Evaluation of Wetted Perimeter and Water Flow Cross ...

Australian Journal of Basic and Applied Sciences, 7(6): 350-358, 2013
ISSN 1991-8178

Evaluation of Wetted Perimeter and Water Flow Cross Section in Furrow
Irrigation by Use Manning, SCS and Ellipsoid Equations

Abubakr Rahimi and Motalleb Byzedi

Department of Water Science Engineering, Sanandaj Branch, Islamic Azad University, Sanandaj,
Iran.

Abstract: Since the most important and strategic products such as sugarcane, sugar beet, corn and etc
are irrigated by Furrow irrigation method and. The most important factors influencing the penetration
of water in the furrows are wetted perimeter, flow area , infiltration opportunity time, furrow length,
input flow, geometric shape and furrow slope. Such factors are most important role in estimating the
amount and speed of water penetration into the soil. Therefore the wetted perimeter and flow area
section were assessed in this research. Determination and assessing of wetted perimeter and flow area
section require the measurement of parameters such as geometry, inlet flow rate, water depth, water
surface width, slope, roughness coefficient, etc. After land preparation to determine the land slope,
square networking bay 20*20m was applied and topography maps were prepared. Then, almost
parabolic cross-sectional shape of furrows was created by Furrower with 0.75 m distance from each
other 80m long. In whole 5 test furrow and 10 lateral furrows were created and 4 irrigation applied. To
aim the scopes of project based on Gauge section, parabolic equation, Manning's formula and Soil
Conservation Organization (SCS) method the data were analyzed using the software MSTAT-C, SPSS
and Microsoft Office. Analysis of variance showed there are significant differences at 1% level for
wetted perimeter between measurement blocks (furrows first to 5th) and measurement methods (Gauge
section, parabolic equation). The coefficient of variation equal to 0.03 percent. The average of wetted
perimeter for Gauge section and parabolic equation methods was 48.361 and 48.306 cm respectively.
Also results showed there are significant differences at 1% level for wetted cross section area between
measurement blocks (furrows first to 5th) and measurement methods (Gauge section, parabolic
equation). The coefficient of variation equal to 2.18 percent. The average of wetted cross section area
for Gauge section and parabolic equation methods was 306.279 and 347.426 cm2 respectively. For
more surveying the regression line and fitted line equation and there correlation coefficient were
evaluated for wetted perimeter and wetted cross section by Gauge section, parabolic equation for all
furrows. The correlation coefficient for wetted perimeter and wetted cross section were 1 and .09879
respectively.

Key words: Evaluation - Wetted Perimeter - Water Flow Cross Section -Furrow Irrigation - Manning,
SCS and Ellipsoid Equations.

INTRODUCTION

Surface irrigation is one of the most common irrigation procedures used in Iran and in the world. In spite of
the considerable made in other irrigation procedures, Surface irrigation is performed in a traditional ways in Iran
and a majority of countries and has not been significantly changed. Paying attention of the growth of population
and the limited resources of water & soil it is clear that current irrigation outputs cant be continued and there
fare it is required that irrigation outputs be in creased. To do so, especially in the case of surface irrigation, one
should have a basic know ledge regarding the intricate phenomenon of water permeation in the soil. Surface
irrigation is performed in these ways: Basin irrigation, border irrigation and furrow irrigation. Mostly, the
permeation of water in the basins and border is a mono dimensional process which takes place vertically and
based on the direction of gravity. In furrows, the permeation of water is a two dimensional process which takes
place both vertically and horizontally baled on the gravity and capillarity. It is because of the fact that most of
the strategic crops like sugar cane, sugar beet and corn are irrigated in furrow way. Also the most effective
factors for the permeation of water in furrows are. Wetted perimeter, water flow cross section, and permeation
time, the length of the furrow, the intensity of input flow, geometric shape and the slope of furrows. Due to the
important role of the parameters likes geometric shape of the furrow. Wetted perimeter and water flow cross
section in a majority of water permeation equations, they are evaluated here. According to the definition the
shared are a between water and soil. Which has been located in the cross section of the furrow is celled wetted
perimeter. Through different steps of furrow irrigation, the wetted perimeter changes based on the time and
place and it is required that its permeation effect be checked so as to ameliorate the designing quality,

Corresponding Author: Abubakr Rahimi, Department of Water Science Engineering, Sanandaj Branch, Islamic Azad
University, Sanandaj, Iran.
E-mail: [email protected]; [email protected]
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management and performance in surface irrigation models. The changing flow of the wetted perimeter a long
the furrow is dependent on the soil type roughness of the furrow shortage of soil moisture, the slope of the
furrow and the value of input flow. Therefore the deter emanation of how the wetted perimeter affects on the
value of permeation is equal to the indirect determination of the effect of the above cited parameters.

