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Retardance coefficients and otherdata for a vegetated irrigation border
RETARDANCE COEFFICIENTS AND OTHER DATA FOR A VEGETATED IRRIGATION BORDER
by
Kenneth Telia Atchison
A Thesis Submitted to theTFaculty of theDEPARTMENT OF SOILS, WATER AND ENGINEERING
In Partial Fulfillment of the Requirements For the Degree ofMASTER OF SCIENCE
WITH A MAJOR IN AGRICULTURAL ENGINEERING
In the Graduate CollegeTHE UNIVERSITY OF ARIZONA
1973
STATEMENT BY AUTHOR
This thesis has been submitted in partial fulfillment of requirements for an advanced degree at The University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the Library0
Brief quotations.from this thesis are allowable without special permission, provided that accurate acknowledgment of source is madee Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his judgment the proposed use of the material is in the interests of scholarship. In all other instances, however, permission must by obtained from the author.
■- 7' I • M- * y ■ — " - - ~ ~ I — - ISIGNED: A
APPROVAL BY THESIS DIRECTOR
This thesis has been approved on the date shown below:
^3 /? 23UtiLMAK D. FANGMEIEJf "77 D a t e 7
Professor of Agricultural Engineering ^
ACKNOWLEDGMENTS
The author wishes to express his gratitude to the Arizona Agricultural Experiment Station and the Department of Soils 3 Water and Engineering, University of Arizona for the opportunity of conducting this research.
Most sincere appreciation is extended to Dr. Delmar. Fangmeier, who served as advisor for this study, for his guidance, suggestions,
and patience. Thanks are also due to the Soils, Water and Engineering personnel, who helped in the collection of field data.
Finally, the author wishes to thank his wife, Diane, for her
patience and understanding displayed throughout many hours spent read
ing, correcting, and typing innumerable preliminary drafts and the
Relationships Found ........ .. . . . . 57Suggestions for Future Study . . . . . . . . . 58
APPENDIX A: PHOTOGRAPHS OF VEGETATION FOR IRRIGATION V-6 . 59APPENDIX B: MEASURED FLOW DEPTHS FOR EACH IRRIGATION . . . 63APPENDIX C: AVERAGE VELOCITIES FOR EACH IRRIGATION . . . . 71
APPENDIX D: RETARDANCE COEFFICIENTS . . . . . 79APPENDIX E: MEASURED VALUES FOR EACH IRRIGATION
LIST OF REFERENCES . . . . . . . . ................ 113
LIST OF TABLES
Table Page
1, Summary of Data for Irrigations . . . . .............. 272c Water Surface Slopes for Irrigations 17, V-l,
V-2, V-3, V-4, V-5, and V-6 293. Percent Soil Moisture on a Dry Weight Basis for
Irrigations V-2, V-3, V-4, V-5, and V-6 . e e e „ 6 „ 324. A Border Volume Balance Analysis for Irrigation V-5 L e . 385* Advance and Recession Times for Irrigation 1 7 ....... 41
6C Advance and Recession Times for Irrigation V - l ....... 41
7* Advance and Recession Times for Irrigation V-2 . . , „ . 428c Advance and Recession Times for Irrigation V-3 42
9c Advance and Recession Times for Irrigation V-4 , , 0 „ „ e 43
10o Advance and Recession Times for Irrigation V-5 . c . , . * 43
11c Advance and Recession Times for Irrigation V-6 , c „ e . 0 44
, 12c Computed Advance and Recession Equations forIrrigations 17, V-l, V-2, V-3, V-4, V-5, and V-6 , . . 45
13* Flow Depth/Station/Time for Irrigation 1 7 ............... 64
14e Flow Depth/Station/Time for Irrigation V-l e e e e » » « - 65
15c Flow Depth/Station/Time for Irrigation V-2 . .......... 66
16c Flow Depth/Station/Time for Irrigation V-3 6717c Flow Depth/Station/Time for Irrigation V-4 e . • • , c « o 6818. Flow Depth/Station/Time for Irrigation V - 5 ............. . 69
10. Average Manning's n for Irrigations V-l, V-2, V-3,V-4, V-5, and V-6 54
11. Schematic Showing Grid Positions . . . . . . . . . . . . . 6012. Vegetation Between Camera and Grid Position 1 . . . . . . 61
13. Vegetation Between Camera and Grid Position 2 . . . . . . 61
14. Vegetation Between Camera and Grid Position 3 . . . . . . 61
15. Vegetation Between Camera and Grid Position 4 . . . . . . 62
16. Vegetation Between Camera and Grid Position 5 . . . . . . 62
17. Vegetation Between Camera and Grid Position 6 . . . . . . 62
ix
ABSTRACT
Seven irrigations were conducted on a precision field border of fixed slope on which alfalfa was growing6 The discharges used on the border ranged from 0,3 to 0„7 c.f.s. Inflow, outflow, water sur
face elevations, and soil surface elevations were measured. Data are
also presented for advance and recession times, infiltration functions,
water surface slopes, soil moisture conditions, flow depths, average flow velocities, and retardance coefficients. Retardance coefficients
were calculated from steady, uniform flow equations at different time
intervals and reaches to determine the resistance to flow.
Results from seven irrigations showed a wide range in values of
retardance coefficients. Soil roughness was determined from physical
measurements made on the soil surface.
x
CHAPTER 1
INTRODUCTION
As world population increases9 even heavier demands will be
placed upon supplies of food and fiber. Existing lands will be called upon for maximum yields and economic returns; thereby necessitating
optimized management of water, labor and capital. As water becomes a
more valuable commodity, efficient management of irrigation water will
become mandatory for each user. The efficiency of a surface irrigation system in distributing and providing water for storage in the root zone
is mainly dependent on the relationship of the rate of advance of water along a furrow or border to the length of run in the field, the intake
rate of the soil, discharge, surface storage in the border, and land slope* The amount of surface storage is related to the resistance of
flow* If the roles of these factors are better understood, irrigation
efficiencies can be increased.In recent years, attention has been given toward refinements in
designs of surface irrigation systems. In the general problem of sur
face irrigation system design, Fenzl-(6) found inadequate information existed with respect to many individual facets. He reported one defi
ciency is the inability of commonly used resistance equations to de
scribe and predict the hydraulic resistance encountered in irrigation
flows in borders. Myers (12) reported that simplified empirical flow
equations have been used despite discrepancies between calculated and
2observed flow processes because the information needed for the use of
rational flow equations has not been developed adequately. In order to
develop new or refine existing flow relationships, accurate field data
must be obtained.
ObjectivesThe objectives of this study were:
1. To collect accurate field data of water flowing through non
submerged vegetation in a border. '2. To provide data for future use in studying flow characteristics
in vegetated borders and for calibrating computer models simu
lating border irrigation. This would help in the development of more accurate methods of describing vegetative roughness parameters.
3. To determine how resistance to flow varies during the irriga
tion and along the border on a vegetative surface of an
irrigation border.
Literature Review
The first resistance formula for open channel flow was proposed
in the 1760 fs by Antoine Chezy (in 20) as follows
(i)where V is the mean velocity.
C is a flow resistance factor called Chezy*s CE is the hydraulic radius, and
Sf is the slope of the energy grade line.
3The difficulty was then to evaluate Ghezy’s C for different channels. Three formulas for the determination of Chezy's C were given by Ganguillet and Kutter, Bazin, and Powell (in 3). All were determinedifrom measured field data.
One of the most widely used equations for open channel flow is the Manning equation
V = 1.486 R2/3 Sf1/2 (2)n (
were n is a roughness coefficient known as Manning’s n0 The other
terms are as previously defined. Manning1s n.is normally assumed to be constant for a channel section. As many as eight or ten factors are known to influence Manning’s n„ Chow (3) states that the value of
n is dependent on the roughness of channel surfaces, vegetation, chan
nel irregularity and alignment, scouring, obstructions, channel size
and shape, and stage and discharge.
Experiments on the hydraulic characteristics of vegetation
were conducted by the Soil Conservation Service in Spartanburg, South
Carolina, in 1939 (4). Three series of tests, each using different
types of vegetation, were conducted under the following limitations:
1. Flow rates varied from 4.58 cubic feet per second (c.f.s.) to
23.19 c.f.s.2. Mean velocity from 3.04 feet per second (f.p.s.) to 5.24 f.p.s.
3. Slope from 0.059 feet per foot (ft./ft.) to 0.065 ft./ft.
The retardance results were presented in terms of Manning’s n which varied from 0.0418 to 0.0563 and Kutter’s n which varied from 0.0323 to
0.0397.
4Similar tests were conducted at the Stillwater Hydraulic Lab
oratory at Stillwater, Oklahoma, by Palmer (14)e He studied flow of
water through alfalfa without completely inundating the plantse Eight tests were conducted under the following constraints:
1* Average flow depth from 0.143 ft. to 0.583 ft.2. Mean velocity from 0.229 f.p.s. to 1.03 f.p.s.3* Slope from 0.0191 ft./ft. to 0.038 ft./ft.4. Vegetative submergence to 50 per cent.
The retardance of flow was expressed in Manning's n which varied from 0.178 to 0.257. During Palmer's experiments a constant discharge was delivered to the unit channels. After the outflow became constant,
point gauge measurements were made at three stations ten feet apart to establish water depth.
At the Stillwater Hydraulic Laboratory during the late 1940's,
Ree (16) observed a great range of Manning's n. For small flows, large
n values were obtained. As the flow depth increased in the range of
point of 30 per cent submergence, the retardance coefficient decreased
rapidly. After complete submergence with the depth increasing, the
retardance coefficient gradually approached a constant value.
When Ree plotted n values against the depth (n-depth), similar
vegetation was found to have different n-depth curves for channels of different slope or cross section. With each combination of channel slope, channel cross section and vegetation, different n-depth curves were found. After plotting n values against the product of mean veloc
ity times hydraulic radius (VR), Ree found that vegetation with similar
characteristics had similar n-VR curves6 He then proposed five vegetal < ■
retardance classifications which provided a value for Manning’s n in agraphical form.
Many investigators have studied the effects of both artificial and natural vegetation on n values. Chow (3) states that vegetation
may be regarded as a kind of surface roughness. The roughness effect
depends mainly upon density, height, distribution, and type of vegeta
tion. In most calculations, roughness caused by the soil and the
vegetation are combined into one roughness value.
The use of the Manning equation for shallow flow has been questioned. From both field and laboratory data. Bowman (1) points out that the Manning equation can be used for all flows, including shallow
flow with vegetation by carefully selecting an n value. Bowman first evaluated n for a number of field trials with vegetative cover. After plotting observed measurements, a graphical means was proposed to de^ *
termine n values in terms of vegetative cover density, flow depth, and average velocity.
Fenzl (6) concluded that most existing equations used to define
hydraulic resistance in large unobstructed channels are not applicable
to shallow flow in vegetated channels. He proposed resistance relationships as determined by dimensional analysis. For describing the
hydraulic resistance for shallow flow in vegetated channels, Fenzl in
dicated that the total drag could be separated into the components of
surface and vegetative drag effects. The variables for the vegetative
effects were
Y v is the vegetation drag per unit area,V is average velocity.
g is the acceleration of gravity.b is the stem diameter
Z7 is the mass density of fluid.
