 132

. 171

. 182

. 188

. 153

. 192

. 160

.214

. 240

0. 162

. 202

.250

. 262

. 306

. 294

. 324

r=io.5° c

0.25

. 35

.38

. 65

. 61

.65

. 66

; v= 1.40X10-5 sq ft per sec]

31

61

92

122

153

184

214

245

276

306

337

367

398

429

459

0. 048

.097

. 131

. 161

.202

.207

. 308

.426

.441

.439

. 307

.414

. 302

. 451

. 517

58. 04

14. 51

7.96

5.21

3.32

3. 18

1.433

.749

.701

.706

1.441

. 796

1.489

. 669

. 509

2.

4.

5.

7.

8.

9.

13.

18.

19.

19.

13.

17.

13.

19.

22.

11

69

03

81

00

41

55

17

10

37

99

15

63

50

0. 2972

. 1486

. 1115

. 0910

. 0726

. 0724

. 0473

. 0334

. 0327

. 0332

.0499

. 0362

.0517

. 0334

. 0290

Test 2-15

[ 7=3.25 in. per hr;

1

2

4 _____________

5

6

7

9_

jj

12

13

14

15

0. 00008

. 00015

. 00023

. 00030

. 00038

. 00045

. 00053

. 00060

. 00068

. 00075

. 00083

. 00090

. 00098

. 00105

. 00113

0. 0047

. 0040

. 0037

. 0053

. 0047

. 0053

. 0053

. 0040

. 0050

. 0043

. 0060

. 0060

. 0060

. 0050

. 0057

0. 016

. 038

. 061

.057

. 080

. 085

. 099

. 150

. 135

. 175

. 150

. 163

. 210

. 198

5=0.0170 ft per ft;

0. 147

. 145

. 200

. 201

910

. 184

. 219

T=9.0° C;

0.26

39

.43

. 75

.83

. 82

. 96

v=1.46X10~5 sq ft per sec]

21

41

62

82

103

124

144

165

185

206

226

247

268

288

309

0. 041

. 106

. 177

. 138

.206

.206

.240

.418

. 337

.470

.411

.341

. 370

.524

.463

80. 41

12. 13

4. 36

7. 16

3.22

3. 21

2.37

.799

1. 202

. 615

.804

1. 168

. 989

.497

. 637

1.

4.

7.

6.

8.

8.

10.

18.

14.

20.

17.

14.

16.

22.

20.

79

61

69

00

95

95

43

19

64

47

90

85

14

77

11

0. 3430

. 1297

.0767

. 1043

.0686

.0699

. 0601

. 0329

. 0424

. 0296

. 0347

. 0431

. 0396

.0273

. 0315
THE HYDRAULICS OF OVERLAND FLOW ON HILLSLOPES

E. Summary of laboratory data for artificial rainfall Continued

A55

Downslope distance

(ft)

Discharge, g

(cfs per ft)

Average

depth, D (ft)

Mean

velocity,

F(fps)

[ 7=11.35 in. per hr;

2_______--_____

3 _ . _______

4

5-_____________

6_________-____

7

8

9______________

10 ___________

11. ____________

12-_________-__

13_________.___

14__ _____---__

15-_-_________-

0. 00053

. 00079

. 00105

. 00131

. 00158

. 00184

. 00210

. 00236

. 00263

. 00289

. 00315

. 00341

. 00368

. 00394

0. 0047

. 0047

. 0053

. 0050

. 0050

. 0063

. 0057

. 0067

. 0063

. 0073

. 0077

. 0077

. 0067

. 0057

0. 112

. 168

. 198

. 263 .

. 315

. 292 .

. 369

. 353 .

.417

. 396 .

.409

. 444 .

. 549

. 691 .

Surface Velocity

velocity, ratio,

V, (fps) V

V,

Test 3-10

S=0.0342 ft per ft; T=7.0° C

0. 194 0. 58

. 333 . 60

. 417 . 46

. 545 . 68

. 556 . 75

. 526 . 78

. 760 . 72

Test 3-11

[7=8.51 in. per hr; S=0.0342ft per ft; T=4.0° C;

2_________-____

3_______.______

4

5______________

6--_________-_-

7 _- _ _ _

8_____-_______-

9______________

10_________._._

11_ ___________

12_____________

13_____________

14_____________

15___-___-_____

0. 00039

. 00059

. 00079

. 00099

. 00118

. 00138

. 00158

. 00177

. 00197

. 00217

. 00236

. 00256

. 00276

. 00296

0. 0037

. 0053

. 0057

. 0053

. 0053

.0060

. 0063

. 0067

. 0060

. 0080

. 0067

. 0070

. 0060

. 0063

0. 106

. 112 .

. 138

. 186 .

. 223

. 230 .

.250

.265 .

. 328

.271 .

. 353

.366 .

.460

.469 _

0. 164 0. 65

. 314 . 44

. 380 . 59

. 447 . 56

. 509 . 64

. 690 . 51

. 673 . 68

Test 3-12

[ 7=6.36 in. per hr; S=0.0342 ft per ft; T=7.0° C;

2_-_______.____

3__

4__ ____________

5_ ____________

6______________

7 _

8______________

9

10___

ll._ __________

12_____________

13_____________

14 __ __________

15

0. 00029

. 00044

. 00059

. 00073

. 00088

. 00103

. 00117

. 00132

. 00147

. 00161

. 00176

. 00191

. 00206

. 00220

0. 0037

. 0050

. 0053

. 0047

. 0050

. 0057

. 0063

. 0053

. 0053

. 0067

. 0077

. 0073

. 0060

. 0060

0. 079

. 088 .

. Ill

. 156 .

. 176

. 180 .

. 186

. 249 .

.277

. 241 .

.229

. 261 .

. 343

. 367 _

0. 190 0. 42

. 326 . 34

.411 .43

3Q9 47

. 394 . 70

. 432 . 53

.601 . . 57

Reynolds

number, R

Froude

number, F

DarcyWeisbach

friction

factor, //

Chezy

coefficient,

C

Manning

resistance

coefficient,

n

; »=1.47X10-5 sq ft per sec]

143

214

286

357

429

500

572

643

715

786

857

929

1000

1072

0.288

.432

.479

. 656

. 786

. 649

.862

.761

. 927

. 816

. 821

.892

1. 183

1. 614

3. 301

1.467

1. 191

. 637

.444

. 651

. 368

.474

. 319

.410

.406

. 344

. 196

. 105

8.83

13. 25

14.71

20. 11

24. 09

19.89

26.43

23. 32

28.41

25. 06

25. 20

27.36

36. 27

49.48

0. 06^5

. 0463

. 0426

. 0318

. 0257

. 0324

. 0240

.0279

.0227

.02°4

. 02^5

. 02*4

. 0180

. 0128

v= 1.68X10-5 sq ft per sec]

94

141

188

235

281

328

375

422

469

516

563

610

657

704

0. 307

.271

. 322

. 450

. 540

. 523

.556

.571

. 745

. 533

.761

. 771

1. 045

1. 042

2.90

3. 72

2. 64

1. 350

Q3Q

.999

.888

.841

.491

. 960

.474

.460

.250

.252

9.42

8. 32

9.88

13. 81

16. 56

16. 06

17. 03

17. 51

22. 90

16.38

23. 32

23. 65

32. 11

31. 95

0. 0626

. 0753

.06U

.0453

. 0378

. 0378

.0378

.0372

.0279

.0409

.0279

.0277

. 0199

.0202

p=1.47X10-5 sq ft per sec]

80

120

160

200

240

280

320

360

3QQ

439

479

^IQ

559

599

0.229

.219

.269

. 401

4^Q

.421

.413

. 603

. 671

. 519

. 460

. 538

.780

. 834

5.22

5. 69

3. 79

1. 701

1.422

1. 550

1. 604

. 753

. 609

1. 016

1. 294

. 944

.449

. 393

7. 02

6. 73

8.24

12.31

13.46

12. 89

12.67

18. 50

20. 58

15.92

14. 11

16. 52

23.94

25. 62

0. 0841

. 0922

.0760

. 0499

. 0461

. 0492

.0509

. 0339

. 0304

. 0409

.0472

. 0400

. 02ii7

.0250
A56 DYNAMIC AND DESCRIPTIVE STUDIES OF HILLSLOPES 

E. Summary of laboratory data for artificial rainfall Continued

Mean

Downslope distance Discharge, a

(ft)

Average velocity,

(cfs per ft) depth, D (ft) V (fps)

Surface Velocity

velocity,

V. (fps)

ratio,

V

V,

Reynolds

number, R

Froude

number, F

DarcyWeisbach

friction

factor, //

Chezy

coefficient,

C

Manning

resistance

coefficient,

n

Test 3-13

2

4_ _________

g

7_ _ .

8

10

H

12 _

14

15

.__ 0.00023

.00034

.__ .00045

.__ .00056

.00068

.__ .00079

.__ .00090

.00101

.00113

.__ .00124

.__ . 00135

.00146

.__ . 00158

.__ .00169

[7=4.86 in.

0. 0040 0.

. 0040

. 0047

. 0047

. 0053

. 0047

. 0043

. 0050

. 0047

. 0050

. 0057

. 0080

. 0060

. 0057

perhr;S=0.0342ftperft;

056

096

120 _

127

168 _

209

203 _

249

248 _

237

183 _

263

296 _

0. 186

. 248

. 323

. 341

.353

.359

. 571

T=7°C;

0. 30

.39

.39

.61

.71

.66

.46

v=1.47Xl(H sq ft per sec]

61

92

122

153

184

214

245

276

306

337

367

398

429

459

0. 156

.234

.247

. 308

. 308

.432

. 562

. 506

. 640

. 618

. 554

. 360

. 598

. 692

11.24

4. 99

4.49

2.88

2.90

1.467

.867

1. 069

.668

. 716

.894

2. 105

.764

.573

4.79

7. 18

7.57

9.47

9.43

13.25

17. 23

15. 52

19.64

18.97

16.98

11. 06

18.36

21.20

0. 1249

.0832

. 0811

.0649

. 0664

. 0463

. 0351

. 0400

. 0313

.0327

. 0373

. 0606

. 0348

.0299

Test 3-14

[7=3.12 in. per hr; S=0.0342 ft per ft;

2

3

4 _ ____ __.

g

7

8.----------.

9 ____-_._-..

jj

12

13

14 _ _ ____ .

.__ 0.00014

.__ .00022

.__ .00029

.__ .00036

. 00043

. 00050

. 00058

.._ .00065

... .00072

.._ .00079

._- . 00087

... .00094

.-_ .00101

._. . 00108

0. 0027 0.

. 0030

. 0040

. 0037

.0043

. 0040

. 0040

. 0040

. 0033

. 0047

. 0043

. 0057

. 0047

. 0047

053

072 _

072

097

101

126 _

14-4

162 _

218

169 .