In basins and border. The permeation of water is an intricate phenomenon. It depends on the type of the soil
and the condition of the surface. Due to the water – soil contact - surface, the permeation effects of adjacent
furrows, the geometric shape of furrow, etc are more intricate. It is clear that the participation of the effects of

all parameters in permeation equations makes the investigation be more intricate, therefore are tries to check the
effects of different parameters and to choose the more effective ones for permeation equation. Except the soil

type and the conditions of its surface, in the case of water permeation in furrows, the most important effective

parameters are permeation opportunity, the distance between furrows, the geometric shape, surface flow
velocity, the intensively of input flow, ground slope, the wetted parameter, air and the soil gaps.

The geometric shape of the furrows affects on the permeation value.
Theoretically and experimentally, Philip (1984) showed that the permeation value of water in a curved
surface is significantly higher in comparison with a flat surface.

Fok and chiang (1984) assumed the furrow to have a rectangular shape and represented a two – dimensional
permeation for furrows. Based on the geometric shape is of no significant effect on the permeation value. They

thought of permeation to be rectangular and represented the two – dimensional permeation equations of water in

the furrows.
Shmitz (1993) has criticized the rectangular shape assumption of the furrow which was mentioned by Fok

& chaing. He considers the assumption as an unreal one and, based on the work performed by Philip, he has
represented a model so as to determine the effect of the genetic shape of the furrows on the permeation
equations.

In Trout’s opinion (1992) the effect of surface flow Velocity on the permeation value of water in furrows is
due to erosion, transportation of the particles, recurrent sedimentation, blacking the porosity of the permeable

surface, the permeation of soil crack or the consequent sheer stress. To preview the permeation variations, in
Hanson ET all opinion, it is necessary to find a permeation relation between the intensively of input flow and

that of the furrows. Due to the inaccessibility of such a relation, they utilized UN artificial procedure to
determine the effect of this phenomenon. It was in a way that they first configured the permeation of water in
the furrows based on the wetted perimeter and the normal flow intensively and then to configure the permeation

value based on the mentioned flow intensively, they multiplied it into the ratio of the wetted perimeter with the
mentioned intensively to the wetted perimeter with normal intensively.

Utilizing classical statistic theory and categorization, Hart (1995) studied the effects of local changes on the

intensively of input flow, cross section, the depth of the flow, roughness coefficient and the geometric shape of
the flow section in a furrow. The circum stances of the flow and also the strangely of water made the permeation

value of water increased in the clay loam However the rapid increase of the flow in a similar type of soil which
had less cracks also made the permeation value increased.

The researchers found that there is a somewhat linear connection between the wetted perimeter and the

furrow, in a way that the more the wetted permeation the more the permeation value.
Using the procedures of: input – out put, rotating and blocked furrows in both fixed and variable depths,

Behzad (1996) performed permeability test and investigated some equations so as to study the effect of wetted

perimeter on the permeation of watering the furrows. For Applying each of the equations, the results of the
variance analysis for each of the previewed values showed that the permeation equations which paid no

attention to the effects of the wetted perimeter and the cross section of the flow upon the permeation value of
water had got the highest error value and contrarily the equations which paid attention to the effects of both the
wetted perimeter and the water flow cross section not only had got less error value but also were more flexible
in the case of corresponding to hydraulic variations in comparison with the previous equations. Finally it was
suggested that wetted perimeter equation or that of the water in the efficiency of the irrigation.

In order to study the effects of both the wetted perimeter and that of the water flow cross sections on the
permeation value in the furrows and to deter mine the two parameters with cross- section method, Ellipsoid
equations, Manning, and SCS equations, one should perform permeability tests in both input and output way

and collects the required data which consists of advance - récession time, the infectivity of the input flow, depth
and the width of water surface and the slope of the furrows. Then, applying the following formulae, the shape

coefficients of the furrows were determined so as to finally asses the wetted perimeter and water flow cross
section through applying the a above cited procedures.

TW  a1Y a2 (1)

A  1Y 2 (2)

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WP   1Y  2 (3)

A  1WP 2 (4)

Tw= the width of water surface

A= the cross section of the furrow

Y: the depth of the flow

WP= the wetted perimeter of the furrow

A1, a2, δ1, δ2, Υ1, Υ2, P1 & P2 = equal parameters or the coefficients for the geometric shape of the furrows.
Based on the depth and the width of the water surface in the furrows and the assumption of ellipsoid for the

furrows one can determine the wetted perimeter and water for cross section in the following way:

 WP
  Top  1  X 2  1 Ln X  1 X2 
2 X 
(5)
X  4Y (6)
Top (7)

 A2
 3 Y .Top

Y= the depth of the flow
Top= width the water surface
A= the cross section of the flow
WP= the wetted perimeter.

A assuming a study flow for the water, Manning suggested the following equations to configure the wetted
perimeter.

3

WP  aP  nQin  (52 2)
 S 
(8)

5 (9)

a P 1 (52 2)

Q in = the intensively of the input flow

S= the slop of the furrows

n = Maninegs roughness coefficient

To deter mine shape coefficients for the furrows one should use the data acquired by cross- section method

procedure. If we know the values for Manings coefficient, the slope of the furrows and the intensively of input

flow, we can configure the wetted perimeter at the beginning of the furrows. Using the equation No (9) SCS also

suggested the following equation to determine the wetted perimeter.