A is the dynamic viscosity of fluid.
h is vegetation stem length.
d is average flow depth.
/L is characteristic length defining spacing of plants, and
0 is a dimensionless measure of effective plant form.After conducting a series of tests in a flume for the case of partial submergence of wires5 a new relationship was formed
Tv = f0 / Vb . ~R V N b R /> V2 (4)V b y
where N is the number of roughness elements per square foot of
channel bottom.To evaluate Vb/> and R a drag coefficient was used. This al-
blowed comparison of observed values of Gq with published values.
Relationships between Crv and 7c were presented in graphical form/» V2
where 7Z is the total shear acting on the channel bottom.
Fenzl concluded that ^ must be considered a dependentp H
variable of no less than four dimensionless ratios as follows:
1, The relative roughness of the soil.
2. The relative roughness of the vegetation.
3C A measure of plant form0 4tf Reynolds numbere
If the vegetation is deflected, a fifth parameter might be required„ Fenzl conducted field experiments using alfalfa to provide vegeta
tive resistance. For alfalfa he found that
?v = CD -N b h V2 (5)
described the vegetative resistance.
Kouwen, Unny, and Hill (9) investigated the n-VR relationship using
submerged vegetation. They found that the representation of n as a
function of VR was not satisfactory. Instead, they proposed
V = C, + C9 In ZlnX (6)v* . vk y
where V* = ygRS^ is the shear velocity,Cj_ is a parameter depending on density of vegetation
and relative roughness,Cg is a parameter depending on the vegetation stiff
ness,
yn is normal depth, andk is the deflected height of roughness.
For a vegetated channel, the ratio of the total cross-sectional area. A,
to the area of the cross section blocked by vegetation, Av , is A/Ay.
For wide vegetated channels, this ratio (A/A^) is the same as (yn/k).
Equation 6 then becomes
which defines the flow in.vegetated channels on the basis of vegetative characteristics when k y^.
Michael and Pandya (11) conducted hydraulic resistance studies using wheat spaced 8.7 in. by 5.9 in. in border strips. Once the
plants became established, they found that a linear relationship exist
ed between n and q and found no substantial differences in n values during different post-emergence irrigations.
Nnaji and Wu (13) investigated the characteristics of flow re
sistance due to cylindrical simulated crop stems. This roughness was to be expressed by a single parameter, , which was described in terms of the geometrical characteristics of the cylindrical stems used.
A relationship for the standard deviation of roughness profile, ^5 , was expressed in terms of normal flow depth, stem diameter, and roughness concentration. This may be used to quantify roughness and is a
good measure for the estimation of the hydraulic roughness. They determine a power-type relationship for ̂ of the same form as obtained
by Kruse (10). By knowing the value of , the velocity was eventu
ally determined from equation 9.
Soil RoughnessRoth (18) made an extensive literature review of soil roughness
studies. Only a few of his pertinent findings are included in this
section.Some of the equations reviewed on vegetative roughness also ap
ply to soil roughness. For instance, the Chezy and Manning equations
are used to describe both vegetative and soil roughness.
The Darcy-Weisbach equation is used mainly for pipe flow, but can be used for open channels in the following form:
v = 8 S R Sf (8)
where f is a friction factor. The coefficient f is commonly plotted
as a function of both the Reynolds number and the relative roughness,Sayre and Albertson attempted to arrive at a solution to the
hydraulic resistance problem for surfaces with a wide range of roughness. Their equation based upon experimental data is
V = 6,06 log Z J A (9)V* Vx-/
where d is the flow depth occuring when the slopes of energy gradient, water surface, and channel bed are all equal, and
% is a single roughness parameter that is dependent on thesize, shape, and spacing of the roughness elements.
The relationship of flow resistance to physical measurements of
the boundary roughness was explored by Kruse (10) in laboratory studies using small parabolic and rectangular channels having natural soil
roughness. He determined that
X = 12.9 S 1-66 (10)where 45 is the standard deviation of boundary elevation measure
ments about a mean elevation,
Roth (18) used plaster cast impressions of the soil surface and
a roughness measuring device to measure soil surface roughness. Values
of <5 were obtained to be used in equation 10 which then determined ^
10values of soil surface roughness„ He concluded that measured val
ues from soil castings gave reasonable agreement with the computed
Sayre-Albertson1s 0^ values„
The ratio of average velocity to shear velocity relates Chezy, Manning, Darcy-Weisbach, and Sayre-Albertson roughness coefficients.
V C = 1.486 R1/6 = n / 8 = 6.06 log Z d X (11)v* vs nyg V f xx z
Reynolds Number ( -Surface flow has been described as either laminar or turbulent.
In laminar flow, head loss is proportional to velocity and inversely proportional to the depth squared. In turbulent flow, head loss is
proportional to velocity and depth raised to the same power. The param
eter used to distinguish between the two is the Reynolds number (Re),
Re = Vd (12)zi/-
where d is the depth of flow, and
Xr is kinematic viscosity.
Myers (12) reported that there is no single value of Reynolds
number distinguishing laminar from turbulent flow. In open channel
flow, considerable disagreement exists concerning the critical Reynolds number at which flow changes from laminar to turbulent.
Myers stated that some critical Reynolds numbers have ranged from 550 to 700. The use of Reynolds number as a satisfactory crite
rion of flow regime in open channels was questioned. He concluded that satisfactory determination of a critical Reynolds number for shallow
flow has not been made. However, Kruse (10) indicated that the
11critical Reynolds number in practice is around 500 and would probably
be applicable.to all wide irrigation channelse For practical purposes,
the transitional range of Reynolds number for open channel flow may be assumed between 500 and 2,000 according to Chow (3) and very rarely does laminar flow occur*
In the calculation of a Reynolds .number for shallow flow
through vegetation, there is a question concerning the satisfactory
dimension of length to be used* Myers stated that the length factor
should be more closely related to the vegetative characteristics than
to the hydraulic radius or the flow depth which does not consider vegetation* He suggested characteristics which would consider diameter,
spacing, and flexibility of plant stems and. leaves of vegetation*
In Bowman’s (1) studies, stem diameters were used as the length factor. With simulated vegetation, strong vortices were formed and turbulence resulted at a Reynolds number of 29,5 and velocity of 0*035
f op es,
Fenzl (6) recognized the need to consider vegetative parameters such as diameter, length, flexing, and spacing of plants* By using
stem diameters as measure of length values, Reynolds numbers from 40 to
300 were obtained with partial submergence of alfalfa*
Vegetative DensityEarly vegetative density studies were done by visual observa
tion, . Stand counts and stem measurements often accompanied these
observations* Similar methods are still used for reporting vegetative
densities*
12Palmer's (14) vegetation measurements included the average
length and a stem count per square foot plus a visual observation of
the stand* Ree (16) obtained the vegetation condition from visual ob
servations and the average stem length. Fenzl (6) used stand counts
and stem diameter measurements to describe vegetation.Bowman (2) developed a capacitance meter for field vegetative
density measurements. The principle used was the change in capacitance
between parallel plates in air and then in vegetation. Usefulness was limited because of the influence of stem moisture content upon the readings.
InfiltrationInfiltration is the movement of water through the soil surface
and into the soil. Because of the extreme variability of the soil, in
filtration is one of the more complex aspects of surface irrigation.Factors known to influence infiltration are soil texture and structure,
antecedent moisture, surface crusts, and vegetative cover.Accumulative infiltration depth (z) is the depth of water which
infiltrates during a given time interval. Philip (15) reported that an
equation proposed by Kostiakov can be used to express accumulative in
filtration. The Kostiakov equation is
z = k t^ a (13)where t^ is the intake opportunity time, and
k and a are arbitrary constants.
This equation gives good results at the lower end of the time scale andfits moderately well over the entire time scale.
13According to Israelsen and Hansen (8) the best method of meas
uring infiltration rates is direct measurement, which can be made by subtracting outflow from the inflow. He reported that infiltrometer
cylinders can be used with reasonable success when direct measurements are not feasible and describes how to use such cylinders.
Gilley (7) described a precise method for obtaining total infiltration in a border. It involved subtracting outflow and the change In surface storage from inflow. From his trials, he concluded that the infiltration rates obtained from the border inflow-outflow method were higher than those obtained with infiltrometer cylinders.
Gilley also used a technique which mathmatically solves for the constants k and a in equation 13. This gives correct results; however,
it has the disadvantage to this study of being useable only during the
advance phase of border inflow.
CHAPTER 2
EQUIPMENT AND. PROCEDURE
All data for this study were collected at the Agricultural Engineering Irrigation Laboratory, University of Arizona Agricultural Experiment Station, Campbell Avenue Farm, Tucson, Arizona. The irrigations were conducted on a precision field border. Alfalfa, planted ten months prior to the trials, was used in the vegetative trials.
Equipment
Water Conveyance System
A well was used to supply water to a large sump. From there
the water was pumped to the border for irrigation. The inflow was
measured with a four-inch Sparling meter. Water was delivered to a
plastic lined stilling pond before introduction to the border.
Runoff System
At the border end, another stilling pond channeled water
through a critical depth flume for outflow measurement (17). Water from the flume was collected and pumped back to the sump to be recirculated to the border. A Belfort water stage recorder measured the flow
depth in the stilling well. The flume was capable of measuring flow from 0.001 to 8.0 cubic feet per second.
14
Precision Field BorderThe precision border used was bounded by two parallel 300-foot
long concrete curbs spaced 19.33 feet apart (inside to inside)„ Scissor type automotive jacks were mounted on top of the curbing at 15-foot intervals. The jacks support steel rails running the entire border length and could be adjusted to slopes ranging from 0e 0 to 0.3 per cent. For this study, the rails were set at a 0.1 per cent slope. The rails provided a track for a 20-foot wide rolling trolley used to facilitate measurements.
RecordersWater surface elevations were measured with floats and portable
water stage recorders. Eleven recorders were spaced at 30-foot inter
vals near the center of the border to record water surface elevations.
Three recorders (18) measured the border subsidence.
The water stage recorders (Figure 1) were Belfort and Bendix
(Friez) type portable water level recorders model FW-1. Prior to use,
each recorder was calibrated against a point gauge. One foot of water
depth was recorded as 10 inches on the chart. The six-hour chart, Bel
fort chart number 5-1940-AB, had increments of one minute as the smallest time division.
A 1-gallon can served as a stilling well for the water stage
recorders. Numerous perforations were made in the can to facilitate water movement in and out.
16
Figure 1. Portable Water Stage Recorders for Measuring Water Surface Elevations.
17The floats were made from small glass bottles with eye bolts
through the center of the lid. Heavy nylon fish line connected the
floats and recorders with metal nuts serving as counter weights.
Soil Profile Board .Soil surface elevations and soil roughness were measured with a
soil profile board. The soil profile board (Figure 2) consisted of 35 aluminum probes one inch apart with a grid scale behind them. After
mounting on the trolley, the probes were released and individually low
ered until they just contacted the soil surface then were locked into
position. The soil profile could then be read from the grid. Point gauge measurements from the trolley down to each end of the profile
hoard were taken.