201

164

215

230 _

0. 164

.221

. 281

. 240

.287

. 303

.366

T=7.0° C

0.32

.33

. 36

. 60

.76

.66

.59

; v=1.47XlCHi sq ft per sec]

39

59

78

98

118

137

157

177

196

216

235

255

275

294

0. 180

. 232

. 201

.281

.272

. 351

.401

.451

. 669

.434

. 540

.383

. 553

. 591

8.47

5. 10

6.80

3.46

3.71

2.22

1.699

1.343

.612

1.450

.938

1.867

.896

.783

5.52

7. 11

6. 16

8.62

8. 33

10.77

12. 31

13.85

20. 52

13.33

16.57

11.75

16.96

18. 14

0. 1015

. 0802

.0971

.0684

. 0726

. 0555

. 0486

. 0432

.0282

.0461

. 0365

. 0540

. 0362

.0338

Test 4-11

[7=11.19 in. per hr; S=0.0550 ft per ft;

l

2___. _.__._..

4

5

6___-___.___.

1. ...........

Q

10

]_J

12

13. ___._._...

15

.__ 0.00026

.__ . 00052

... . 00078

. 00104

.__ . 00130

.__ . 00155

.__ .00181

 . 00207

.__ . 00233

. 00259

.._ . 00285

._. .00311

... . 00337

.__ . 00363

. 00389

0. 0040 0.

. 0043

. 0050

. 0047

. 0057

. 0053

. 0067

. 0063

. 0063

. 0070

. 0087

. 0067

. 0070

. 0080

. 0070

065 .

120

155 .

220

227 .

293

271

329

370 _

370

327 _

464

481

453

555 _

0.287

4Qfi

. 612

.823

.800

1.036

1. 307

T=13.0° C; *=1.31X10-S sq ft per sec]

0.42

.44

.48

.40

.46

.45

.35

7Q

158

237

316

395

475

554

633

712

791

870

949

1028

1107

1186

0. 181

. 323

. 387

. 566

.530

70Q

. 584

. 731

.822

.779

. 618

1.000

1. 013

.892

1. 168

13.42

4.23

2.95

1. 376

1. 567

.875

1.293

.825

.652

.725

1. 153

.441

.429

. 552

.322

4. 38

7.80

9.35

13.68

12.82

17. 16

14. 12

17.67

19.88

18.86

14. 95

24. 17

24. 51

21.60

28.28

0. 1364

.0775

. 0664

.0449

. 0495

. 0365

.0461

. 0365

. 0324

. 0348

. 0455

.0269

.0268

.0311

. 0232
THE HYDRAULICS OF OVERLAND FLOW ON HILLSLOPES 

E. Summary of laboratory data for artificial rairifall Continued

A57

Downslope distance

(ft)

1

2-- 

4

5--. -- _

6_ . _

7..-- -- 

8--. _

9--- ---_

10--- 

12--- - 

14

15---- - - -----

Discharge, q

(cfs per ft)

0. 00020

. 00040

. 00060

. 00080

. 00101

. 00121

. 00141

. 00161

. 00181

. 00201

. 00221

. 00241

. 00262

. 00282

. 00302

Average

depth, D (ft)

[/=

0. 0037

. 0043

. 0043

. 0050

. 0047

. 0050

. 0047

. 0053

. 0043

. 0060

. 0067

. 0063

. 0070

. 0060

. 0057

Mean

velocity,

V (fps)

Surface Velocity

velocity, ratio

V, (fps) V

V,

Test 4-12

=8.69 in. per br; S=0.0550 ft per ft; T=12.0° C;

0. 054 _

. 094

. 140 _

. 161

. 214 _

. 241

. 300 _

. 304

.421 _

.335

.330 _

. 383

. 374 _

.469

. 529 _

0. 245 0.

. 345

.551

. 690

. 707

.881

1. 070

Test 4-13

38

47

44

44

47

44

44

[7=6.38 in. per br; S=0.0550ft per ft; T=10.0° C;

l

2

3 _

4 _ ___ _ _ __

6 __ ___________

7_._ _

8_ 

q

10.. 

12

13.. 

15-.. 

1 _ _ _ _

g

4 _

5..- 

6_ _-_-__-_-_-_

8.- 

q

11

12.. 

14

15

0. 00015

. 00030

. 00044

. 00059

. 00074

. 00089

. 00103

. 00118

. 00133

. 00148

. 00162

. 00177

. 00192

. 00207

. 00221

0. 00010

. 00021

. 00031

. 00042

. 00052

. 00063

. 00073

. 00084

. 00094

. 00105

. 00115

. 00126

. 00136

. 00147

. 00157

0. 0030

. 0037

.0043

. 0050

. 0053

.0050

. 0047

. 0043

. 0050

. 0040

.0047

. 0060

.0053

. 0053

. 0050

[/=

0. 0027

. 0027

. 0033

. 0037

. 0033

.0037

. 0043

. 0040

. 0037

. 0037

. 0047

. 0053

. 0043

. 0050

.0050

0. 049 _

. 080

. 103 _

. 118

. 139 _

.177

. 220 _

.275

. 266 _

.369

.345 _

.295

. 362 ..

. 390

.443 _

'4.53 in. per hr; S

0. 039 _.

.078

. 095 _

. 113

. 159 .

. 170

. 170 _

. 209

. 259 _

. 283

. 245 _.

.237

. 317 _

. 293

.314 _

0. 210 0.

.402

. 509

.536

. 509

. 631

. 660

Test 4-14

38

29

35

51

73

47

"SQ

=0.0550 ft per ft; T=10.0° C;

0. 228 0.

.326

.442

438

.455

. 504

. 593

34

35

39

48

62

47

49

Reynolds

number, R

Froude

number, F

DarcyWeisbach

friction

factor, //

Chezy

coefficient,

C

Manning

resistance

coefficient

n

x=1.34X10-5 sq ft per sec]

60

120

180

240

300

360

420

480

541

601

661

721

781

841

901

0. 157

.253

.376

.401

. 550

. 601

.771

. 736

1. 132

. 761

.711

. 851

.787

1. 066

1. 236

17 98

6.90

3. 11

2. 73

1.454

1. 220

. 740

.813

. 344

. 758

.872

. 609

. 709

. 387

.289

3 79

6. 11

9. 10

9.71

13.31

14. 53

18. 66

17.81

27. 37

18.44

17. 19

20. 57

19. 06

25.82

29.88

0. 1559

0990

. 0665

. 0639

O4.R1

. 0427

. 0329

. 0352

. 0221

.0347

. 0379

. 0313

. 0344

. 0248

. 0212

p=1.41X10-5 sq ft per sec]

42

84

126

167

209

251

293

335

377

419

461

502

544

586

628

0. 158

. 322

. 170

.294

. 337

.441

. 566

.455

. 663

1. 028

.887

. 670

.877

.944

1. 105

17.70

8. 19

5.74

5. 09

3.89

2. 26

1.376

.806

1.001

.416

.560

.977

.573

.494

. 361

3.81

5. 61

6. 70

7. 12

8. 14

10. 67

13. 68

17.88

16. 04

24.88

21.45

16.24

21. 20

22.84

26.71

0. 14.4

.09C3

. 0872

.0769

. 0581

. 0449

.03?8

.0387

. 0240

. 0286

. 0394

.0295

.0274

. 0232

i»=1.41Xl(H sq ft per sec]

30

59

89

1 1Q

14Q

178

208

238

267

297

327

356

386

416

446

0. 132

.264

. 291

. 328

.488

.493

.457

. 582

.751

.821

. 630

.574

.853

. 731

.783

25. 15

6.29

5. 18

4. 11

1.850

1.814

2. 108

1. 298

. 782

.655

1. 110

1.337

. 606

.825

. 719

3.20

6.40

7. 05

7. 92

11. 80

11.92

11.05

14. 09

18. 15

19. 83

15. 23

13.88

20. 62

17. 67

18.93

0. 1749

.0875

. 0821

. 0745

.0491

. 0495

. 0547

. 0424

. 0325

. 0298

. 04C3

. 0451

. 0293

.0351

. 032°
A58 DYNAMIC AND DESCRIPTIVE STUDIES OF HILLSLOPES

E. Summary of laboratory data for artificial rainfall Continued

Mean 

Downslope distance Discharge, q Average velocity, 

(ft) (cfsperft) depth, D (ft) T'(fps)

Surface Velocity 

velocity, ratio,

v. (fps) r

V,

Test 4-15

[7=3.47 in. per hr; S=0.0550 ft per ft; T=13.5° C;

1

2

3 _

4

5_ _______

6________

7. ________

8________.

9________.

10_______.

11__ ____.

12_ ______

13_______.

14 ___ __.

15_______.

______ 0.00008

______ .00016

______ .00024

______ .00032

______ .00040

______ .00048

______ .00056

______ .00064

______ .00072

______ .00080

______ .00088

______ .00096

______ .00104

______ .00112

______ .00120

0. 0020

. 0027

. 0027

. 0033

. 0030

. 0033

. 0037

. 0037

. 0033

.0033

. 0047

. 0043

.0037

. 0037

. 0040

0. 040

.059

. 089

. 097

. 144

. 146

. 152

. 174

. 219

.243

. 188

. 224

. 282

.304

. 301

[7=11.77 in. per hr:

!_______.

2 __ _____

3__

4 ______

5 _

6________

7

8________.

9

10_______

11- ______

12_ ___.

13-______.

14__ _.__.

15_______.

1__ _____

2

3________

4__ __ _

5__

6

7_

8________

9__

10_______

11__ ____.

12_______.

13_______.

14_ __ _ .

15. __ _ .

______ 0.00027

______ .00054

______ .00082

______ .00109

______ .00136

______ .00163

______ .00191

______ .00218

-__-_- .00245

______ .00272

-__-_. .00300

______ .00327

_-_-_. .00354

______ .00381

___ _. . 00408

______ 0.00020

______ .00039

______ .00059

___. _ . 00078

______ .00098

______ .00117

______ .00137

______ .00156

_-_-_- .00176

-__--_ .00195

______ .00215

______ .00234

______ .00254

______ .00273

.__.__ .00293

0. 0043

. 0043

. 0050

.0057

. 0060

.0063

.0067

.0070

. 0070

. 0080

. 0077

. 0080

. 0077

.0080

. 0083

[7=8.43

0. 0033

. 0040

. 0040

. 0047

. 0050

. 0047

. 0053

. 0060

. 0063

. 0063

.0070

. 0067

. 0070

. 0080

. 0073

0.063

. 127

. 163

1Q1

997

.259

.284

. 311

. 350

.340

.389

.408

.460

.477

. 492

in. per hr;

0. 059

. 098

. 146

. 166

IQE;

. 249

.258

. 260

970

. 310

Qf)7

^.4Q

. 362

.341

.401

0. 132 0.