Vegetative DensityStand counts, stem measurements, and density values were deter
mined from photographs of the vegetation at a representative location. All vegetation was flattened two feet in front of the camera by placing
a metal plate on the ground surface. Starting at this point, a paper grid scale was placed normal to the camera and photographed._ The grid
was then moved away from the camera in two inch increments six times
while photographing the vegetative stems at each position (Appendix A),
The total projected area of vegetation was determined from this series
of photographs. Stand counts and stem measurements were also deter
mined from the photographs. The photographs in Appendix A show the
results of this procedure for Irrigation V-6.
18Procedure
Each irrigation required at least three days field work and
five days to prepare the data for analysis. Additional time was re
quired to complete the analysis.
Initial Border PreparationThe initial soil preparation and sill installation for .Irriga
tion 17 was identical to Rothls (18), This involved soil tillage and leveling as well as head and tail sill installation. On all subsequent irrigations, the soil and sills were left in their natural condition
from previous irrigations.Prior to each irrigation, the alfalfa was allowed to grow to a
height of approximately 18 inches (Figure 3), After the irrigations
were conducted, all measurements made, and the surface allowed to dry,
the alfalfa was cut (Figure 4).The water stage recorders and soil surface elevation pads were
located at chosen stations in the border. The first water stage re
corder was placed in line with bench marks located four feet from the
head sill (Station 1), The remaining ten water stage recorders were
positioned 30 feet apart going downstream (Stations 2 through 11),
Soil surface elevation pads were positioned midway between Stations 1
and 2, 5 and 6, and 9 and 10,The soil profile board was used to determine an average soil
surface elevation. Thirty-five metal probes on the board were cut to 0,993 foot in length. Reference points were established on each side
19
Vegetation Prior to an Irrigation
Figure 4. View of Border Showing Cut Vegetation and the Water Stage Recorders in Position.
20of the board with a connecting line forming the zero point on the board grid scale. The average distance, c, from the trolley to the ends of
the zero point was measured. The average distance, j, from the zero
point on the board to the top of each metal probe was recorded. The 35
values were averaged to determine the average distance that the metal
probes were above the zero point on the soil profile board.
The average border elevation was determined by adding the aver
age distance, c, from the trolley to the zero point on the soil profile
board to the metal probe length, 0.993 ft., and subtracting the average distance, j, measured from the soil profile board zero point to the average soil profile.
The border and water surface elevations were related to each
other as shown in Figure 5. Point gauge readings, w, from the trolley to the bench marks established the trolley elevation for all stations.
The hydrograph from each water stage recorder was related to
specific water surface elevations. At periodic intervals during an
irrigation, point gauge readings, h, to the top of the water surface were made with concurrent time marks placed on the water stage recorder
charts. By using the point gauge readings with the corresponding time
marks on the water surface hydrographs, all water surface elevation
data from the recorders were directly related to a point gauge reading
from the trolley.
All of the water surface elevation floats were installed in
stilling wells. At rest, the buoyancy level of the floats was just be
low the soil surface and the floats would have to rise a distance, u.
B E N C H M A R K
T R O L L E Y
W A T E R S T A G E R E C O R D E RS O I L P R O F I L E / B O A R D B E N C HM A R KQ— CD
S O I L S U R F A C E COCOoc W A T E R L I N E
N O T TO S C A L E
Figure 5. Schematic for Relating the Border and Water Surface Elevations to Each Other at Each Station in the Border.
22to reach the surface. A flow depth was said to exist when the level of
the float exceeded the border elevation. When a flow depth was indicated, the water had advanced to that station. Similarly, when there was no flow depth, recession had occurred.
Generally, one full day was allocated for pre-irrigation preparation. Infiltrometer cylinders were installed near each of the three soil surface elevation pads. Soil samples for gravimeteric soil mois
ture determinations were also taken near these locations. The samples were obtained at selected intervals to a depth of 2.5 feet.
All water stage recorders were supplied with new charts and ad
justed to the correct time. The flume recorder chart reading was calibrated against a point gauge reading for several different water levels
in the flume. A point gauge reading was taken for each subsidence pad
to determine its elevation in relation to the trolley and for calibra
tion purposes.
Photographs of the vegetation were taken as previously de
scribed. When irrigations were conducted on successive days, one set
of photographs adequately described both irrigations.
Readings from the soil profile board taken down the center of
the border at each station in line with the bench marks and water stage recorder determined the "before" border elevation. At each station
point gauge measurements were also taken to the zero reading on the grid of the soil profile board. In addition to the above readings, additional soil profile board readings were taken down both the east and
west sides of the border as an elevation check.
23
Irrigation Procedure
Water was pumped into the head pond and shortly thereafter pro
ceeded down the border0 The moment water reached Station 1, initial
time was markedeAt the initial time, an inflow reading was taken from the Spar
ling meter* Subsequent inflow readings were taken after 1, 3, and 5 minutes and every ten minutes thereafter, A valve was used to maintain
constant inflow.Infiltrometer measurements were started when the water reached
the cylinders and continued until recession had occurred. A field ob
server recorded the time when the water reached each station (advance) and after inflow ceased when water receded from each station (recession) , Recession was recorded when the observer judged that approxi
mately one-half of the area at each station was free of surface water.
Water temperature was recorded in both the head and tail ponds several
times during the irrigation.
Continuous hydrographs were obtained from the water stage re
corders. Periodic checks were made during the irrigation to verify
that the water stage recorders were operating correctly. During the
checks, point gauge measurements from the trolley to the water surface
were made beside the water stage recorder floats. When the point gauge
measurement was taken, a time mark was made on the recorder chart.Later the point gauge readings were used to refer the water stage recorder readings to the border datum.
The soil surface elevation at each soil pad was not recorded continuously since only one recorder was used for three soil pads. As
24the water advanced to a soil pad, the recorder monitored this pad continuously for ten minutes to observe the rapid subsidence change within this period. Once water had advanced past all soil pads, each soil pad was recorded, usually once every ten minutes.
Border inflow ceased when water no longer flowed over the head sill. However, measurements continued until the water receded from all stations and no longer flowed over the end sill.
Post Irrigation
The next day, soil samples were taken close to the same loca~ tions as before the irrigation. Soil profile board readings were also
taken at each station.
CHAPTER 3
RESULTS AND DISCUSSTION
Methods of determining the hydraulic variables necessary to
compute roughness coefficients during a vegetated border irrigation and
the results that were obtained are presented in this chapter. Seven(
irrigations were conducted5 one (Irrigation 17) with a sparse , short
vegetation and six (Irrigations V-l through V-6) with vegetation estab
lished in varying degrees.For analysis, eleven stations divided the border into ten equal
30-foot reaches. The irrigation was also divided into time periods.
The time periods during the advance phase equaled the time it took for water to advance to each station; however, the remaining time periods were arbitrarily chosen for convenience. The first time period represented the interval of time for water to advance from Station 1 to Station 2. Similarity, the second period was the time required for the water to advance from Station 2 to Station 3 and so on until the water advanced to Station 11 (time period 10). The eleventh period was arbi-
tarily chosen so that it ended on the next even minute and the next ten
periods were one minute intervals. The twenty-second time period was
the first time after period twenty-one that was evenly divisible by
four. Four minute periods or intervals continued until the inflow ceased.
25
Table 1 summarizes the results of Irrigations 17, V-l, V-2, , V-3, V-4, V-5, and V-6e The total inflow and outflow were determined by the meter and flume respectively, with the difference going to in
filtration, The infiltration functions are discussed later.
Vegetation
Irrigation 17 was made on five week old uncut alfalfa. All
other irrigations had as cover alfalfa that was at least 10 months old. Some time before vegetated runs V-l, V-2, V-4, and V-6, the alfalfa was
cut off 1-inch from the ground level with the cuttings removed from the
border. The alfalfa was allowed to grow to a height of approximately 18 inches before the irrigations. Irrigations V-2 and V-3 were run on consecutive days as were V-4 and V-5 thereby assuring for all practical
purposes that the vegetation was identical.. The photographs in Figures 6 and 7 show representative vegeta
tion for Irrigations V-2 and V-3 and V-4 and V-5. Figures 12, 13, 14,
15, 16, and 17 in Appendix A show a series of photographs of the vegetation of Irrigation V-6. Diameters of randomly selected stems ranged from 0.0052 foot to 0.0110 foot. A typical diameter was 0.0080 foot.
According to stem counts, the vegetation density ranged from 40 to 100
stems per square foot. For comparison, Fenzl (6) had stem diameters of
0.0078 foot with a density of 48 stems per square foot.
Slopes
The flow in the border was unsteady and nonuniform. That is, the depth changed with time and discharge decreased with distance.
Three slopes are referred to in open channel flow: the slope of the
Table 10 Summary of Data for Irrigations0IRRIGATION NUMBER 17 V-l V-2 V-3 V-4 V-5 V-6
DATE 8 Sept* 71 12 June 72 18 July 72 19 July 72 9 Aug* 72 10 Aug. 72 30 Aug* 72
Number of reaches 10 10 10 10 10 10 10Length of reaches (ft,) 30 30 30 30 30 30 30Border slope, S., (fto/ft0) Inflow rate (c6fese)
A . B0.4 c.f.s. 0.0207 c.f.s./ft. 0 to 86 min. 0.7 c.f,s. 0.0362 c.f.s./ft. 0 to 136 min,0,8 c.f.s. 0,0414 c.f.s./ft. 86 to 135 min. 0.4 c.f,s. 0.0207 c.f.s./ft. 136 to 245 min,0.4 c.f.s. 0.0207 c.f.s./ft. 135 to 190 min.
N>
Figure 6. Representative Border Vegetation for Irriga tions V-2 and V-3.
Figure 7. Representative Border Vegetation for Irriga t ions V-4 and V-5 .
29
Table 2. Water Surface Slopes for Irrigations 17, V-l, V-2, V-3, V-4, V-5, and V-6._
A V G H A T E R S L O P E . 0 0 1 1 5 5 . 0 0 1 3 3 5 . 0 0 1 1 0 5 . 0 0 1 0 9 0 . 0 0 1 1 5 8 . 0 0 1 1 8 0 . 0 0 1 2 5 9A V G S O I L S L O P E . 0 0 1 1 3 0 . 0 0 1 0 9 5 . 0 0 1 0 8 7 . 0 0 1 0 8 8 . 0 0 1 0 8 2 . 0 0 1 0 9 7 . 0 0 1 1 1 5
D I F F E R E N C E . 0 0 0 0 2 5 . 0 0 0 2 4 0 . 0 0 0 0 1 8 . 0 0 0 0 0 2 0 0 0 0 0 7 6 , 0 0 0 0 8 3 . 0 0 0 1 4 4
30channel bed S03 the slope of the water surface and the slope of the
energy gradient S^e According to Daugherty and Franzini (5), the flow
can be considered as steady and uniform when the bed slope is less than
five degrees and the slope lines are approximately equal. The channel bed slope, before the irrigations, ranged from 0.1082 to 0.1128 per
cent, which is less than one degree. This suggests that uniform flow
equations can be used.The border elevation was determined before each irrigation from
the sum of an average of two point gauge readings taken from the trolley to the soil profile board and an average of the 35 soil profile readings at all eleven stations. A least squares regression line through the eleven points was used to obtain the soil slope, S^. The elevation values at the individual stations were then adjusted to fit the least squares regression line. In a like manner, the border elevation was established after each irrigation.
Table 2 lists the water surface slopes in feet per foot for all
seven irrigations. The water surface slopes shown started with the
first four-minute intervals after the water advanced the entire border
length and continued through the last four-minute time period before
the border inflow ceased. The slope also was obtained using a least
squares regression line through the water surface elevation at stations
located at 30-foot intervals.
A typical value of the water surface slope is also listed.
This value was arrived at by averaging the slopes for the last ten time
periods before inflow ceased for each irrigation and border outflow
31approached a constant value* Also presented are the "before" soil sur
face slope and the difference between the water and soil slopes. There were small differences between the "before" soil slope and the water surface slope. Irrigation V-2 had a difference between the water
surface slope and soil surface slope of 0,000018 ft,/ft. Irrigation V-3 had essentially no difference between slopes* Irrigations V-4 and
V-5 have very similar numerical differences between the water surface slope and channel slope, 0,000076 ft,/ft, and 0,000083 ft,/ft, respectively, obtained with irrigations run on successive days. The last irrigation, V-6, had a much higher difference between the slopes,
0,000144 ft,/ft. Although two different inflow rates were used during Irrigation V-6, it had reached equilibrium when the calculations were
made.Once the irrigation outflows reached equilibrium, the water
surface slope was approximately equal to the channel slope. Therefore,
uniform flow equations were used for analysis.
Soil Moisture
Gravimetric soil moisture measurements were made both before
and after each of the last five irrigations. Measurements were made at
0-6, 6-18, and 18-30 inch intervals of depth at three equally spaced
locations along the border. An average per cent moisture value on a dry weight basis for the three locations is shown in Table 3, Each
reading represents the average of three samples. The volume of water infiltrated as determined from these soil moisture measurements closely agrees with the total infiltration shown in Table 1 for Irrigations
32
Table 3. Percent Soil Moisture on a Dry Weight Basis for Irrigations V-2, V-3, V-4, V-5, and V-6.
Irrigations Sampling Depth (inches)0-6 6-18 18-30
V-2 Before , 14.7 11.4 6,6
V-2 After 18.7 16.1 9.6
V-3 Before 18.7 16.1 9.6
V-3 After 16.6 17.4 13.3
V-4 Before 15.7 16.9 12.3
V-4 After 14.7 16.5 18.8V-5 Before 14.7 16.5 18.8V-5 After 18.7 20.0 15.8V-6 Before 5.3 6.7 7.6V-6 After 18.4 16.7 11.5
33V-29 V-4; and V-66 The average soil moisture percentage values for the 0-6 inch depth interval ranged from 5e3 before irrigation to 18.7 after
irrigation.
SubsidenceThe subsidence was the difference between the borderfs average
elevation at the beginning and the end of the irrigation. Subsidence
was divided into two segments, that which actually occurred during the
irrigation and that which occurred after all the water had receded from
the border and readings could be obtained with the soil profile board.
The three soil measuring pads measured the average change during the
irrigation. The "before11 and "after" subsidence elevations were determined from the soil profile board readings. The total subsidence as
measured by the soil profile board was adjusted to equal the subsidence during irrigations as measured by the three soil pads. Time distribution of subsidence during the irrigation was taken from the average of the three subsidence pads.
All seven irrigations had negative subsidence (swelling) in elevation during the irrigation. Irrigations V-2, V-3, V-4, and V-5
had a swelling of 0.013 ft., 0.010 ft., 0.009 ft., and 0.010 ft. re
spectively, while during V-6 surface elevation increased 0.016ft.
Irrigation V-6 had an inflow duration of 245 minutes while the others
inflow ceased after 140 minutes. The longer inflow time provided
greater infiltration, thereby increasing the soil depth in which swell
ing could occur.
34Flow Depth
The depth of flow, d, is the vertical distance between the low
est point of the channel and the free water surface. Normal depth is the depth of uniform flow. In this study, uniform flow was not ob
tained. However, due to the small slope of the channel bed, uniform flow equations were used for calculations..
The channel was originally level transverse to the flow; however, during irrigations the center section became lower than the out
side sections. This situation became apparent when the results of the
profile board readings taken at each side were compared with the readings taken down the center of the channel. The sides were approximately at the same elevation for all trials, however, the channel center was as much as 0.040 ft. lower than the sides. The elevation differences between the border sides and center for Irrigations V-2, V-3,V-4, V-5, and V-6 were respectively 0.020 ft., 0.029 ft., 0.023 ft.,
0.040 ft., and 0.018 ft. There appeared to be no trend in the differ
ences. One reason could have been the fact that the soil profile board readings were not taken at the identical location each time. However,
the locations were not differ by more than six inches between the
irrigations. Due to these elevation differences between the sides and
center a mean border elevation was used.
During the irrigations, the water advanced down the border cen
ter somewhat earlier than the sides at Stations 1 through 10 which confirms the soil profile board elevation readings. At Station 11, the
reverse was noted; the center was higher in elevation than the sides.
The elevation differences between the border center and sides were
35adjusted before calculations were made so that the water depth was considered uniform across the entire border width*
Water surface elevations were obtained from the water stage recorder hydrographs and adjusted by a constant amount as determined by the average difference of several point gauge readings from the trolley to the water surface during the irrigation* The point gauge readings to the water surface were assumed to be correct* Flow depth hydrographs were obtained by subtracting the border elevations from the water surface elevations* The flow depth during any period was the
average of flow depth at the beginning and end of each period*Appendix B lists the flow depths for all seven irrigations.
The flow depth measurements are estimated to be accurate to - 0*006 feet when compared with point gauge readings which were assumed cor?- _ .
rect* The flow depths are given for all stations for all time periods when a reach was wetted.
Equilibrium appeared to have been reached about 60 to 70 minutes after the water advanced the entire border length* The water flow
depths in the border and flume remained almost constant. The inflow
rates for Irrigations V-3, V-4, V-5, and V-6 were approximately 0,4, 0*5, 0*3, and 0*7 and 0*4 c*f*s* respectively* As expected, an increase in inflow brought a corresponding increase in flow depth.
The vegetation offered considerable resistance to flow* For instance. Irrigation V-4 and Roth’s bare soil Irrigations 9 and 11 had approximately the same inflow of 0*5 c*f,s* However, he measured flow depths of 0*080 to 0*094 ft* compared to a depth of 0*170 to 0,200 ft*
during V-4* For the same inflow rate, the flow depths with vegetation
36were approximately 0o1 ft0 greater when compared with irrigations hav
ing a bare soil surfacee
Hydraulic Radius
The hydraulic radius, R, the ratio of the water cross-section
to its wetted perimeter, was determined for each period. The area used was the average of the flow areas at the beginning and end of each pe
riod while the wetted perimeter was the sum of the border width and twice the flow depth*
Average Velocity
The continuity equation was used to determine the average ve
locity at each station. From continuity,AVERAGE VELOCITY = FLOW RATE/FLOW AREA. (14)
For each period the flow rate past each station was determined by di
viding the outflow obtained from the equation,OUTFLOW = INFLOW - CHANGE IN CHANNEL STORAGE - INFILTRATION, (15)
by the duration of the period.
Equation 15 was solved for outflow for all reaches and periods.All other data in the equation was either known or computed. Inflow
into the first reach was the measured border inflow. Inflow into the
remaining reaches was the computed outflow of the upstream reach. Surface storage change in each reach was computed from the upstream and
downstream flow depth hydrographs. Constants in the infiltration func
tion^ Equation 13, were initially estimated from the infiltrometer
data. Equation 13 was then used to compute the infiltration into each
37reach. Subsequently, the constants were varied to give an infiltration
function which better described the border volume flow balance.Two values of border infiltration were obtained for each period
as shown in Table 4, The first value was an infiltration volume as computed from a volume balance of the entire border using the measured inflow, measured outflow and measured surface storage changes. The
other infiltration volume was the summation of infiltration for each
reach as estimated by the infiltration function, A more detailed ex
ample of the volume balance analysis may be found in Roth (18),
Listed in Appendix C are the average velocities for all seven
irrigations as computed from a volume balance analysis of the flow.
The velocities are given on the same format as the flow depths, with the period refering to the time at the end of the period.
The velocities for Irrigations V-3, V-4, V-5, and V-6 ranged
from 0,12 to 0,16 f*p,s. Comparing velocitites at Station 1 while the outflow was constant, the velocitites were 0,14, 0,13, 0,12, and 0,14 f6p,s, respectively. With the exception of Irrigation V-3, the velocity increased with increasing inflow. No reason for the variation of Irrigation V-3 from the trend is known. Generally, for each irrigation the velocity remained nearly constant.
Table 4* A Border Volume Balance Analysis for Irrigation V-5«
The time of advance and recession for each station was deter
mined from the* flow depth hydrographs when the flow depth was zero.
For comparisons5 visual observations were made. The advance times were
easily determined, but the recession times were difficult to determine and became a judgment matter for the observer.
The observed and computed times of advance and recession are
given in Tables 5, 6, 7, 8, 9, 10, and 11 for all seven irrigations.
The computed advance times for Irrigations V-3, V-4, V-5, and V-6 compare reasonably well with the observed advance times. However, recession times as computed do not compare well. It was difficult for the observer to judge when recession occurred. The advance and recession equations for the computed values are listed in Table 12.
Once again, comparing Roth's Irrigations 9 and 11 advance and recession times (computed) with Irrigation V-4, the bare soil surface irrigations took 12.5 and 12.6 minutes (computed) for advance to Sta
tion 5 while it took 11.9 minutes in the vegetated irrigation. To ad
vance to Station 11, it took 41.2 and 39.5 minutes in the bare soil and
only 31.5 minutes in vegetation. The bare soil was tilled and rough
initially and lost more water due to infiltration than did the hard-
crusted, vegetated border and thus the flow took more time to advance
to a given station. However, recession took longer to occur on the
vegetated border than on the border with bare soil. It took 19.8 and
24.9 minutes after inflow stopped for recession to occur at Station 5
for Roth's Irrigations 9 and 11 respectively and 56.2 and 52.0 minutes
at Station 11 on the bare soil surface. However, with the vegetated
41
Tablef 50 Advance and Recession Times for Irrigation 17.
Table 12. Computed Advance and Recession Equations for Irrigations 17, V-l, V-2, V-3, V-4, V-5, and V-6.