. 308

. 351

. 390

41Q

. 398

.417

Test 5-10

45

39

49

45

58

56

73

; S=0.0775 ft per ft; T=14.0° C

0. 372 0.

. 600

701

.939

1. 156

1. 036

1. 460

Test5-U

34

39

33

33

29

39

33

S=0.0775 ft per ft; T=14.0° C;

0 974 0

. 531

. 567

.714

7QQ

S7n

1. 176

36

31

44

36

49

40

29

Reynolds 

number, R

Froude 

number, F

Darcy- Chezy Manning 

Weisbach coefficient, resistance 

friction C coefficient, 

factor, // n

c=1.29X10-5 sq ft per sec]

25

50

75

100

124

149

174

199

224

249

274

299

324

349

373

0. 158

. 200

. 302

.298

.463

. 448

. 441

. 504

. 672

. 745

.483

. 602

.817

.881

. 838

17.71

10. 99

4. 83

4.97

2. 05

2. 19

2.27

1. 732

.975

. 792

1.884

1. 214

. 659

. 567

. 626

3. 81

4.84

7. 30

7.20

11.21

10.84

10. 66

12. 20

16.25

18. 04

11. 69

14.57

19.77

21. 32

20. 29

0. 1396

. 1156

. 0767

. 0804

. 0508

. 0534

. 0554

. 0484

. 0356

. 0321

.0525

. 0415

. 0298

. 0277

. 0295

; c=1.27X10-5 sq ft per sec]

86

172

257

343

429

515

600

686

772

858

943

1029

1115

1201

1286

0. 169

. 341

.406

.446

. 516

. 576

. 612

. 655

. 737

. 669

.781

.803

. 936

.939

.952

21. 63

5. 32

3.76

3. 12

2. 32

1. 875

1. 658

1.445

1. 141

1.381

1.016

. 959

.726

. 702

. 684

3.45

6.96

8.28

9.09

10. 53

11. 72

12.47

13.35

15.03

13. 66

15.92

16. 39

18.84

19. 16

19.41

0. 1753

. 0869

. 0749

. 0698

. 0607

. 0550

. 0523

. 0491

. 0437

. 0491

. 0419

. 0409

. 0354

. 0350

. 0348

p=1.27X10-s sq ft per sec]

61

123

184

946

307

369

430

492

553

614

676 707

7QQ

860

922

0. 181

.273

.407

.427

.486

. 640

. 625

. 591

. 620

. 689

. 646

.752

. 762

. 671

. 827

18.92

8. 31

3.75

3.40

2. 63

1. 513

1.589

1.771

1. 615

1. 309

1. 482

1. 098

1. 066

1. 373

. 906

3. 69

5.57

8.29

8. 70

9. 91

13.05

12. 73

12. 06

12.63

14. 03

13. 18

15.32

15.55

13. 70

16.86

0. 1569

. 1074

. 0721

. 0706

. 0626

. 0470

. 0492

. 0530

. 0510

. 0459

. 0498

. 0425

. 0422

. 0490

. 0392
THE HYDRAULICS OF OVERLAND FLOW ON HILLSLOPES

E. Summary of laboratory data for artificial rainfall Continued

A59

Downslope distance

(ft)

Discharge, q

(cfs per ft)

Average

depth, D (ft)

Mean

velocity,

V (fps)

Surface Velocity

velocity,

V. (fps)

ratio,

V

V,

Reynolds

number, R

Froude

number, F

DarcyWeisbach

friction

factor, //

Chezy

coefficient,

C

Manning

resistance

coefficient.

n

Test 5-12

[7=6.07 in. per hr;

1 ___________

2__-______---_-

3___________-__

4___________-__

5---- - - ---

6_--________-_-

7 - -

8 __ ___________

9_--__-___-____

10_______--_-_-

11_ ___________

12______-______

13 __ _______-_-

14____________-

15- _____.__---

0. 00014

. 00028

. 00042

. 00056

. 00070

. 00084

. 00098

. 00112

. 00126

. 00140

. 00154

. 00168

. 00183

. 00197

. 00211

0. 0030

. 0040

. 0037

.0047

. 0047

. 0050

. 0053

. 0057

. 0053

. 0067

. 0063

. 0067

. 0067

. 0070

. 0063

0. 047

. 070

. 114

. 119

. 149

. 168

. 185

. 197

. 238

. 210

. 245

. 251

.272

.281

.334

S= 0.0775 ft per ft;

0. 267

. 531

. 571

.714

.741

701

1. 093

T=14.0° C;

0. 26

.22

.29

.28

.28

. 32

.26

K=1.27X10-5 sq ft per sec]

44

88

133

177

221

265

310

354

398

442

486

531

575

619

663

0. 151

. 195

. 330

.306

.383

.419

. 448

.460

.576

. 453

. 544

. 541

. 586

. 592

. 742

27. 11

16. 29

5. 68

6.63

4.23

3.54

3.09

2. 93

1. 868

3. 032

2.095

2. 126

1. 808

1.769

1. 127

3.

3.

6.

6.

7.

8.

9.

9.

11.

9.

11.

11.

11.

12.

15.

08

98

73

74

81

54

13

37

74

21

09

01

94

07

12

0. 1848

. 1504

. 0876

.0984

. 0786

.0727

.0686

. 0676

. 0533

. 0707

. 0581

. 0592

. 0546

. 0544

. 0426

Test 5-13

[7=4.64 in. per hr;

1 _ _

2 _ __ _________

3__ _.______---

4

5

6____-_--__---_

7 _____

8_.__ -----~

9 __-_ _ __

10_____________

11_ ______ -__

12 __ ____.___-_

13_ ____-___-_-

14____._ _

15 __ __________

0. 00011

. 00021

. 00032

. 00043

. 00054

. 00064

. 00075

. 00086

. 00097

. 00107

. 00118

. 00129

. 00140

. 00150

. 00161

0. 0023

. 0040

. 0037

.0040

. 0040

. 0043

. 0047

. 0040

. 0047

.0047

.0047

. 0060

. 0050

. 0057

. 0057

0.047

. 054

. 087

. 107

. 134

. 150

. 160

.215

. 206

.229

.251

. 215

.279

.264

. 283

S=0.0775 ft per ft;

0. 217

.428

. 560

. 536

. 612

.645

. 823

T=14.0° C;

0.25

.25

.27

.40

.37

. 33

.32

K=1.27X10-5 sq ft per sec]

34

68

101

135

169

203

237

271

304

338

372

406

440

474

507

0. 173

. 150

.252

. 298

. 373

.403

.411

. 599

. 530

. 589

. 645

.489

. 696

.617

.661

20.78

27.38

9.76

6.97

4.45

3.82

3.67

1.727

2.211

1.789

1.489

2. 591

1. 282

1.632

1.421

3.

3.

5.

6.

7.

8.

8.

12.

10.

12.

13.

9.

14.

12.

13.

52

07

14

08

61

22

38

13

79

00

15

97

18

56

46

0. 1548

. 1949

. 1149

.0984

.0785

. 0736

. 0732

. 0493

. 0569

.0512

. 0467

. 0641

. 0438

.0505

. 04V 1

Test 6-10

!.___________--

2_ ____________

3

4

5 __ _____ _-__

6_____._-___-_-

7_____--_--_-_-

8___-_ __ -

9_____._--__-_-

10____-_____-__

11__ ___ ___ __

12 ____________

13

14_ ___________

15-__-___--_-_-

0. 00025

. 00050

. 00075

. 00100

. 00126

. 00151

. 00176

. 00201

. 00226

. 00251

. 00276

. 00301

. 00326

. 00351

. 00377

[7=

0. 0030

. 0040

.0040

.0053

.0063

.0063

. 0073

.0077

. 0060

.0077

. 0090

. 0083

.0087

.0097

. 0093

10.85 in. per hr; S=0.0775 ft per ft;

0. 084

. 126

. 183

189

. 199

. 239

.241

. 261

.377

.326

. 307

. 363

. 375

. 362

.405

0. 271

. 504

.714

.909

. 844

1. 156

1. 156

T=14.0° C;

0.46

.38

. 34

.29

. 39

. 31

. 31

K=1.27X10-5 sq ft per sec]

79

158

237

316

395

474

553

632

711

791

870

949

1028

1107

1186

0.270

. 351

. 524

.458

.442

. 531

.497

. 524

.857

. 655

.571

.702

.709

.648

.740

8.49

5.03

2.26

2.96

3. 18

2.20

2. 51

2.26

. 843

1.446

1.906

1.257

1.235

1.477

1. 132

5.

7.

10.

9.

9.

10.

10.

10.

51

16

69

33

01

82

13

69

17.48

13.

11.

14.

14.

13.

15.

35

63

32

44

21

09

0. 10?4

. 08? 5

. 05CO

. 0672

. 0716

. 05f <>

. 06f 2

.06?4

. 03 7

. 04f 9

. 058^

. 0471

. 0471

. 0525

. 0456
AGO DYNAMIC AND DESCRIPTIVE STUDIES OF HILLSLOPES

E. Summary of laboratory data for artificial rainfall Continued

Downslope distance Discharge, q Average 

(ft) (cfs per ft) depth, D (ft)

Mean 

velocity, 

V (fps)

Surface Velocity 

velocity, ratio, 

V. (fps) V 

V,

Reynolds Froude 

number, R number, F

Darcy- Chezy Manning 

Weisbach coefficient, resistance 

friction C coefficient, 

factor, // n

Test 6-11

[7=8.20 in. per hr; 5=0.0775 ft per ft;

1_ ._ __ .

2

3_. ._ ._.

4

5_ _-___.

6_ __ --__.

7_____-__.

8.--- --.

9

10____-__

11 _____-.

12____-__.

13____--_.

14_ ___._.

15_______.

_-.___ 0.00019

______ .00038

.00057

.00076

______ .00095

______ .00114

______ .00133

______ .00152

______ .00171

______ .00190

. _ _ _ _ . 00209

.__ .00228

. _ _ _ . 00247

______ .00266

______ .00285

0. 0017

. 0030

. 0037

. 0040

.0043

.0043

.0043

.0057

.0060

.0070

. 0083

. 0083

. 0100

. 0093

.0097

0. 112

. 127

. 154

. 190

. 221

.265

.309

.266

.285

.271

.252

. 274

. 247

. 286

.294

0. 251

.462

. 576

. 749

. 755

. 851

1.053

T=18.0°C;

0. 51

.41

.46

. 36

.36

.32

.27

v= 1.14X10-5 sq ft per sec]

67

133

200

267

333

400

466

533

599

666

733

799

866

932

999

0.479

.408

.446

.529

. 594

. 712

. 831

. 621

. 648

.571

.487

. 530

.436

. 523

. 526

2.70

3.71

3. 11

2.21

1.757

1. 222

.899

1.608

1.474

1.902

2. 609

2.207

3.373

2.269

2. 240

9.76

8. 33

9. 10

10.79

12. 11

14.52

16.93

12. 66

13. 22

11. 64

9.94

10.80

8.87

10. 66

10. 72

0. 0531

. 0684

. 0649

.0553

. 0500

.0417

.0304

.0501

. 0484

.0564

. 0679

.0625

.0785

. 0646

. 0646

Test 6-12

1_ .-___

2

3

4

5___-_-_-

6__----__

7____---_.

8__ ---__.

9__. ------

10__-- . 11_.__ . 12_______

13 _ ___ _.

14 ______

15______-

____ _ 0. 00014

______ .00028

______ .00041

______ .00055

______ .00069

______ .00083

______ .00096

______ .00110

..____ .00124

______ .00138

______ .00152

______ .00165

______ .00179

______ .00193

. 00207

[7=

0. 0020

. 0023

.0030

.0040

.0037

. 0040

. 0040

. 0047

. 0047

. 0047

. 0050

. 0057

. 0063

. 0070

. 0067

5.95 in. per hr;

0.069

. 120

. 138

. 138

. 186

.207

.241

.235

.264

.293

.303

.290

.284

. 276

. 309

5=0.0775 ft per ft;

0. 236

. 500

.468

. 612

. 625

. 612

. 844

T=18.0° C

0. 51

. 28

.44

. 38

.47

.47

.33

; p=1.14XH-5 sq ft per sec]

48

97

145

193

242

290

338

387

435

484

532

580

629

677

725

0.272

.441

.444

.384

.539

.577

. 671

. 604

. 679

.753

. 756

. 678

. 631

. 581

. 666

8.39

3. 19

3. 14

4. 19

2. 14

1. 863

1. 375

1. 699

1.346

1. 093

1.087

1.353

1. 559

1.834

1.401

5.54

8.99

9. 05

7. 84

10.98

11.76

13. 69

12.31

13. 83

15.35

15. 39

13.80

12.85

11. 85

13. 56

0. 0960

. 0606

. 0629

. 0762

.0537

.0508

.0437

. 0499

. 0444

. 0400

. 0403

. 0459

. 0501

i 0554

.0480

Test 6-13

[ 7=4.72 in. per hr;

l___-_-_-

2____--._

3___-_-_-

4 _____

5____ 

6

7

8_______-

9_ ______

10___--_-

11 ______

12_______

13_______

14

15__ ____

______ 0.00011

___ __ . 00022

______ .00033

_ ____ . 00044

______ .00055

.-_-_- .00066

______ .00076

______ .00087

______ .00098

______ .00109

______ .00120

.-_-_- .00131

______ .00142

______ .00153

__ __ .00164

0. 0017

. 0017

. 0027

.0027

.0027

.0033

. 0050

.0040

.0040

.0047

. 0043

. 0057

. 0070

. 0073

. 0050

0. 064

. 128

. 121

. 162

. 202

1QQ

. 153

.218

. 246

. 232

. 279

.230

. 203

. 209

. 328

5=0.0775 ft per ft;

0. 192

.375

. 366

.560

. 645

. 639

.870

T=16.5° C;

0. 67

.43

. 54

.39

.36

. 36

. 24

v=1.19X10-5 sq ft per sec]

37

73

110

147

184

220

257

294

330

367

404

440

477

514

551

0.274

. 547

.410

. 549

. 685

. 610

. 382

.607

. 685

. 596

. 750

.537

.427

.431

.818

8. 28

2.07

3.68

2.05

1.321

1.663

4.26

1. 680

1.319

1.743

1. 103

2. 151

3.39

3.34

.928

5. 58

11. 15

8.37

11.20

13.96

12.45

7.73

12. 38

13.98

12. 16

15.28

10.94

8. 72

8.79

16. 66

0. 0929

. 0465

. 0669

. 0500

.0401

.0465

. 0798

. 0483

.0428

.0505

.0396

. 0579

.0753

. 0752

. 0372
THE HYDRAULICS OF OVERLAND FLOW ON HILLSLOPES 

E. Summary of laboratory data for artificial rainfall Continued

Aei

Downslope distance

(ft)

Discharge, q

(cfs per ft)

Average

depth, D (ft)

Mean

velocity,

V (fps)

Surface Velocity

velocity,

V, (fps)

ratio,

V

V,

Reynolds

number, R

Froude

number, F

DarcyWeisbach

friction

factor, //

Chezy

coefficient,

C

Manning

resistance

coefficient,

n

Test 7-13

17=11.70 in. per hr; S=0.0550 ft per ft;

1_ __. __ ___

2__ ___________

3____-__-_---_-

4 ______

5__ ___________

6 __ _-_.__-___-

7 -_ __- _

8______--------

9 __ ___________

10____ _--_-_-

ll______-_____-

12____-_-------

13____-_--_--_-

14_____________

15___-_--------

0. 00027

. 00054

. 00081

. 00108

. 00135

. 00162

. 00189

. 00216

. 00244

. 00271

. 00298

. 00325

. 00352

. 00379

. 00416

0. 0030

.0040

. 0057

. 0057

.0070

. 0070

.0090

.0093

.0077

. 0080

.0083

.0090

.0097

.0100

.0097

0. 090 _

. 135

. 142 _

. 190

. 193 _

.232

.211 .

.233

. 316 _

.338

. 359 _

.361

.363 _

.379

.419 _

0. 324

.484

. 673

.697

.760

1. 036

1.504

T=14.0° C;

0.42

.39

. 35

.33

.45

. 35

. 25

v =1.27X10-5 sq ft per sec]

85

171

256

341

426

512

597

682

767

853

938

1023

1108

1194

1279

0.289

.376

.332

.444

.406

.488

.392

.426

. 635

.665

. 694

.671

. 649

. 668

.750

5.25

3. 11

4. 01

2.24

2. 66

1. 843

2.86

2.43

1.093

.992

.913

.979

1.043

.986

.783

7.01

9. 10

8. 02

10.73

9.84

11.82

9.48

10. 30

15. 35

16. 12

16.80

16.22

15.72

16. 16

18. 14

0. 0313

.0657 .07-n

.os<n

.06<V7

.05*1

.0721

.06^8

.0434

. 0416

.0402

.0422

.0441

.0431 .03">2

Test 7-14

[7=8.46 in. per hr; S=0.0550 ft per ft;

1_ ____________

2______________

3____.____---_-

4______________

5_ ______ _____

6________----_-

7_____-___-___-

8_____ _ __

9_ __--_____---

10______-_---_-

11 __ __________

12____-__------

13______--_--_-

14____-_---_-__

15 ____----__-_

0. 00020

. 00039

. 00059

. 00078

. 00098

. 00117

. 00137

. 00157

. 00176

. 00196

. 00215

. 00235

. 00254

. 00274

. 00294

0. 0020

.0037

.0053

.0057

. 0053

.0053

. 0060

.0070

. 0063

. 0067

.0073

. 0087

. 0077

.0077

.0087

0. 098 .

. 106

. Ill _

. 137

. 185 _

.222

.228 _

.224

.280 .

.292

.295 .

.270

. 330 _

.356

.337 _

0. 153

.314

.375

. 673

. 690

.844

1.070

T=14.0° C;

0. 69

.44

.59

. 33

.42

. 32

.33

y=1.27X10-6 sq ft per sec]

62

123

185

247

308

370

431

493

555

616

678

740

801

863

925

0. 386

.307

.269

. 320

.448

.538

. 518

.472

.434

. 629

. 608

. 510

. 663

. 715

.637

2.95

4. 67

6. 10

4.30

2. 19

1.524

1. 636

1.977

1. 139

1. 113

1. 189

1.691

1.002

.861

1.085

9. 34

7.43

6. 50

7. 74

10.84

13.00

12.55

11.42

15.04

15.21

14. 72

12.34

16.03

17.30

15.41

0. 1)570

.07M

. 09*3

.0819

.0578

.0482

.0510

.0575

.0429

.0428

. 0449

.0551

.0416

.03"5

.0442

Test 7-15

1_ __ __________

2_ __ __________

3__.__--_ _

4__ ___ __ _ __

5_ __ __________

6______ 

7____--__-_---_

8___-_--___--_-

9_. __-._______-

10_____________

ll____-____-__-

12__ __________

13_-_-__-------

14 __ -_-___--_

15 __ __-____-._

0. 00014

. 00028

. 00042

. 00056

. 00070

. 00084

. 00098

. 00112

. 00126

. 00140

. 00154

. 00168

. 00183

. 00197

. 00211

U=

0. 0020

. 0027

.0037

. 0043

.0047

. 0047

. 0057

. 0050

. 0047

.0050

.0067

.0070

.0077

.0073

. 0077

6.07 in. per hr; S=0.0550 ft per ft;

0. 070 _

. 104

. 114 _

. 131

. 149 _

.179

. 172 _

.225

.269 _

.281

.231 _

.241

.237 .

.269

. 274 _

0. 186

.353

.468

. 513

.571

. 606

.858

T=14.0° C;

0.56

.37

. 39

.44

.49

.40

. 31

y=1.27Xl(H sq ft per sec]

44

88

133

177

221

265

310

354

398

442

486

531

575

619

663

0.276

. 353

.330

.352

. 383

.460

.402

. 561

. 692

. 701

.498

.507

.476

.555

. 550

5.78

3. 54

4.03

3. 55

3.00

2.08

2. 73

1.400

.920

.897

1. 779

1.708

1.943

1.430

1.453

6. 67

8.53

7.99

8. 52

9.27

11. 13

9.71

13. 57

16. 73

16.95

12.03

12.28

11. 51

13.42

13. 32

0. 07^8

.0656

. 07.°8

.0710

.06^3

. 0552

.0653

. 0457

. 03"7

.03*3

.0541

.0534

.0579

.0492

.0501
A62 DYNAMIC AND DESCRIPTIVE STUDIES OF HILLSLOPES 

E. Summary of laboratory data for artificial rainfall Continued

Downslope distance Discharge, q Average 

(ft) (efs per ft) depth, D (ft)

Mean 

velocity, 

F(fps)

Surface Velocity 

velocity, ratio, 

V. (fps) V 

V,

Test 7-16

[7=4.77 in. per hr; S=0.0550 ft per ft; T=14.5° C

1 _______

2

3 ______..

4____ ._.

5 ______..

6_______-

7 __._

8_______-

9_____--_.

10____.__.

11_______.

12____ ..