Irrigation______ _______________ 17__________ V-l_________ V-2_______ V-3_________ V-4_________V-5.________ V-6Advance Equation s = F t̂ 1, s is in feet and t is in minutesF 19.98 16.16 14.08h 0.803 0.750 0.881Correlation coefficient
1.00 r.oo 1.00Recession Equation r = G (t = s>*. r is in6 0.03 26.84 0.31m 2.144 0.426 1.53tr(min.) 190.0 220.0 150.0correlation coefficient
surface, it took 82»7 minutes (computed) for recession to occur at Sta
tion 5 and 130*1 minutes at Station 11* The vegetation offered more resistance to the movement of water through the border than did the . bare soil surface during the recession phase* The results showed that for the same inflow rate, water advanced down the border at a faster
rate in the vegetation than a border with a bare tilled soil surface* However, it took twice as long for the water to recede from the vegetated border than the border with bare soil. ,
Infiltration Function Constants in the infiltration function were obtained in vari
ous ways* Equation 13 was the infiltration function used, with the
constants k and a to be determined* Initially, the constants were es
timated by using the data obtained from the cylinder infiltrometers*
This became a starting point for a trial and error solution for the
constants to obtain a volume balance of the flow of water along the
border* The trial and error solution, in addition to lack of precis
sion, required many iterations to obtain acceptable results*
Because of the shortcomings in the trial and error method, dif
ferent solutions were sought* As previously pointed out, Gilley (7)
presented a technique for solving for the constants mathmatically which is valid only for the advance phase* The restriction placed upon Gil
ley's method is that the advance equation and accumulated infiltration volume both fit power law equations* Using this approach, an optimum volume balance for the border was obtained through the advance phase*
Because of the restrictions on Gilley*s technique, only the constants
47in Irrigations 17, V-2, and V-5 could be evaluated strictly according to the power laws. However, for Irrigations V-l, V-3, V-4, and V-6
values were extrapolated in order to give an approximate value of the constants k and a using Gilley's method. The equation was tried for the entire irrigation. As one would predict, the results of the volume balance were excellent during the advance phase, but when using the
same equation for the entire irrigation the accumulated infiltration by
equation was much less than the infiltration as calculated by a volume
balance analysis. When two different equations were used to describe
infiltration, Gilley's equation could be used during the advance phase with a trial and error solution used to describe the continuing and recession phases. By using Gilley's equation in conjunction with the trial and error solution, generally a better volume balance analysis was obtained*
Strelkoff (21) modified Gilley's method slightly so that it be
came readily apparent that a shape factor for the subsurface volume was
included. The shape factor is the ratio between the average depth infiltrated and the maximum depth which occurs at Station 1. Strelkoff further converted the results so the Gamma functions could be used to
obtain the value of the shape factor. He also proposed a method for
determining an infiltration function based on both advance and continu
ing phases. The method proved unstable but prompted further efforts
which were sucessful.
Fangmeier (in 19) developed a method for evaluating k and a by subtracting outflow and surface storage from inflow. A shape factor is
obtained from Gilley's method for the advance phase. The total volume
48infiltrated at the end of the ten time periods during advance is con
verted to average depths and then divided by the shape factor to obtain ten values for z at Station le Values for k and a are obtained for advance by a least squares regression analysis. These values compare very closely with those obtained by Gilley's method.
During the continuing phase values of z are calculated for each station for the next time period using the last values of k and a. The values are integrated to obtain an infiltration volume and the volume
is divided by the area to obtain an average depth. The shape factor for the time period is calculated using the average depth and the depth
calculated for z at Station 1. The actual volume infiltrated is now
divided by the area to obtain an actual average depth which is divided by the shape factor to give a new value of z at Station 1. New values for k and a are obtained at the end of each time period and the process
repeated until inflow stops. The result is an equation for infiltra- . tion based on a least squares regression line obtained from values of z and t during advance and continuing phases of the irrigation.
Fangmeier!s solution gives satisfactory results for both the advance and continuing phases by using actual infiltrated volumes of
water in the irrigation. This method also yields good results in the
volume balance analysis. . However, it still gives accumulated infiltra
tion by equation slightly lower than the accumulated infiltration by
volume balance analysis. During recession, there is a tendency to un
derestimate infiltration.
Table 4 shows the actual volume balance analysis results for
Irrigation V-5 using Fangmeier * s solution for the infiltration
, 49equation. A comparison of infiltration as computed by subtraction<■(volume balance) with that from an infiltration equation shows that the percentage difference is initially high during the advance phase, be
coming very small at the end of the continuing phase and increasing
during recession. Characteristically, the per cent difference immediately before recession between the two methods was 2 per cent. How
ever, Irrigation V-3 had a 19 per cent difference between the two
methods. (Figure 8 shows infiltrometer data and two infiltration func
tions for Irrigation V-5. Gilley's function has a higher intercept than Fangmeier's function and the infiltrometer data. Fangmeier1s
function has a much steeper slope than Gilley's function and appears closer to the slope of the infiltrometer data. This meant that Fangmeier 1s function had a tendency to underestimate infiltration when com
pared to Gilley's function in the early time periods in order to
balance out the infiltration in later stages. The slope of Fangmeier's function appears similar to the slope of the infiltrometer data. Most
irrigations analyzed showed the same relationships.
Figure 9 shows the infiltration functions using, Fangmeier's
method for Irrigations V-l, V-2, V-3, V-4, V-5, and V-6. All functions
are within a narrow band. The intercept decreases in value with each
additional irrigation indicating that the initial accumulated infiltration depth soon after application of water decreased with each succes
sive irrigation.
Excluding Irrigation V-6, the slopes also decreased in magnitude with each additional irrigation, which supports the idea of
ACCU
MULA
TED
DEPTH,
Z (F
EET
100
80
60
A A40 G OZ-0.0060 T 0,4439 G O
Z = 0 .1392 T 0,0772 " G G
GIL L E Y ' S METHOD F A N G M EIER 'S METHOD8 1NF I L T R O M E T E R ONE I N F I L T R O M E T E R TWO A I N F I L T R O M E T E R THREE
O 0
20 20050 70 1006 8 10 302 3 41INF I L T R A T I O N O P P O R T U N I T Y TIME, t (MINUTES)
Figure 8. Infiltrometer Data and Infiltration Functions for Irrigation V-5.
ACCUM
ULAT
ED
DEPT
H51
400
V-6200
V-lV-2V-3100
80V - 4 V-560
40
20
1086
4
2
16 8 101 20 30 2003 4 50 70 1002
I N F I L T R A T I O N O P P O R T U N I T Y TIME, t (MINUTES)
Figure 9. Infiltration Functions for Irrigations V-l, V-2, V-3, V-4, V-5, and V-6.
52decreasing infiltration with additional irrigations.• This trend would he expected when comparing Irrigations V-2 with V-3 and V-4 with V-5.
Irrigations V-3 and V-5 were run one day after Irrigations V-2 and V-4, therefore, the soil moisture would have been much greater before Irrigations V-3 and V-5 which would decrease the infiltration rates for
these irrigations.
All irrigations with vegetation, with the exception of V-6, showed the trend of decreasing infiltration with time. The main factor
causing a decrease in infiltration was probably surface crusts. When taking soil profile board readings after Irrigation V-6, three gopher
holes were observed in the border. This could easily account for the
deviation of Irrigation V-6 from the trend.
Flow RetardanceOne of the most important hydraulic characteristics of vegeta
tion is the resistance that it offers to flowing water. A common measure of the resistance is called a roughness coefficient. In this section, however, the roughness coefficient will be termed retardance
coefficient since it includes the effect of all factors tending to
retard the flow of water. Four retardance coefficients are presented:
Manning's n, Darcy-Weisbach's f, Chezy's C, and Sayre-Albertson's^^ . However, only Manning's n is discussed in detail because of its univer
sal use. The other roughness parameters showed the same trends. All
values were obtained through the use of steady and uniform flow equa
for Manning's n were calculated from equation 2 using the water surface slope and are presented in Tables 27, 28, 29, 30, 31, 32, and 33 respectively in Appendix D. In Appendix D, all retardance coefficients for each station were calculated at the end of the time periods shown. Darcy-Weisbach's f, Chezy's C, and Sayre-Albertson's were calculated from equations 8,1, and 9 respectively and values are listed
in Appendix D in Tables 34 to 54. (
Figure 10 shows average values for Manning's n from 0.077 to 0.253 using the water surface slope at all eleven stations during Irri
gations V-l through V-6 for a selected time interval. The values of
Manning's n at each station during each irrigation were obtained by averaging the last ten 4-minute time periods at each station before
inflow ceased.
Irrigation V-l had much higher average values for Manning's n than all other irrigations. Compared with Irrigations V-2 and V-4,
which had similar inflow rates, Irrigation V-l had retardance coeffi
cients two times higher. These high retardance coefficients were due to the inadequate removal of alfalfa cuttings from the winter months.
Irrigations V-2 and V-3 were run on consecutive days with the
only differences being inflow rates of 0.5 and 0.4 c.f.s. respectively.
In both irrigations, the retardance coefficient dropped in value from Station 1 until Station 4, then increased until Station 10, and then dropped off at Station 11. The average difference in Manning's n val
ues between the two irrigations at any station was slightly more than
0.009.
RETA
RDAN
CE
COEF
FICI
ENT
260
. 2 4 0
220
200
. 1 8 0
160
V-6140
120
100 V-3
. 0 8 0
81 94 7 115 102 3 6
STATIONS
Figure 10. Average Manning's n for Irrigations V-1, V-2, V-3, V-4, V-5, and V-6.
55Irrigation V-4 had an inflow rate of 0,5 c.f.s. while Irriga
tion V-5 had only 0,3 cefcs. These irrigations were also run on successive days* Irrigation V-4, with the higher inflow rate, had an average Manning's n value 0,027 higher than Irrigation V-5, In both irrigations, the retardance coefficient generally decreased in value when going down the border. The retardance coefficient for Irrigation V-5 decreased going downstream at a nearly constant rate. However,
Irrigation V-4 decreased until Station 4 with five of the seven remaining stations remaining almost constant.
The last Irrigation, V-6, had a varied inflow rate with only
the last rate of 0,4 c.f.s, plotted. However, with the 0.7 c.f.s. in
flow rate, the retardance coefficients were almost identical in value
to those with the 0.4 c.f.s. inflow rate. This indicates that retar
dance coefficients were constant. The average Manning's n decreased
from a maximum of 0.153 to 0.102 going down the border.
The average values of Manning's n for these studies ranged from
0.077 to 0.253. At Station 1, the average Manning's n values ranged
from 0.097 to 0.253. With the exception of Irrigations V-l and V-5, the range of the average Manning's n values tended to converge when going downstream. Excluding Irrigations V-l and V-5, the average values of Manning's n ranged from 0.111 to 0.123 at Station 10 and from 0.102 to 0.110 at Station 11. An "average” value of Manning's n describing Irrigations V-l, V-2, V-3, V-4, V-5, and V-6 is 0.127.
Soil roughness determinations were made with the soil profile
board. The same principle was employed as used by Roth with a soil
cast; however, no attempt was made to compare the results of the two
56different methods,, Values of 6? obtained from the soil profile board
determined /C values of soil surface roughness from equation 10.
Table 55 in Appendix E lists the measured values before and after Irrigations 17, V-l, V-2, V-3, V-4, V-5, and V-6 using the soil profile board. Using Equation 10, the average values due to soil
roughness only for Irrigations V-2, V-3, V-4, V-5, and V-6 ranged from
0.01553 to 0.02188.
Tables 48, 49, 50, 51, 52, 53, and 54 list X values as ob
tained from Equation 9. These X values are due to the retardance offered by both the soil and vegetation and for Irrigations V-2 through
V-6 ranged from approximately 0.05 to 0.11. These X values are from
3 to 7 times the values obtained from soil roughness alone.
CHAPTER 4
CONCLUSIONS
Seven irrigations were conducted on a precisely instrumented
border: one with sparsely populated vegetation and six with 10 to 13
month old alfalfa vegetation. Field measurements were made of border
inflow and outflow, border surface elevations, water surface elevations, and infiltration. From these observations border surface slope, water surface slope, flow depth, velocity, surface water storage, infiltration function, advance and recession times, and retardance coefficients were determined.