13 ______

14_______

15_______

______ 0.00011

______ .00022

______ .00033

______ .00044

______ .00055

______ .00066

______ .00077

______ .00088

______ .00099

______ .00110

______ .00121

______ .00132

-__.__ .00144

______ .00155

______ .00166

0. 0020

. 0023

.0027

. 0033

. 0030

. 0037

.0040

. 0047

. 0043

. 0040

.0053

. 0057

.0077

. 0073

. 0053

0. 055

. 096

. 123

. 134

. 184

. 179

. 193

. 188

. 231

.276

. 229

.232

. 186

.212

. 312

[7=3.67 in. perhr;

1

2_______-

3 _ ______

4________

5___.____

6 _ _

7________

8________

9_ ._ _..

10_______

11 _____

12

13_______

14 ____.

15_______.

______ 0.00008

______ .00017

______ .00025

______ .00034

______ .00042

______ .00051

______ .00059

______ .00068

______ .00076

______ .00085

______ .00093

...___ .00102

_____ .00110

______ .00119

______ .00127

0. 0017

. 0017

. 0017

. 0023

. 0027

. 0030

. 0037

. 0033

.0033

. 0033

.0037

.0047

. 0047

. 0047

. 0053

0.050

. 100

. 150

. 137

.157

. 170

. 160

.206

. 231

. 257

. 252

. 217

. 235

.253

. 240

0. 222 0.

. 271

. 390

.435

.435

4Qfi

R1Q

Test 7-17

43

4Q

46

43

63

47

34

S=0.0550ft per ft; T=15.0° C;

0. 178 0.

.211

. 332

. 398

41Q

.455

.560

Test 8-13

56

65

51

5?,

61

48

45

[7=11.95 in. per hr; S=0.0342 ft per ft; T=14.0° C;

1 ___ __ _

2________

3 __ _____

4________.

5

6 _______

7______._.

8________.

9_______.

10_______.

!!___. ._..

12_______

13_ _____

14 __ ____.

15__ ____.

______ 0.00028

______ .00055

______ .00083

______ .00111

______ .00138

______ .00166

--_-__ .00194

______ .00221

______ .00249

______ .00277

______ .00304

______ .00332

______ .00359

______ .00387

______ .00415

0. 0033

. 0043

.0060

. 0083

. 0077

. 0087

0097

. 0097

. 0097

. 0090

. 0113

. 0093

. 0107

. 0103

. 0090

0. 084

ion

. 138

. 133

. 180

91 c.

. 200

. 228

. 257

.307

.269

. 357

.336

. 376

. 461

fl 94-4. 0

. 339

R1Q

.673

. 583

coo

. 760

53

°.Q

35

34

53

61

50

Reynolds 

number, R

Froude 

number, F

DareyWeisbaeh 

friction 

factor, //

Chezy Manning 

coefficient, resistance 

C coefficient, 

n

; v=1.25X10-5 sq ft per sec]

35

71

106

141

177

212

247

283

318

353

389

424

459

495

530

0.217

.353

.417

.411

. 592

. 519

.538

.483

. 621

.769

. 554

.542

.373

.437

. 755

9. 37

3.54

2. 53

2. 60

1.256

1. 636

1. 522

1.884

1. 142

.744

1.432

1.501

3. 15

2. 30

. 772

5. 24

8. 54

10. 09

9.95

14.32

12. 55

13.01

11. 69

15. 02

18. 61

13.41

13. 10

9. 04

10. 58

18.27

0. 1015

. 0639

. 0555

. 0582

. 0398

. 0470

. 0459

. 0525

. 0403

. 0321

.0467

. 0484

. 0738

.0625

. 0343

,=1.23X10-S sq ft per sec]

28

55

83

110

138

165

193

221

248

276

303

331

359

386

414

0. 214

.427

. 641

. 504

. 532

. 547

.464

. 632

. 709

. 788

. 730

.558

. 604

. 650

. 581

9. 64

2. 41

1.071

1. 736

1.552

1.471

2.04

1. 102

.876

. 708

.826

1.414

1.206

1.040

1. 304

5. 17

10.34

15. 51

12. 18

12.88

13.23

11.22

15.29

17. 15

19.08

17.66

13.50

14. 62

15. 74

14.06

0. 1002

. 0501

.0334

. 0447

. 0435

. 0431

. 0526

.0379

. 0338

.0303

. 0334

. 0455

.0420

. 0390

. 0446

,=1.27X10-5 sq ft per sec]

87

174

261

348

435

523

610

697

784

871

958

1045

1132

1219

1306

0.258

. 347

. 314

. 257

. 361

.406

. 358

.408

. 460

.571

.446

. 653

. 572

. 653

. 857

4. 12

2. 28

2. 78

4. 13

2.09

1. 658

2. 14

1.644

1.294

. 841

1. 376

. 643

.835

. 642

.373

7.91

10. 64

9. 63

7.89

11.09

12.47

10.98

12.52

14. 11

17. 50

13. 68

20. 02

17.56

20. 03

26. 28

0. 0732

. 0569

. 0664

. 0850

. 0601

. 0883

. 0631

. 0553

.0491

. 0391

. 0519

. 0344

. 0401

. 0349

.0260
THE HYDRAULICS OF OVERLAND FLOW ON HILLSLOPES

E. Summary of laboratory data for artificial rainfall Continued

A63

Downslope distance

(ft)

Discharge, q

(cfs per ft)

Average

depth, D (ft)

Mean

velocity,

V (fps)

Surface

velocity,

V, (fps)

Velocity

ratio,

V

V,

Reynolds

number, R

Froude

number, F

DarcyWeisbach

friction

factor, //

Chezy

coefficient,

C

Manning

resistance

coefficient,

n

Test8-14

[7=8.78 in. per hr; ,8=0.0342 ft per ft;

1 __-____--____

2 ____________

3 ______-_-_-._

4 _ _ _ _

5

6_ ______

7

8_______-_-_-_-

9_____-_____.__

10____-_-----__

11 __ __________

12_ ___________

13______-____._

14 ____________

15_ ___________

0. 00020

. 00041

. 00061

. 00081

. 00102

. 00122

. 00142

. 00163

. 00183

. 00203

. 00224

. 00244

. 00264

. 00284

. 00305

0. 0030

.0043

. 0050

.0057

. 0060

. 0070

.0087

. 0077

.0067

. 0077

. 0100

. 0080

.0073

. 0083

. 0080

0.068

.095

. 122

. 143

.169

. 174

. 163

.211

.273

. 264

. 224

. 305

. 362

. 343

. 381

0.221

.372

.496

. 560

.625

.619

. 667

T=14.0° C;

0.43

.38

. 35

.38

.42

.49

. 51

v=1.27X10-5 sq tt per sec]

64

128

192

256

320

384

448

512

576

640

704

768

832

896

960

0. 219

. 255

. 304

. 334

. 384

. 366

. 308

.424

.607

. 530

. 395

. 600

. 746

. 663

. 750

5.71

4. 20

2.96

2.46

1.851

2. 16

2.89

1.524

.792

.973

1.756

.758

.491

. 622

.486

6.71

7.83

9.33

10. 24

11. 80

10.92

9.45

13.00

18. 04

16. 27

12. 11

18.44

22.91

20. 35

22.02

0. 0849

.0772

. 0665

OfMQ

. 0542

. Of 01

. 0720

. 0513

. 0361

. 0410

. 0575

. 0?54

.0288

. OP32

.0291

Test 8-15

1_ ____________

2

3______________

4______________

5________._____

6____-_-______-

7 _ _ _ _

8

9 _ ____ _ __

10____________.

!!___ _ ____ __

12 _____ ______

13_____________

14_____________

15_____________

0. 00014

. 00028

. 00042

. 00057

. 00071

. 00085

. 00099

. 00113

. 00127

. 00141

. 00156

. 00170

. 00184

. 00198

. 00212

[/=

0. 0027

. 0030

. 0050

.0043

. 0043

.0060

. 0060

. 0060

. 0063

. 0053

. 0070

. 0067

.0077

. 0073

.0063

! 6.11 in. per hr;

0.052

. 094

. 085

. 132

. 164

. 141

. 165

. 189

.212

. 267

. 222

. 253

.239

. 271

.337

,8=0.0342 ft per ft;

0.208

. 362

. 398

.491

.465

.484

. 683

T=14.5° C;

0.45

.37

. 35

.39

. 57

. 52

.40

x=1.25X10-5 sq ft per sec]

45

90

136

181

226

271

317

362

407

452

498

543

588

633

679

0. 176

. 302

. 212

.355

.441

. 320

. 375

.430

.471

. 646

.467

.545

.480

. 559

. 749

8. 80

2.99

6. 10

2.17

1.408

2. 66

1.942

1.479

1. 234

.655

1.215

.922

1. 180

.876

.489

5.41

9.28

6.50

10.89

13. 53

9. 84

11.52

13. 20

14.45

19.83

14.35

16. 72

14. 73

17. 15

22.95

0. 1035

. OP14

.0954

. Of 56

. 0447

. OP50

. Of 55

. 0485

. 0446

.0?16

.0458

.0^90

. 0453

. Of85

.02^1

Test 8-16

1_ __ __ _._ _

2

3______________

4_ __ _________

5_

6______________

7________._____

8_____________-

9______________

10_____________

11

12_____________

13

14_____________

15_. ___________

0. 00011

. 00022

. 00033

. 00044

. 00055

. 00066

. 00077

. 00088

. 00100

. 00111

. 00122

. 00133

. 00144

. 00155

. 00166

[/=

0. 0023

. 0030

. 0033

. 0037

. 0037

. 0057

. 0043

. 0050

. 0050

.0047

. 0057

. 0063

. 0087

. 0070

. 0050

4.78 in. per hr;

0.048

.074

. 101

. 120

. 149

. 116

. 180

. 177

. 199

. 235

. 213

. 211

. 165

. 221

. 332

8=0.0342 ft per ft;

0. 191

.347

. 375

.408

. 370

. 394

. 600

T=16.0°C;

0. 39

. 35

. 31

.43

. 64

.54

.37

*=1. 20X10-5 sq ft per sec]

37

74

111

147

184

221

258

295

332

369

406

442

479

516

553

0. 176

. 233

. 310

. 348

.432

.271

.484

.441

.496

. 604

.498

.469

. 312

.465

. 828

8.80

4. 83

2. 85

2.26

1.468

3.73

1. 169

1.406

1. 112

.750

1. 107

1.247

2.82

1.263

. 400

 5.41

7. 31

3. 51

10.67

13.25

8. 31

14. 85

13. 54

15.22

18.53

15. 26

14.37

9. 58

14. 28

25. 38

0. 1C07

.0780

. Of09

. Of 53

. 0445

.0763

. 0407

. 0458

. 0408

.0331

. 0416

.0448

. 0710

. 0459

.0244
A64 DYNAMIC AND DESCRIPTIVE STUDIES OF HILLSLOPES

E. Summary of laboratory data for artificial rainfall Continued

Mean 

Downslope distance Discharge, q Average velocity, 

(ft) (cfs per ft) depth, D (ft) V (fps)

Surface 

velocity, 

V, (fps)

Velocity 

ratio, 

V 

V,

Reynolds 

number, R

Froude 

number, F

DarcyWeisbach 

friction 

factor, //

Chezy 

coefficient, 

C

Manning 

resistance 

coefficient, 

n

Test 8-17

[7=3.61 to. per hr;

1 ______

2

3________

4 ______

5 _ _

6

7_____-__.

8 .-__

9 _ _

10_______

ll___-.__.

12___._ .

13______-

14_______.

15____.__.

______ 0.00008

-___-- .00017

______ .00025

______ .00033

______ .00042

______ .00050

______ .00058

______ .00067

______ .00075

______ .00084

______ .00092

______ .00100

______ .00109

______ .00117

______ .00125

0. 0020

. 0033

. 0027

. 0033

. 0033

. 0043

. 0037

. 0037

.0040

.0040

.0043

.0057

.0060

.0053

.0057

0. 042

.051

. 093

. 101

. 127

. 117

. 158

. 181

. 188

. 209

.214

. 176

. 181

. 221

.220

8=0.0342 ft per ft; T=17.0° C; p=1.17X10~5 sq ft per sec]

0. 172

. 279

. 319

. 380

. 345

.402

. 504

0.30

. 36

. 37

.48

.61

.44

.44

29

57

86

114

143

171

200

228

257

285

314

343

371

400

428

0. 165

. 156

.315

. 310

. 390

. 315

.458

.525

. 524

. 582

. 575

.411

.411

. 535

. 514

9.99

11. 18

2. 75

2.85

1.639

2.77

1. 306

.995

.997

.807

.827

1.621

1. 614

. 956

1. 038

5.08

4.80

9.68

9.51

12.54

9. 65

14.05

16.09

16.07

17.87

17. 65

12.61

12. 63

16.42

15. 75

0. 1048

. 1206

.0578

. 0609

.0462

. 0627

.0420

. 0367

.0372

.0335

.0343

. 0503

. 0506

.0382

. 0402

Test 9-13

[7=11.40 in. per hr; -8=0.0170 ft per ft;

1 _______

2_ .____.

3 _______

4 _______

5--_-___-

6

7_--_---_.

8_--.--__.

9________

10_______

11. ______

12__-_-__

13_--____

14_______

15-------

______ 0.00026

______ .00053

______ .00079

______ .00106

______ .00132

______ .00158

______ .00185

______ .00211

______ .00238

. 00264

______ .00290

______ .00317

______ .00343

______ .00369

______ .00396

0. 0060

. 0067

. 0070

. 0083

. 0080

. 0090

. 0100

. 0087

. 0090

. 0087

. 0107

. 0117

.0117

. 0130

. 0117

0. 044

07Q

. 113

. 127

. 165

. 176

. 185

.243

.264

. 303

071

. 271

. 293

.284

. 338

0. 165

. 297

. 357

. 522

. 560

. 645

. 800

T=15.0° C;

0.48

. 43

40

.47

. 54

.42

. 36

i-=1.23X10-5 sq ft per sec]

86

172

257

343

429

515

601

687

772

858

944

1030

1116

1201

1287

0. 100

. 170

.238

.246

. 325

.327

. 326

. 459

.491

. 573

.462

.441

.477

.439

. 550

13.57

4.70

2.40

2.25

1.287

1.273

1.280

. 645

.566

.415

. 638

. 698

. 599

.706

. 449

4. 36

7.40

10. 36

10. 69

14. 15

14.23

14. 19

19. 98

21.33

24.91

20.09

19.21

20.77

19. 10

23.95

0. 1468

. 0880

. 0633

.0631

.0474

. 0481

. 0491

. 0340

. 0321

.0273

.0350

.0372

. 0344

.0382

. 0298

Test 9-14

1 -___-__

2 ______

3____.___

4 ______

5.. ._.._-.

6____

7_

8

9________.

10____-__.

11 _...

12-____._.

13-____-_.

14-_-__._.

15_____-_.

______ 0.00020

______ .00039

______ .00059

______ .00078

______ .00098

______ .00117

______ .00137

______ .00156

______ .00176

______ .00195

______ .00215

.____- .00234

______ .00254

______ .00273

.00293

[7=8.44 in

0. 0043

. 0063

.0063

. 0080

.0077

.0057

. 0073

. 0077

.0070

. 0077

. 0110

. 0100

. 0107

.0110

. 0080

. per hr;

0. 045

. 062

. 093

. 098

197

. 206

. 187

. 203

. 251

.254

. 195

.234

.237

94.O

. 366

-8=0.0170 ft per ft;

0. 131

.252

. 335

.442

.419

. 462

coo

T=14.5° C;

0.47

. 39

. 62

.46

.61

. 51

.42

K=1.25X10-s sq ft per sec]

62

125

187

250

312

375

437

500

562

625

687

750

812

875

937

0. 121

. 138

.207

. 193

.255

.481

. 386

.408

. 528

. 510

. 328

.413

.404

.418

.720

9.30

7. 18

3. 19

3.65

2.09

.588

.914

.818

.487

. 523

1.267

.800

.834

.777

. 262

5.26

5.99

8.99

8.40

11. 10

20.93

16.79

17.75

23.00

22. 19

14.26

17.94

17. 58

18.21

31.36

0. 1149

. 1076

.0717

.0798

. 0601

. 0303

.0394

.0376

. 0394

. 0300

.0496

. 0388

. 0401

.0389

.0214
THE HYDRAULICS OF OVERLAND FLOW ON HILLSLOPES

E. Summary of laboratory data for artificial rainfall Continued

A65

Downslope distance

(ft)

Discharge, q

(cfs per ft)

Average

depth, D (ft)

Mean

velocity,

V (fps)

Surface

velocity,

V, (fps)

Velocity

ratio,

V

V,

Test 9-15

[7=5.93 in. per hr; 5=0.0170 ft per ft; T=14.0° C

1 _

2

4 _ _ _ _

5

7

8 _ _ _

9

11

12 - -__

13 _

15- 

1

2

3_ _____________

5

6--_ 

7_ -__ _ _ _

9 _

10 __

12 _

13--- 

15

0. 00014

. 00027

. 00041

. 00055

. 00069

. 00082

. 00096

. 00110

. 00123

. 00137

. 00151

. 00165

. 00178

. 00192

. 00206

0. 00011

. 00023

. 00034

. 00046

. 00057

. 00069

. 00080

. 00092

. 00103

. 00115

. 00126

. 00137

. 00149

. 00160

. 00172

0. 0043

. 0040

. 0053

. 0050

. 0063

. 0077

. 0080

. 0070

. 0067

. 0057

.0087

. 0093

. 0103

. 0100

. 0070

[7=

0. 0043

. 0050

. 0047

. 0050

. 0053

. 0077

. 0070

. 0057

. 0060

. 0050

. 0073

. 0073

. 0100

. 0083

. 0067

0. 032

. 069

. 078

. 110

. 109

. 107

. 120

. 157

. 184

.241

. 173

. 177

. 173

. 192

. 294

4.95 in. per hr;

0. 027

. 046

. 073

. 092

. 108

. 089

. 115

. 161

. 172

.229

. 173

. 188

14Q

. 193

.256

0. 143

. 313

. 323

. 345

. 364

. 309

.438

0.48

. 35

. 33

.46

. 66

. 57

. 44

Test 9-16

5=0.0170 ft per ft; T=14.5° C;

0. 150

. 203

. 234

.328

.341

. 313

.447

0.31

.45

. 38

.49

. 67

. 60

.43

Test 9-17

[7=3.57 in. per hr; S=0.0170 ft per ft; T=13.0° C;

1

2

4 ______ __.

5__-__-_-___-__

6 _

7. -------------

9_ _

jj

12-_--_-_--_-_-

13-_------_--_-

15

0. 00008

. 00017

. 00025

. 00033

. 00041

. 00050

. 00058

. 00066

. 00074

. 00083

. 00091

. 00099

. 00107

. 00116

. 00124

0. 0040

. 0047

. 0027

. 0040

.0047

. 0057

. 0047

. 0040

. 0047

. 0043

. 0053

. 0057

. 0073

.0073

. 0060

0. 021

. 035

. 092

nCQ

.088

. 087

. 123

. 165

. 158

. 192

. 171

. 174

. 147

. 158

.207

0. 168

193

. 246

. 248

. 270

. 281

.372

0. 21

.43

. 35

.67

. 71

. 62

.43

DarcyReynolds

number, R

Froude

number, F

Weisbach

friction

Chezy

coefficient,

C

factor, //

Manning

resistance

coefficient,

n

; »=1.27X10~5 sq ft per sec]

43

86

130

173

216

259

302

345

389

432

475

518

561

605

648

0. 086

. 192

. 189

. 274

. 242

. 215

. 236

. 331

. 397

. 563

.327

. 324

. 300

. 339

. 619

18

3

3

1

2

2

1

1.

1

1

1

39

68

82

810

32

95

43

244

867

430

273

300

507

188

355

3. 74

8.37

8.21

11. 93

10. 53

9.35

10. 29

14. 39

17.24

24.48

14. 23

14.08

13.07

14. 73

26.94

0. 1617

.0714

. 0762

. Of 20

. 0612

. 0713

. 0 52

. 0456

.0?78

.0259

.0478

. 0489

. 0535

. 0473

. 0244

/*=1.25X10-5 sq ft per sec]

37

73

110

147

183

220

257

293

330

366

403

440

476

513

550

0. 073

. 115

. 188

.229

. 262

.242

.376

.391

.571

.357

. 388

.263

. 373

. 552

25

10

2

1

2

1,

1

84

35

386

59

990

426

32

963

848

418

068

905

Q73

976

448

3. 16

4.99

8. 17

9.98

11.38

7.78

10. 54

16. 36

17.43

24.83

15.53

16.87

11.43

16.25

23. 98

0. 1915

. 1243

. 0752

. 0622

. 0550

. 0857

. 0622

.0388

. 0367

. 0250

.0425

.03^2

.0609

. 0415

. 0272

/*=1.23X10-5 sq ft per sec]

27

54

81

107

134

161

188

215

242

269

295

322

349

376

403

0. 058

. 090

. 312

.231

.226

. 203

. 316

.460

.406

. 516

. 414

.407

.303

. 326

.470

39

16

1

2

3

1

1

1

73

81

3Q7

54

66

30

361

644

825

511

794

825

480

281

613

2.55

3.92

13. 58

10.07

9.85

8.84

13.76

20. 01

17.68

22.46

18. 01

17.68

13. 19

14. 18

20.49

0. 2348

.0412

. 0624

. 0717

. 0446

. 02^9

.034,7

. 02-9

. 034,8

. 0501

.04*56

. 0729
A66 DYNAMIC AND DESCRIPTIVE STUDIES OF HILLSLOPES

F. Summary of field data for overland flow sites

Downslope distance Discharge, q 

(ft) (cfs per ft)

l_-_-____

3-_-____-

5-_______

7___---__.