Relationships Found
Specific conclusions are difficult to draw; however, analysis of the data from this study suggests some general relationships:
1. There is a wide variation in Manning!s n with different inflow
rates with the same vegetation.
2. Cutting the vegetation changes its characteristics so that even
with the same inflow rates the Manning's n value had large
variation.
3. When irrigation was conducted on consecutive days, the secondhad smoother soil surfaces as indicated by smaller values of
Manning's n.
57
58
4. Fangmeier’s method of calculating an infiltration functiongives satisfactory results during advance and continuing phases of a border irrigation*
5C With the same inflow rate, water advanced faster with vegetation on the border than with a bare tilled soil surface. However, because of the retardance offered by vegetation recession was much slower in the border with vegetation.
,6. Infiltration rates decreased with each additional irrigation.
Suggestions for Future Study
Parameters other than retardance coefficients should be eval
uated. The results obtained from these data should be compared with
other investigators1 observations. For instance, n-VR curves should be compared with those obtained by Ree. Comparisons using these data
should be made with Fenzlfs; Kouwen, Unny, and Hill’s; and Nnaji and
Wu’s work using their developed relationships which attempt to base flow formulas for vegetated channels on the vegetation characteristics.
Different types of equations should be considered. Other advance, recession, and infiltration functions should be evaluated.
In any formulas concerning vegetation, accurate description of the vegetation is mandatory. Future studies with vegetation should include accurate measurements of stem diameters, stem lengths, and density for many samples.
APPENDIX A
PHOTOGRAPHS OF VEGETATION FOR IRRIGATION V-6
A one inch grid background was used in each of the photographs
to measure the vegetation. Successive photographs were taken with the
grid two inches farther away from the camera.
59
G R I D P O S I T I O N 0 1 2 3 4 5 6
C A M E R A
S O I L S U R F A C E V E G E T A T I O N D O W N S T R E A MM E T A L P L A T E
N O T T O S C A L E
Figure 11. Schematic Showing Grid Positions.
o\o
61
T ~ r1 : |
1 +
Figure 12. Vegetation Between Camera and Grid Position 1,
/ - f/weip
Figure 13. Vegetation Between Camera and Grid Position 2,
Figure 14. Vegetation Between Camera and Griu Position 3.
Figure 15. Vegetation Between Camera and Grid Position 4
Figure 16. Vegetation Between Camera and Grid Position 5
Figure 17. Vegetation Between Camera and Grid Position 6
APPENDIX B
MEASURED FLOW DEPTHS FOR EACH IRRIGATION
The flow depths are given in feet for each station at the times
140.0 .269 .244 .231 .218 .216 .214 .219 .226 .222 .205 .136144.0 .262 .240 .230 .217 .213 .214 .207 .215 .210 .193 .138147.0 .206 .194 .187 .177 .173 .175 .157 .174 .168 .154 .139148.0 A A A A A .869 .934 .959 A .139150.0 .435 .316 .266 .223 .220 .180 .215 .210 .193 .132152.0 .490 .316 .234 .185 .193 .151 .189 .182 .167 .127154.0 .532 .369 .259 .20 2 . 210 .154 .196 .182 .168 .12415 6.0 A .408 .296 .229 .237 .168 .220 .197 .186 .120158.0 A A .384 .284 .281 .192 .256 .223 .209 .117160.0 A • A .347 .252 .254 .174 .242 .209 .201 .116162.0. . A A .315 .223 .234 .163 .234 .196 .189 .117164.0 A A .284 .207 .226 .156 . 230 ' ,191 .185 .118166.0 A A .278 . 201 .218 .149 .225 .186 .181 .119168.0 A A .276 .197 . 211 .142 .222 .183 .17 9 .121170.0 A A A .207 .221 ' .145 .234 .191 .186 .124172.0 . A A A A .316 .196 .299 .230 .222 .127174.0 A A A A .291 .180 .275 .217 .212 .131176.0 A A A A A .187 .281 .224 .218 .13517 8.0 A A A A A ’ A .325 . 25o .243 .140ISObO A A A A A A .295 o 240 .231 .146132.0 A A A A A A .333 .312 .314 .152184.0 A A A A . A A .321 .298 .300 .161186.0 A A A A A A A .306 .307 .170168*0 A A A A A . • A A A .315 .179192g8 . ' . A A . A A A A A A .312 .19419640 A A A A A A A A A A200.0 b . A A A A A A A A A A204.0 A A A A A A A A A A208.0 A • A A A A A A A / A A212.0 *<> A A A A A A A A A A216.0 A A A A A A A A A A220.0 A A A A A A A A A A224.0 A A A A A A A • A A A228.0 A A A A A A A A A232.0 A A A A A A A , A A236.0 A A A A . A A A A A A .240.0 A A A A A A A A . A A244.0 . A A A A A A A A A A248.0 A A A A A A A A A A252.0 A A A A A A A A _ A A256.0 A A A A A A260.0 A A A A A264.0 A A A A A268.0 A A A A27 2.0 A A A A276.0 A A A A28 0.0 ~ A A A234.0 A A A288.0 A A A292.0 A A A296.0300.0304.0 ° A ° A308.0 A A312.0 A A316.0 A A320.0324.0328.0 0 Q o O o
A— DIO NOT MEET THE REQUIRMENTS OF TURBULENT FLOW: R.E>50 0 AND ROUGH BOUNDARIES.
82
Table 29. Manning's n/Station/Interval for Irrigation V-2 .STATIONPERIOD
.111 .103 .104 .103 .110 . « 094 .094 • .079A .108 .10 5 .105 .112 .093 .095 .076A .090 « 088 .093 .101 .084 .087 .071A A A .154 .145 .113 .113 .069A A A .139 .126 .102 .103 .069A A A .124 .103 .092 .095 .067A A A .109 .091 .082 .088 .063A A A .094 .075 .073 .079 .057A A A A A' A . .148 .052A A A A A A .135 .047A A A A A A .128 . .043A A A A A A ,117 .041A A A A A A .105 .040A A A A A A A. AA A A A A A A AA A A A . A A A AA A A A A A A AA A A . A A A A AA A A A A A A .
A A A A A A AA A A A A AA A A A AA A A A A
A A A A AA A A A A
A A A AA A A0 « - 0 A A e0
A— 0X0 NOT MEET THE REQUIRMENTS OF TURBULENT FLOWS RE>500 AND ROUGH BOUNDARIES.
152*0 A A *145 • 134 *122 • 112 .123 • 100 .105 .084154*0 A A *121 • 116 • 108 .101 . Ill .0 92 .096 .084156*0 A A *119 • 118 .108 .102 .114 .095 .096 .083158*0 A A A • 123 • 110 .106 • 119 • 095- .094 .081160*0 A - A A • 106 • 095 • 094 • 109 *086 . 084 .078162.0 A A A ■ A • 138 • 128 • 142 .108 .104 .076164*0 A A A A • 122 *126 ■ .146 .109 .103 .075166*0 A A A A • 107 • 118 • 132 *098 .096 .072168*0 A A A A • 091 • 110 *118 • 089 .091 .068170*0 A A A A • 077 • 101 .105 • 079 • 085 .064172.0 A A A A A A A *121 • 129 .065174*0 A A A A A A A *109 .119 .073176.0 A A A A A A A *112 .119 • 084178.0 . A A A A . A A A • 099 .106 • 093180*0 A A A A , A A A *064 .090 A182*0 A A • A A A A A A .103 A18 6*0 A A A A A A A A .091 A190.0 A A A A A A . A A • 074 A194*0 A A A A A ... A A A A A198*0 A A A A A A A A A A202*0 A A A A A A A A206*0 A A A A A A A A210*0 A A A A A . A A A214*0 A A A A A A218*0 ° A A A A A A A222*0 A A A A A A A226.0 A A A A A A • A230.0 A A A A234*0 A A A238.0 A A A A242*0 - A. A A246.0 A A A250*0 A A A254.0 A A258*0262*0266*027 0*0 A274*0 A .278.0 A282.0 A286*0 e e O O o O O A
■ A--DI0 NOT MEET THE REQUIRMENTS OF TURBULENT FL0H8 RE»5QQ AND ROUGH 1BOUNDARIES*
85Table 32. Manning's n/S tat ion/Interval for Irrigation V-5.
100*0 .103 .100 *098 .095 .0 93 .090 .088 .086 ,084 .083 .077104*0 *10 4 .102 *099 . 097 .0 95 .0 92 . 090 .088 .085 .084 .07 710 8*0 .104 . .102 .099 .097 .095 .092 . 090 .088 *0 85 .083 .076112*0 *103 .102 .098 .097 .0 95 .092 . 090 .088 *085 .083 ,077116,0 .103 .101 ,099 .097 .095 . 092 .090 .088 .0 86 .083 .0 77120*0 *104 *101 .100 .097 .095 .092 .0 90 .088 *086 .083 .077124*0 ,105 .102 .100 .098 .095 .094 .091 . 089 .087 .065 .077128.0 .105 .103 .100 .098 .096 .093 .092 .089 .087 .085 .078132*0 *104 *104 *102 .101 .099- . 097 .095 .093 .090 .087 ,078136*0 .10 2 .099 .095 .092 .0 89 .086 .083, .081 .078 .076 .077140,0 *100 .098 .094 *091 .089 . 086 . 083 .081 .079 .077 .078142*0 *266 .143 .102 .083 . 073 .067 . 065 .065 .067 .080144*0 A .119 .088 .075 . 068 .064 . 064 * 0 66 .070 .084146* 0 A *112 .087 .076 .071 .070 .071 .074 .081 .087148.0 A *103 .082 .075 .071 .072 .074 *078 .03 3 .087150*0 A *079 .067 .063 . .062 .063 .065 *070 .076 .0 86152*0 A A *083 . 078 • .077 .078 .078 *081 .084 .085154*0 A A *076 .072 . 070 .069 .069 .070 .0 71 .083156*0 . A A A .065 . 064 .064 o 065 .067 .068 .030158*0 A A • A .056 . .058 .059 .060 .062 . 064 , .077160*0 A A A *045 .048 .051 . 053 .055 .057 .075162*0 A A A A A A A A A .054164*0 A A A A A A .099 .077 .081 .040166*0 A A A A A A .090 *069 .074 .042168*0 A A A A A A .083 .064 .070 .044170*0 A A A A A A .079 *059 * 066 .046172*0 A A A . A . A A A .069 .07 9 .050174*0 A A A A ■ A A A .062 .072 .055176,0 A A A A A A A .054 .066 A178*0 A A A A A A A .052 .063 A180*0 A A A A A A A .059 A182,0 A A A A A A A A A186,0 A A A A A A A A190*0 A A . A A A A A A194*0 A A A A A A A198*0 A A A A A A A '202*0 A A A A A A A206.0 A A A A A A . A210*0 A A A A214*0 A A A A218*0 A A A A222*0 A A A A226.0 A A A A230*0 A A A •234*0 A A238*0 A A242*0 0 A ■246*0 . A250*0 A254*0 A258*0 A262*0266*0 e o270*01?5:8 0 I * • o I
A— 010 NOT MEET THE REQUIRMENTS OF TURBULENT FLOW! RE>500 ANO ROUGH BOUNDARIES.