9__-__-_-

ll___-___.

13_ _

15_______.

17.__ _..

19_______

21_ ______

23_______

25_______.

27. _______

29_______

31_______

33______.

35______.

37_______

39_______.

41 _ .__

43_______.

1_ ______

3

5________.

7___.____.

9________.

!!_______.

13 _

15 _

17_______.

19. _______

21_______.

23_______.

25_______.

27---____.

29_______.

31_______.

33_______.

35_______.

37-___.__.

39_______.

41_______.

______ 0.00007

._.___ .00021

______ .00035

______ .00049

______ .00062

______ .00076

______ .00090

.__.._ .00104

_-__.- .00118

______ .00132

______ .00146

...___ .00160

______ .00173

______ .00187

______ .00201

______ .00215

______ .00229

______ .00243

______ .00257

______ .00271

.-____ .00285

______ .00298

______ 0.00008

---___ .00024

______ .00039

.-__-_. .00055

_-_-_- .00071

______ .00087

______ .00102

._____, .00118

______ .00134

__ ___ . 00150

______ .00165

______ .00181

______ .00197

______ .00212

______ .00228

______ .00244

______ .00260

______ .00275

______ .00292

______ .00307

.___._ .00323

Average 

depth, D (ft)

[1=7.02 in.

0. 0004 

. 0066 

. 0071 

. 0081 

. 0046 

. 0106 

. 0143 

. 0214 

. 0180 

. 0204 

. 0176 

. 0136 

. 0151 

.0265 

. 0249 

. 0246 

. 0189 

. 0209 

. 0361 

. 0280 

. 0380 

. 0486

[1=7.41 in.

0. 0011 

. 0006 

. 0052 

. 0182 

. 0095 

. 0184 

. 0119 

. 0199 

. 0160 

. 0201 

.0098 

. 0249 

. 0266 

. 0203 

. 0295 

. 0230 

. 0228 

.0299 

. 0240 

. 0284 

. 0206

Mean 

velocity, 

V (fps)

per hr; 72=3.0 in.

0. 174 

.032 

.049 

.060 

. 136 

. 072 

.063 

.049 

. 066 

. 065 

. 083 

. 117 

. 115 

.071 

. 081 

.088 

. 121 

. 116 

. 071 

. 097 

. 075 

. 061

per hr; R =3.4 in.

0. 072 

. 394 

. 076 

. 030 

. 075 

. 047 

. 086 

. 059 

. 084 

. 074 

. 169 

. 073 

. 074 

. 105 

.077 

. 106 

. 114 

.092 

. 121 

. 108 

. 157

Surface 

velocity, 

V. (fps)

Velocity 

ratio, Reynolds Froude 

V number, R number, F 

V^

Pole Creek Site 1

per hr; S=0.0960 ft per ft; T=10° C;

0. 026 

.032 

. 090 

. 122 

.119 

. 167 

. 148 

. Ill 

. 084 

. 064 

. 101 

. 146 

. 144 

.255 

. 165 

.244 

. 275 

.248 

.175 

. 190 

.219 

. 204

6. 67 

. 98 

. 55 

.49 

1. 14 

.43 

.43 

.44 

.78 

1. 01 

.82 

.80 

. 80 

.28 

.49 

. 36 

.44 

.47 

.41 

. 51 

.34 

.30

Pole Creek Site 2

per hr; S=0.3320 ft per ft; r=13°C;

0. 127 

. 109 

. 128 

. 147 

. 122 

. 119 

. 130 

. 147 

. 168 

. 172 

. 175 

. 189 

.204 

. 195 

.250 

.286 

.250 

.260 

. 225 

.207 

. 265

0. 56 

3. 60 

. 59 

.21 

. 61 

.39 

. 66 

.40 

. 50 

.43 

.96 

. 39 

. 36 

. 54 

.31 

.37 

.46 

.35 

. 54 

. 52 

. 59

Darcy- Chezy Manning 

Weisbach coefficient, resistance 

friction C coefficient, 

factor, // n

v= 1.41X10-5 sq ft per sec]

20 

59 

98 

138 

177 

217 

256 

295 

335 

374 

413 

453 

492 

532 

571 

610 

650 

689 

728 

768 

807 

847

1. 529 

.068 

. 102 

. 117 

.353 

. 123 

. 093 

. 059 

. 086 

.080 

. 110 

.177 

. 165 

.077 

. 090 

.098 

. 155 

. 142 

. 066 

. 102 

.068 

. 049

0.33 

164. 48 

73.46 

55. 65 

6. 17 

50. 56 

88.82 

224. 03 

103. 74 

120. 87 

63.48 

24.41 

28.28 

131. 08 

94.31 

79.45 

31.83 

38. 28 

176. 58 

74.04 

167. 45 

318. 78

27.98 

1. 25 

1.87 

2. 15 

6.46 

2.26 

1.70 

1.07 

1. 58 

1.46 

2. 01 

3.25 

3.02 

1.40 

1. 65 

1.80 

2.85 

2. 59 

1.21 

1.87 

1.24 

.90

0. 0146 

. 5187 

. 3511 

. 3123 

. 0944 

.3128 

.4336 

.7373 

.4870 

.5372 

.3797 

. 2255 

. 2470 

. 5841 

.4908 

. 2424 

2724 

. 3037 

. 7147 

. 4434 

. 7012 

1. 0075

v=1.31X10-5 sq ft per sec]

24 

72 

120 

168 

216 

264 

312 

360 

409 

457 

505 

553 

601 

649 

697 

745 

793 

841 

889 

937 

985

0. 380 

2.831 

. 185 

.040 

. 135 

. 061 

. 139 

.074 

. 116 

.092 

.300 

.081 

. 080 

. 130 

. 079 

. 123 

. 133 

. 094 

. 138 

. 113 

. 192

18.40 

. 33 

77.60 

1695. 50 

145. 99 

712. 34 

136. 60 

483. 98 

195. 79 

310. 54 

178. 10 

402. 91 

415. 42 

158. 37 

421. 13 

174. 73 

150. 30 

301. 45 

139. 50 

207. 84 

71.89

3.74 

27.90 

1. 82 

.39 

1.33 

.60 

1.37 

. 73 

1. 15 

. 91 

1.20 

.80 

.79 

1.28 

.78 

1.21 

1. 71 

. 92 

1. 36 

1. 11 

1.89

0. 1288 

. 0156 

.3427 

1. 9726 

. 5198 

1. 2824 

. 5220 

1. 0697 

. 6565 

.8586 

.5768 

1. 0132 

1. 0413 

.6145 

1. 0662 

.6589 

. 4660 

. 9044 

. 5928 

. 7444 

.4147
THE HYDRAULICS OF OVERLAND FLOW ON HILLSLOPES

F. Summary of field data for overland flow sites Continued

A67

Downslope distance Discharge, q 

(ft) (cfs per ft)

Average 

depth, D (ft)

Mean 

velocity, 

V (fps)

Surface 

velocity, 

V, (fps)

Velocity 

ratio, Reynolds 

V number, R

Darcy- Chezy Manning 

Froude Weisbach coefficient, resistance 

number, F friction C coefficient, 

factor, // n

Pole Creek Site 3

1

5 _ _

7

9

13

15_-_--_-

17

19

21

23 _

25-- . 27. . 29

31

33

35

37--- .

41

43

45-_-_---.

47 .

______ 0.00010

______ .00031

______ .00052

______ .00073

______ . 00094

.00115

______ .00135

______ .00156

______ .00177

______ .00198

______ .00219

______ .00240

______ .00261

--_-_- .00281

______ .00302

______ .00323

______ .00344

.___ _ . 00365

______ .00386

______ .00406

______ .00427

______ .00448

______ .00469

.__ __ . 00490

[1=8.50 in.

0. 0051

. 0093

. 0083

. 0128

. 0103

. 0243

. 0151

. 0200

. 0142

. 0329

. 0193

. 0350

. 0313

. 0235

. 0356

. 0338

. 0299

. 0428

. 0433

. 0436

. 0400

. 0556

.0475

. 0441

per hr; R=4.5 in. per hr; S=0.2080 ft per ft; T=13C

0.020

. 034

. 063

. 057

. 091

. 047

. 090

.078

. 125

. 060

. 113

. 069

. 083

. 120

.085

. 096

. 115

. 085

. 089

. 093

. 107

. 081

. 099

. Ill

0. 097

. 101

. 160

. 116

. 242

. 184

. 190

. 147

. 173

. 182

. 182

. 177

. 201

. 250

. 184

. 187

.267

.267

. 200

. 238

. 238

. 312

.288

. 225

0.21

. 33

. 39

.49

. 38

. 26

.47

. 53

. 72

. 33

. 62

. 39

.41

.48

.46

. 51

.43

. 32

.45

. 39

.45

.26

. 34

.49

' C; i.=1.31X10-s sq ft per sec]

32

95

159

223

286

350

414

477

541

605

668

732

795

859

923

986

1050

1114

1177

1241

1304

1368

1432

1495

0.050

.061

. 121

. 089

. 158

. 053

. 129

. 097

. 184

.058

. 144

. 065

. 083

. 138

. 079

.092

. 117

. 073

. 075

.079

. 094

. 060

. 080

. 093

656. 71

441. 40

112. 76

211. 09

66. 64

584. 43

100. 55

175. 24

48. 93

486. 42

80. 42

399. 66

242. 27

87.88

264. 63

198. 16

121. 14

315. 92

292. 89

268. 94

187. 90

458. 57

261. 26

191. 43

0. 63

. 76

1. 51

1. 11

1.97

.66

1. 60

1. 21

2. 30

. 73

1.79

.80

1. 03

1.71

.99

1. 14

1.46

.90

. 94

.98

1. 17

. 75

.99

1. 16

0. 9P41

.9004

.4467

. 6565

. 3559

1. 5421

.4661

. 6448

. 3216

1. 1663

.4340

1. 0684

.8168

.4689

.8717

.7482

. 5732

.9P25

.9476

.9090

. 7491

1. 2P72

.9091

. 7C86

New Fork River Site 1

1 _ ____.

5

1. ........

9_ ____-_..

13

15_______.

19

21

23

25

27

29

31

33

35 _ ___..

37_ ______

39. __. .

43

._ _ 0. 00010

______ .00031

______ .00052

. ___ .00073

______ .00094

______ .00115

______ .00135

______ .00156

. __ _ .00177

.__.__ .00198

______ .00219

.__ __ . 00240

______ .00261

______ .00281

._ __ .00302

______ .00323

______ .00344

______ .00365

______ .00386

.00406

______ .00427

______ . 00449

[1=8.50 in.

0. 0018

.0070

. 0104

. 0139

. 0138

. 0178

.0176

. 0255

. 0203

. 0195

. 0209

. 0233

. 0269

. 0221

. 0233

.0215

. 0283

. 0385

. 0200

.0219

. 0263

. 0214

per hr; JJ=4.5 in.

0.058

. 045

. 050

.052

. 068

. 064

.077

. 061

. 077

. 102

. 105

. 103

.097

. 133

. 130

. 150

.122

. 095

. 193

. 186

. 162

. 209

per hr; S=0.1000 ft per ft; T=13°

0. 000 __

. 110

. 169

. 223

. 261

.261

.286

.261

.273

. 317

. 375

.465

. 375

.402

.375

.429

.438

. 500

. 514

. 550

. 625

. 714

0.40

. 30

. 24

. 26

.25

.27

. 23

.28

. 32

.28

. 22

. 26

. 33

. 35

. 35

. 27

. 19

.37

. 34

.26

. 29

C; i.=1.31X10-5 sq ft per sec]

32

95

159

223

286

350

414

477

541

605

668

732

795

859

923

986

1050

1114

1177

1241

1304

1368

0.240

. 094

.087

.078

. 102

. 085

. 102

. 068

. 095

. 128

. 128

. 119

. 104

. 158

. 150

. 181

. 127

. 085

. 240

. 221

. 176

. 252

13. 83

90. 25

106. 74

129. 91

76.88

110. 56

76.47

174. 81

88. 20

48.76

49. 11

56.69

73.95

30. 59

35. 68

24. 55

49.38

110. 59

13. 86

16. 38

25.69

12.57

4. 32

1. 69

1.55

1.41

1. 83

1. 53

1. 84

1. 21

1. 71

2.30

2. 29

2. 13

1.87

2.90

2.69

3. 24

2. 29

1. 53

4. 31

3.97

3. 17

4. 53

0. 1212

. 3FS4

. 4510

. 5224

.4014

.5023

.4169

. 6703

. 4f 84

. 3438

. 3730

. 4400

. 2738

.2S83

.2442

. 5712

. 2C01

. 2585

. 1746
A68 DYNAMIC AND DESCRIPTIVE STUDIES OF HILLSLOPES

F. Summary of field data for overland flow sites Continued

Downslope distance Discharge, q 

(ft) (cfs per ft)

1

3_ __ ..__

5_ _____

7________

9________

!!_______

13_______

15_______

17____-__

1Q

21_______

23_______

25_______

27_______

29___--_-

31_______

33_ _____

35_____._

37____-_-

39______-

41_______

43_______

1 _____

3 _______

5___.____

7________.

9__-_____

11

13_ _____

15 __ ____.

l7-___-__.

19_______

21_______

23__ ____.

25__ ____.

27 _______

29_______.

31_ _____

33_______.

35_______.

37___-_-_.

39 _.___.

41_______.

43_______.

__ _ _ 0. 00009

______ .00028

______ .00047

.00066

______ .00085

______ .00104

______ .00123

______ .00142

______ .00161

______ .00180

______ .00199

______ .00218

______ .00237

______ .00256

______ .00275

______ .00294

______ .00313

______ .00332

______ .00351

______ .00370

.00389

______ .00408

______ 0.00010

______ .00031

__ __ .00052

______ .00073

._ __ .00094

.-____ .00115

______ .00135

______ .00156

______ .00177

______ .00198

. _.__ . 00219

.__.__ .00240

. ___ . 00261

.00281

______ .00302

. _ _ . 00323

.___._ .00344

______ .00365

______ .00386

______ .00406

______ .00427

______ .00448

Mean 

Average velocity, 

depth, D (ft) V (fps)

[/=8.08in.

0. 0155 

. 0114 

.0155 

.0341 

. 0111 

.0124 

.0148 

.0280 

. 0164 

.0234 

. 0294 

. 0296 

. 0154 

. 0664 

.0398 

.0250 

. 0418 

. 0706 

.0945 

.0941 

.0486 

.0905

U=8.50in.

0. 0026 

. 0144 

.0025 

. 0164 

. 0188 

. 0206 

. 0146 

. 0103 

.0055 

.0125 

.0195 

. 0180 

.0148 

. 0343 

.0191 

.0310 

.0204 

.0389 

. 0293 

. 0349 

. 0422 

.0281

Surface 

velocity, 

V. (fps)

Velocity 

ratio, Reynolds 

V number, R 

V.

New Fork River Site 2

per hr; .R=4.1 in. per hr; £1=0.0290 ft per ft; T=13°

0.006 

. 025 

. 031 

. 020 

.077 

. 084 

.083 

.051 

.098 

.077 

. 068 

. 074 

. 154 

.039 

.069 

. 118 

.075 

.047 

.037 

. 039 

.080 

.045

per hr; .R=4.5 in.

0.040 

.022 

.208 

. 045 

.050 

.056 

. 093 

. 152 

. 322 

. 158 

. 112 

. 133 

. 176 

. 082 

. 158 

. 104 

. 169 

.094 

. 132 

. 116 

. 101 

. 160

0. 042 

. 067 

. 125 

. 163 

. 163 

. 184 

. 160 

. 146 

. 158 

. 223 

. 190 

.204 

.232 

. 183 

.207 

.429 

. 429 

. 244 

. 101 

.071 

. 103 

. 125

0. 15 

. 38 

.25 

. 12 

.47 

.46 

. 52 

.35 

. 62 

.35 

.36 

. 36 

. 66 

.21 

. 33 

.28 

. 18 

. 19 

. 37 

.55 

.78 

. 36

Boulder Lake Site 1

per hr; ,8=0.1880 ft per ft; T=10°

0. 082 

. 090 

. 129 

. 129 

. 130 

. 165 

. 165 

. 132 

. 136 

. 177 

. 181 

. 141 

. 130 

. 197 

.236 

. 173 

.252 

. 268 

.263 

. 270 

. 336 

.338

0.49 

. 24 

. 61 

.35 

. 38 

. 34 

.56 

1. 14 

2. 37 

.89 

. 62 

.94 

1. 35 

.42 

.67 

.60 

. 66 

.35 

.50 

.43 

. 30 

.47

Froude 

number, F

DarcyWeisbach 

friction 

factor, //

Chezy 

coefficient, 

C

Manning 

resistance 

coefficient, 

n

C; i-=1.31X10-5 sq ft per sec]

29 

87 

145 

203 

261 

319 

377 

435 

493 

551 

609 

664 

724 

782 

840 

898 

956 

1014 

1072 

1130 

1188 

1246

0.009 

.041 

.043 

. 019 

. 129 

. 133 

. 120 

.054 

. 104 

.089 

. 070 

. 075 

. 219 

. 026 

.061 

. 131 

.065 

.031 

. 021 

.023 

. 064 

. 026

3112. 50 

136. 25 

123. 66 

669. 98 

14. 02 

13.07 

15.90 

81. 05 

12.65 

29.41 

47.78 

40. 71 

4.84 

332. 91 

62.27 

13.48 

65. 66 

238. 74 

510. 13 

455. 15 

56. 58 

332. 37

0.29 

1.38 

1. 44 

. 62 

4.29 

4. 44 

4. 02 

1.78 

4.51 

2.96 

2.32 

2.52 

7. 29 

.88 

2.03 

4.37 

2. 15 

1.04 

. 71 

.75 

2. 13 

.88

2. 6007 

.5175 

. 5191 

1. 3777 

. 1653 

. 1625 

. 1845 

.4636 

. 1676 

.2710 

.3591 

.3314 

. 1026 

1. 0847 

.4309 

. 1856 

.4108 

.9281 

1. 4238 

1. 3450 

.4246 

1. 1421

C; ^=1.41X10-5 sq ft per sec]

30 

89 

148 

207 

266 

325 

384 

443 

503 

562 

621 

680 

739 

798 

857 

916 

975 

1035 

1094 

1153 

1212 

1271

0. 139 

.032 

. 153 

.061 

.064 

.068 

. 135 

. 263 

.765 

.250 

. 142 

.175 

.255 

.078 

.202 

. 104 

.208 

.084 

. 135 

. 110 

.087 

. 168

78.31 

1481. 29 

2.78 

401. 10 

365. 66 

322. 73 

82. 11 

21.68 

2.57 

24. 13 

75.02 

49.21 

23. 14 

247. 05 

36.96 

138. 28 

34. 76 

214. 12 

81.94 

124. 75 

199. 55 

53.49

1.81 

.42 

9. 61 

.80 

.84 

. 89 

1. 77 

3.45 

10. 02 

3.27 

1.85 

2.29 

3. 34 

1. 02 

2. 64 

1.37 

2.72 

1. 10 

1.77 

1. 44 

1. 14 

2. 19

0. 3067 

1. 7743 

. 0575 

.9439 

.9220 

.8795 

.4187 

.2030 

. 0629 

.2212 

.4200 

.3356 

.2227 

. 8374 

. 2938 

.6159 

.2881 

. 7959 

.4697 

.5967 

.7791 

. 3840

Boulder Lake Site 2

[/=8.08 in. per hr; tf =4.1 in. per hr; ,8=0.3315 ft per ft; T=10° C; j.=1.41X10-5 sq ft per sec]

1 - -

3 _______

5________

7 ________

9________

11 _ ____.

13_______

15_______.

17

19_______.

21

23_______.

25_______.

_____ 0.00009

______ .00028

______ .00047

______ .00066

-_--__ .00085

______ .00104

-_--__ .00123

______ .00142

.--___ .00161

______ .00180

----__ .00199

_ __ _ . 00218

.__.__ .00237

0. 0008

. 0026

. 0051

. 0041

. 0139

. 0123

. 0128

. 0144

. 0139

. 0178

. 0215

. 0129

.0185

0. 119

. 110

. 093

. 162

. 061

. 085

.096

OQQ

. 116

. 101

. 093

. 169

. 128

. 051

. 057 07**

. 101

. 198

.204

. 198

. 258

. 365

. 500

. 625

1. 125

1. 333

2.35

1.92

1.28

1. 61

.31

.42

.49

.38

.32

.20

. 15

. 15

. 10

27

81

135

188

242

296

350

404

458

512

565

619

673

0. 739

.378

.229

. 446

.092

. 135

. 150

. 145

. 174

. 134

. Ill

. 263

. 166

4.86

18.52

50.35

13.34

314. 84

145. 71

117. 62

125. 71

88. 06

148. 12

213. 64

38.48

96. 12

7.28

3. 73

2. 26

4.39

.91

1.33

1.48

1.43

1.71

1.32

1. 10

2. 59

1.64

0. 0628

. 1491

.2751

. 1366

.8127

. 5419

. 5009

.5170

.4301

. 5811

. 7203

.2808

.2424

U.S. GOVERNMENT PRINTING OFFICE: 1969 O--368-391