Table 33. Manning's n/Station/Interval for Irrigation V-6,
Table 35. Darcy-Weisbach1s f/Station/Interval for Irrigation V-l. 88STATION 1 2 3 4 5 6 7 8 9 10 11PERIOD2«0 1*5226*5 2*313 162611*5 4.182 3.357 .. *70614*3 4*755 4.259 3.234 *62019*4 5,482 4.645 3.828 2.817 1.21625*3 5.781 5.353 4.683 3.618 4.104 1.76830*0 6.140 5.640 4. 901 3.932 4.092 4.816 .36534.9 6.908 6.477 5.649 4.652 4.502 4.951 2.891 1.10941*1 7,028 6.675 2.552 2.973 2*794 3.062 2.075 2. 054 .3 8647*3 7.039 6.675 4.722 10.352 10.545 12.324 10.701 13.773 17.980 A48*0 7.162 6.799 6*389 5.28 0 5.129 5.611 4.898 5.318 5.301 4. 88049.0 7,204 6.838 6.425 5. 310 5,193 5.678 5.033 5.377 5.495 5 .457- *A5 0*0 7.245 6.918 6.501 5.339 5.294 5.785 5.177 5.476 5.787 6.123 A51*0 7.287 6.942 6.495 5.385 5.380 5.859 5.160 5.667 6.520 6.737 A ‘52*0 7.329 6.939 6*531 5.452 5.408 5. 857 5.129 5. 794 6.579 7.007 A53*0 7.371 6.979 6*608 5.520 5*474 5.883 5.229 6.08 8 6.858 7.509 6.87954*0 7*456 7.018 6.644 5.551 5,542 5.910 5.331 6. 393 7.145 8.036 5 .61655.0 7.499 7.053 6.681 5.582 5.610 5.979 5.394 6. 707 7.502 8.665 5.63556*0 7*342 6*904 6.501 5.418 5*375 5. 712 5.214 6.120 6.084 5.986 5,21657*0 7*384 6.943 6*537 5.448 5.404 5.740 5.316 6.230 6.191 6.187 4.6196 0 *0 7.468 7.021 6.610 5.510 5*538 5. 836 5.483 6.457 6.461 6 .609 4.11464*0 7.638 7.160 6*771 5.798 5,850 6.112 5.885 6. 873 7.028 7.092 3.78568*0 7*845 7.418 6.973 6.066 6.070 6.334 6.270 7. 0 80 7*210 6.982 3.58772*0 7.960 7.589 6.980 6. 028 6.043 6.234 6.367 6. 873 7.093 6.724 3.37176*0 8.031 7.647 6.920 6. 0 6 8 6.223 6.416 6.639 6.895 7.290 6.747 3.17380*0 8.158 7.721 7.044 6.294 6.536 6.693 6.949 . 7.016 7.545 6.849 3.03034*0 8.294 7.843 7.223 6. 465 6.637 6. 658 6.798 6.837 7.370 6.62 0 3.02188*0 8.337 7.792 7.128 6.415 6. 584 6.604 6.732 7.041 7.474 6.650 2.93592*0 8*473 7.813 7*103 6.422 6.644 6.701 7.112 7.756 7*973 7.105 2.85396,0 . 8.611 7.880 7*162 6.469 6.759 6.328 7.215 7.748 7.643 6.765 2.801100,0 8,705 8.009 , 7.239 6, 53 8 6.851 6.942 7.281 7.672 7.420 6.510 ' 2.776104,0 8.655 ■ 8.019 7.244 6.657 6. 951 6. 998 7. 180 7.467 7.277 6.314 2.778108.0 8.701 8.050 7.348 6.794 6.961 7.047 7*134 7.459 7.261 6.338 . 2.789112,0 8.640 7.95 7 .7.367 6* 736 6,788 6. 864 6.952 7.270 7*0.67 6.230 2.837116*0 8.672 7.995 7.421 6.710 6.740 6.771 6. 906 7.181 7.019 6.195 2.932120*0 8.949 8.169 7.500 6.782 6.820 6 .818 6.993 7.177 7.103 6.314 3.026124.0 9.497 8.357 7*575 6.827 6.905 6. 844 7.029 7.348 7.337 6.469 3.098128*0 9.497 8.308 7*546 6.751 6.812 6.721 6. 897 7. 311 7.086 6.199 3.127132*0 9.447 8.304 7.497 6.734 6.775 6.673 6.385 7. 360 7.064 6.177 3.170136*0 9*756 8.575 7.740 6.993 7*015 6.889 7.197 7.648 7.386 6.460 3.189140*0 10*736 9.011 8*174 7.388 7.256 7.145 7.513 7. 935 7.752 6*733 3.209144*0 10*291 8.821 8.156 7.354 7.121 7. 206 6.762 7.250 6*95 7 6.00 8 3.29614 7*0 6*537 5*774 5*375 4. 888 4.709 4.808 3.953 4.716 4.468 3.841 3.361148*0 A A A A A 123.691 138.580 147.323 A 3.39015 0*0 33.967 17.693 12.641 9.012 8.667 6.021 3.237 7*899 6.839 3.428152*0 49*975 19* 843 10.940 6.986 7.371 4.691 7* 045 6, 534 5.605 3.509154* 0 66.834 30*526 15.005 9.148 9.580 5.382 8.262 7.171 6.229 3*60 6156*0 A 40*568 21.178 12*773 13.136 6.927 11.024 8.973 8.020 3.604158*0 A A 37*452 20.568 19.351 9.394 15.573 11.913 10.556 3.57516 0*0 . A A 32.12 0 17*131 16.607 8.086 14.489 10.896 10.117 3.676162*0 A A 27.559 14,102 14.679 7.430 13. 965 10.036 9.223 3.853164*0 . A A 23*454 12*696 14*343 7.123 14.024 9.876 9.167 4.080166*0 A A 23.587 12*530 13.903 6.767 13.921 9.720 9,165 4.328168*0 A A 24*376 12*586 13 .638 6.478 14.061 9.725 9.246 4.598170*0 A A A 14*218 15*286 6.916 15.842 10.753 10.097 4.894172*0 A A A A 31.497 12.745 26.082 15.687 14.425 5.165174*0 A A A A 26*885 10.875 22.291 14.005 13.155 5,518176*0 A A A A A 11*772 23.-331 14.980 13.885 5.90 8173*0 A A A A A A 31.457 19.490 17 . 368 6.339180*0 A ■ A A A A A 26.121 17*161 15.660 6.817182*0 A A A A A A 33*717 29*458 29.013. 7.475184, Or A A A A A A 31* 53 0 .27.018 26.760 8.414186*0', , A A A . A A A A 28*720 28.139 9.443188*0-, A A A : A A A • A A 29*790 10.509192,0 9 ' A A A A A A A • A 29*477 12.455.196*0 A A A A A A A A A A200,0 A A A A A A A A A A204*0 A A A A A A A A A A208,0 A A A A A A A A A A212.0 A A A A A A A A A . A216*0 A A A A A A A A A - A220*0 A A A A A A A ■ A A A224*0 A A A . A A A A - A • A A228.0 A A A A A A A A A232.0 A A A A A A A A A236.0 A A A A A • A A A A A240*0 A A A A A A A A A A244.0 A : A A A A A A A A A248*0 A A A A A A A A • A A252*0 A A A A A ‘ A ■ A A A A256*0 A A A A A A260*0 A A A A A264*0 A A A A A268.0 A A A A272*0 A A A A276*0 A A A A280*0 ' ■ A A A284*0 A A A288*0 A A A292*0 A A A296*0300,0304*0 ° A ° A30 8*0 A A312*0 A A316*0 A A -320*0324*0
176.0 A A . A A A A A A A A180,0 A A A A A A A A A A184.0 A A A A A ' A A A A A188.0 A A A A A A A A A A192.0 A A A A A A A196.0 • A A A A A A A200.0 . 204.0 • Aaa 2 AA : A208.0212.0216*0220.0 . _ ■ : c o :AAA
AAAA
AAA,A
AAAa
AAAA224.0 o A A A228.0 A, A232.0236.0 . . e O 0 O * d e o
A— DID NOT MEET THE REQUIRMENTSI - .
OF TURBULENT 1FLOW? RE>5QQ AND ROUGH BOUNDARIES.
97
Table 44. Chezy's C/Station/Interval for Irrigation V-3,STATION
S. 8. 8c 8.8. 8. 8. 8.9. 9. 9. 9.9. 9. 9. 9o2 o 4. 4.5 o 6. 7.3 0 5. 7.A 5« 60A • 5. 7.A - 5. 6.A A 5cA A * 60A A AA A AA A AA A AA A Ac A A AA A. ‘ AA A A.. A A AA A AA - A AA A AA A AA A AA A AA A A0 A A A0 , 0 0
>010 N O T M E E T TH E R E Q U I R M E N T S
1;i t :11.IS;10.88:10.10.10.
I 9.J:IS;i:9.9.9.IS;9.8.8.8.8.8.-8:8.8.8.8.8.8.8.8.8.8.8.1;8.8:8.8.-9.9.- 4 o 7c8c
5.6c?:!•■ A ASAAAAA
II;II;11.11.IS;is;10.10.-10.it
IS;10.10.10.10.10.10.10.10.10.I;
IS;10.8.8.8c8.8.8.8.8.8.8.I:8.8:1:9.1:9.9.9.
i t :4 .7. 9.8. 8. 8. 8. 8. 6 . 7 .
1:9.A!AiAAAAAA
II1 1 .it:i8:iS:
»:■i":10.10.18:10.10.9.10 I 10. 10.IS;1;8.8.8.8.8.8.9.I;!:1:1:9.9o9.9.9.9.
18:4.7. 9.809.8.i;7 .8. 8. 9. 6. A A A A A A A A A A A A
1 5 8 . 0 A A . * 1 6 0 5 1 * 1 4 7 4 8 . 1 6 6 4 9 . 1 3 1 0 7 . 1 7 9 1 8 . 1 6 5 3 9 . 1 6 1 1 6 . 0 9 8 7 71 6 0 * 0 A A * 1 5 0 4 1 * 1 3 5 6 8 . 1 5 5 2 1 * 1 2 1 3 6 . 1 7 3 2 4 , 1 5 8 3 5 . 1 5 7 8 8 . 0 9 6 6 61 6 2 * 0 A A . 1 4 0 8 2 . 1 2 3 8 6 . 1 4 5 0 6 . 1 1 3 6 5 . 1 6 7 8 1 . 1 5 1 2 1 . 1 5 2 2 1 . 0 9 5 0 01 6 4 * 0 A A . 1 3 1 2 0 . 1 1 4 9 2 . 1 3 7 7 7 , 1 0 7 3 2 . 1 6 3 0 0 . 1 4 5 7 9 . 1 4 7 8 1 . 0 9 3 8 01 6 6 . 0 A A * 1 2 3 6 4 * 1 0 8 7 6 . 1 3 0 3 9 . 1 0 0 8 8 . 1 5 7 5 5 . 1 4 0 4 0 . 1 4 3 5 7 . 0 9 2 5 41 6 8 , 0 A A * 1 1 6 4 2 . 1 0 2 8 9 . 1 2 3 2 7 . 0 9 4 7 0 . 1 5 2 8 7 . 1 3 5 7 8 . 1 3 9 5 5 . 0 9 1 2 21 7 0 . 0 A A A * 0 9 8 3 2 * 1 1 8 7 7 . 0 9 0 3 0 . 1 5 0 4 1 . 1 3 3 7 1 . 1 3 7 3 6 . 0 8 9 8 41 7 2 * 0 A A A A * 1 2 2 3 8 . 0 9 4 9 1 . 1 5 3 0 4 . 1 3 6 4 2 . 1 4 0 9 2 . 0 8 7 8 61 7 4 , 0 A A A A . 1 1 4 3 7 . 0 8 7 8 9 . 1 4 2 8 6 . 1 2 9 3 9 . 1 3 4 9 5 . 0 8 6 3 41 7 6 , 0 A A A A A * 0 8 3 8 6 , 1 3 5 9 5 . 1 2 6 0 5 . 1 3 1 4 9 « 0 8 4 7 61 7 8 . 0 A A A A A A * 1 3 2 7 2 . 1 2 5 6 8 . 1 3 0 3 8 . 0 8 3 1 01 8 0 * 0 A A A A A A . . 1 2 2 5 6 . 1 1 8 6 7 . 1 2 4 9 2 . 0 8 1 3 8i 8 2 * Q : A A A A A A . 1 2 0 2 5 . 1 2 1 6 0 . 1 3 0 4 5 . 0 8 0 5 11 8 4 * 0 A A A A A A • * 1 1 7 0 1 * 1 1 7 2 8 . 1 2 6 1 3 . 0 8 0 9 51 8 6 * 0 A A A A A A A * 1 1 4 7 3 . 1 2 3 5 0 . 0 8 1 2 31 8 8 * 0 A A A A A A A A . 1 2 0 9 1 . 0 8 0 9 11 9 2 * 0 A . A A A A A A A * 1 1 5 8 4 . * 0 8 0 5 21 9 6 * 0 « A A A A A A A ' A A A200*0 A A A . A A A A A A . A2 0 4 * 0 A A A , A A A A A - A ■ A2 0 8 * 0 A A A A A A A A A A212*0 ̂■ A A A A A A A A A . A2 1 6 * 0 A A A A A • A A A . A A .220*0 A A A A A A A A A A2 2 4 . 0 A A A A A A A A . A A2 2 8 * 0 A A A . A A A A A A2 3 2 * 0 A A A A A A A A A2 3 6 * 0 A A A A A A A A A A2 4 0 , 0 A A A A A A A A A A2 4 4 * 0 A A A A ' A A . A A A A2 4 8 . 0 A A A A A A A A A A2 5 2 * 0 A A A A A A A A A A2 5 6 . 0 A A A A A A2 6 0 * 0 A A A A A2 6 4 * 0 A A A A A2 6 8 , 0 A A A A2 7 2 * 0 A A A A2 7 6 * 0 A. A A • A2 8 0 * 02 8 4 * 0
° I AA i i
2 8 8 . 0 A A A2 9 2 * 0 A A A2 9 6 * 0 o3 0 0 . 03 0 4 * 0 A A3 0 8 * 03 1 2 * 3 I I A
AAA
3 1 6 * 0 A A3 2 0 * 03 2 4 * 03 2 6 * 0 o « 0 *
ft— 0X0 NOT MEET THE REQUIRMENTS OF TURBULENT FLOW: k E>500 AND ROUGH BOUNDARIES.
1 4 2 . 0 A A . 0 6 5 7 0 . 0 7 6 3 7 . . 0 8 1 6 9 . 08897 . 0 9 8 6 9 . 0 9 2 0 4 . 0 83051 4 4 . 0 A A . 0 5 5 5 3 . 0 6 4 1 0 . 0 7 2 1 2 . 0 7 8 8 8 . 09 017 . 0 8 3 1 0 . 0 8519 . 0 7 8 7 71 4 6 . 0 A A . 0 5 0 6 7 . 0 5 764 . 0 6 7 0 7 . 0 7 4 0 6 . 0 8 6 2 6 . 0 7 7 7 9 .0 8354 . 0 7 2 6 61 4 8 . 0 A A A . 0 5 3 1 0 . 0 6 1 2 2 . 0 6 9 4 3 . 08200 • . 0 7 2 6 1 . 0 7 9 0 6 . 0 6 5 0 91 5 0 . 0 A A A , 0 4 3 0 5 . 0 5 0 1 6 . 0 6 0 4 6 . 0 7 2 4 5 . 0 6 3 7 7 . 0 7 0 7 2 . 0 5 7 2 01 5 2 . 0 . A A A A A . 0 7 0 7 9 . 07916 o 07025 . 0 7 6 8 4 . 0 5 0 4 21 5 4 . 0 A A A A . A . 0 6 3 2 4 . 06787 . 0 6 1 7 6 . 0 6 8 3 5 . 0 4 5 5 41 5 6 . 0 A A .A A ’ A . 0 5 5 7 1 . 05 667 . 0 5 3 5 3 .0 6096 . 0 3 9 9 815 8 . 0 A A A A A . 0 4 7 6 9 . 04615 . 0 4 5 9 5 . 0 5 4 1 6 . 0 3 3 2 51 6 0 . 0 A A A A - A . 0 3 9 7 8 . 0 3 5 3 9 . 0 3 8 8 7 . 0 4 6 5 0 . 0 2 5 9 216 2 . 0 A A A A A A A A . 0 6 1 8 2 . 02075l p 4 . 0 A A A A A A A A • . 0 5 7 4 7 . 0 1 7 6 1l o 6 » 0 A A A . A A A A A . 0 5355 . 0 1 4 4 11 6 8 . 0 A A A A A A A A . 0 4 8 6 9 . 0 1 2 5 01 7 0 . 0 A A A A A A A A . 0 4 3 3 3 . 0 1 1 8 21 7 2 . 0 6
5A A A A A A A A A A
1 7 6 . 0 A A . A A A A A A A . A1 8 0 . 0 * A A A A A A A A A A1 8 4 , 0 : 4 A A A A ■ A A A A A A1 8 8 . 0 4 . A A A A A A A A A A1 9 2 . 0 A A A A A A A1 9 6 . 0 V A A A A A A A2 0 0 . 0 A A A A A A2 0 4 . 0 A A A ' A A2 0 8 . 0 A A A A A2 1 2 . 0 A A A A A2 1 6 . 0 A A A A A2 2 0 . 0 A A A A2 2 4 . 0 A . A A2 2 8 . 0 A A2 3 2 . 0 '2 3 6 . 0 « e e ' 4> « 0 o O
A — 013 ".NOT MEET THE REQUIRMENTS OF TURBULENT FLOWS KE>500 AND ROUGH BOUNDARIES*
104
. Table 51. Sayre-Albertson's ^-/Station/Interval for Irrigation V-3.STATION
N - Number of roughness elements per squarefeet of channel bottom
R L Hydraulic radiuss L Distance from border head to advancing front
- Slope of total energy line
Sq - Slope of channel bed
S^ - Slope of water surfacet T Timet T Time inflow stopsrt^ T Intake opportunity time
u L Difference between the water level and soilsurface elevation
v - Constant
V LT” *̂ Average velocity
V* LT”**" Shear velocityW L Distance from the trolley to the bench mark
y L Normal depthz L Accumulated infiltration depth
Shape parameter .for vegetative roughness
L Measure of roughness element spaceFTL^ Dynamic viscosity of fluidL^T"^ Kinematic viscosity of fluid
112
Symbol Dimensions DescriptionP FT^L~^ Mass density of fluid£=> L Standard deviation of a roughness profile
9^ FL ̂ Total shear stress acting on channel bottom“*2t'3rv FL Vegetation drag per unit area
L Resistance parameter from Sayre and Albertson/s equation
LIST OF REFERENCES
1. Bowman, C. C. 1960. Manning;s equation for shallow flow. U. S.Department of Agriculture, Proceedings of the ARS-SCS Workshop on Hydraulics of Surface Irrigation. ARS 41-43.
2. Bowman, C. C. 1967. Vegetative density meter. Montana Agricultural Experiment Station. Bulletin 611. Montana State University.
3. Chow, Ven Te. 1959. Open Channel Hydraulics. McGraw Hill.New York. 680p.
4e Cook, H. L. and F. B. Campbell. 1939. Characteristics of somemeadow strip vegetations. Agricultural Engineering.Vol. 20. pp. 345-348.
5. Daugherty, R. L. and J. B. Franzini. 1965. Fluid Mechanics withEngineering Applications. McGraw Hill. New York. 574p.
6. Fenzl, R. N. 1962. Hydraulic resistance of broad, shallow vegetated channels. Unpublished Doctoral Dissertation. University of California, Davis, California. 154p.
7. Gilley, James R. 1968. Intake function and border irrigation.Unpublished Master 1s Thesis. Colorado State University,Fort Collins, Colorado. 13Op.
8. Israelsen, 0..W. and V. E,.Hansen. 1967.. Irrigation Principlesand Practices. John Wiley and Sons, Inc., New York. 447p.
9. Kouwen N., T. E. Unny, and H. M. Hill. 1969. Flow retardance invegetated channels. Journal of the Hydraulics Division, ASCE. Vol. 95(IR2). pp. 329-342.
10. Kruse, E. Gorden. 1962. Effects of boundary roughness and channelshape on resistance to flow of water in very small open channels. Unpublished Doctoral Dissertation. Colorado State University, Fort Collins, Colorado. 198p.
11. Michael, A. M. and A. C. Pandya. 1971. Water front advance inirrigation borders. Journal of Agricultural Engineers Research. Vol. 16(1). pp. 72-80.
113
11412, Myers9 L. E, 1959, Flow regimes in surface irrigation. Agri
cultural Engineering, Vol, 40, pp, 676-677, 682-683,
13, Nnaji, Soronadi, and I. Wu. 1973, Flow resistance from cylindrical roughness. Journal of the Irrigation and Drainage Division, ASCE, Vol. 99 (IR1), pp. 15-26.
14, Palmer, V. J, 1946. Retardance coefficients for low flow inchannels lined with vegetation. Transactions American Geophysical Union. Vol. 27. pp. 187-197.
15. Philip, J. R. 1957. The theory of infiltration: 4. Sorptivityand Algebraic infiltration equations. Soil Science.Vol. 84(3). pp. 257-264.
16. Ree, W. 0, 1949. Hydraulic characteristics of vegetation forvegetated waterways. Agricultural Enginnering, Vol. 30 pp. 184-187.
17. Replogle, John A, 1970. Critical depth flumes for determiningflow in canals and natural channels. Presented at theAnnual Meeting of American Society of Agricultural Engineers. Paper No, 70-125, 36p.
18. Roth, Robert Le 1971. Roughness during border irrigation.Unpublished Master*s Thesis. University of Arizona,Tucson, Arizona. 98p.
19, Roth, R. L., D. W, Fonken, D. D, Fangmeier, and K, T. Atchison,1973. Data for border irrigation models. UnpublishedPaper. University of Arizona, Tucson, Arizona. 19p.
20, Rouse, Hunter and Simon Ince. 1963. History of Hydraulics,Dover Publications, Inc, New York, 269p.
21. Strelkoff, T, S. 1972. Personal communication with D, D. Fangmeier, Department of Water Science and Engineering.University of California, Davis, California.