0.265 nQin  0.4247
S 
WP   0.014

(10)

In this article, were about some goal like = determining the wetted perimeter and water flow cross section
using cross- section method, naming equations 3 – SCS and 4: Elipsoid equations, determining the effects of
both the wetted perimeter and water flow cross section on the permeation value of water in the realm of furrow
irrigation, determining the geometric shape coefficient of the furrows and determining the ratio of water flow
cross section to the wetted perimeter.

MATERIALS AND METHODS

Researching area consists of the land belonging to the agriculture college of 7 AUS which is 10 Km way
from sanandaj on the road to Kermanshah.

In order to assess, design, and simulate a furrow irrigation system and specially to determine the equation of
water permeation in the furrow which signifies the natural condition of the study furrows, it is necessary to

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assess both the wetted perimeter and the water flow cross section. The more the assessment precision, the better
one can assess, design or simulate the systems.

There are several ways to assess the water flow cross section and the wetted perimeter among which one
can refer to cross- section method, ellipsoid equation, Manineg formula and SCS procedure. To assess the
wetted perimeter water flow cross section and their effect upon permeability it’s required that the permeability
tests be performed using on of these procedures, input – output, blacked furrow or rotating penetrometer
(restoring the run off to the end of the furrow). Since the input – output is the most noticeable and the most
applicable in the form irrigations, we used it in our research. Hawing prepared the form to determine the slope
value 20 × 20m2 networks were created and the topographical map of the farm was prepared. Then, using ‫ﻓﺎروﺋﺮ‬
which had an ellipsoid section of 75 cm and the distance of 80 m in a black, the furrows were measured. Totally
5 measurement furrows and 10 separator ones were created so as to perform four consequent irrigations (first to
fourth) and to perform several tests such as tests of geometric shape, input – out put flow intensively, irrigation
depth the width of water surface. The slope of the furrows. Etc. Making use of ¾ ″ and 1¼ ″ siphons and also
the soil creek which was away from the farm the irrigation was performed. Using two ¾ ″ siphon and one with
the size of 1¼ ″ for each of the furrows, they were irrigated in an open – end way. Figures 1 pound 2 show the
required facilities for the perform once of the test and the performance of input – output Permeability test to in
order.

Picture 1: The required facilities for input – output permeability test.

Picture 2: Input – output permeability test.
In order to achieve the required information for the devised goals, to achieve suitable responses for the

research question and to study the effect of the wetted perimeter and the water flow cross section on the
permeation value of water in the furrows, Using input – output method, the permeability test were performed
based on the effects of the wetted perimeter and the intensively of the input flow.

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In order to compare and assess the wetted perimeter and water cross section the required data was collected.
It consisted of advance and récession time, the intensively of input flow, the depth and the width of the water
surface and the slope of the furrows that were collected through the procedure of cross- section method,
ellipsoid equation, Manineg formula and the SCS, in the case of furrow irrigation. Using the soft wares MSTAT
– C, SPSS and Microsoft & discussion.

RESULTS AND DISCUSSION

In order to compare the procedure of cross- section method with that of ellipsoid equation, to determine the
significance of their difference regarding the wetted perimeter and water flow cross section and to determine the
significant of the difference between treatments, the variance analysis was performed in a completely random
way ANOVA testing and MSTAT – C software.

Also, Denken, multi – amply cued test was performed so as to determine the homogeneity of the difference
between treatment. The results of variance analysis of the procedures of cross- section method and ellipsoid
equation has been represented in Table 1 & 2. They consist of the data regarding both the wetted perimeter and
water flow cross section. To determine the precision of the test the variance coefficient was applied. Since it
signifies the error according to the average percentage of testing, we have got the percent value of the variance
coefficient.

Table 1: The results of variance analysis regarding the effect of measuring procedure on the wetted perimeter.

Row Sources of variations Freedom degree The sum of squares
2.284**
1 Block 4 0.007**
0.001
2 Measurement procedure 1
0.03%
3 error 4

4 total 9

5 The coefficient of variance(CV)

**significant at the level of 1% ,* significant at the level of 5%

ns: no significant

Table 2: The results of variance analysis regarding the effect of measuring procedure on the water flow cross section significant at the level
of 1%.

Row Sources of variations Freedom degree The sum of squares

1 Block 4 1817.810**

2 Measurement procedure 1 4232.607**

3 error 4 50.927

4 total 9

5 The coefficient of variance(CV) 2.18%

**significant at the level of 1% ,* significant at the level of 5%

ns: no significant

Variance analysis of the data showed that we range values of both the wetted perimeter and water flow
cross section was significant at the level of 1% in measuring procedures. The results of the variance analysis
regarding the tested data showed that there was a significant difference between the average values of the wetted
perimeter in both measuring blocks (furrows 1 to 5) and measuring procedures (cross- section method and
ellipsoid equation). The level of significant difference was 1% and the variance coefficient was equal to 0.03 y.

The average values of the wetted to 48.361 and 48.306 in order.
Figure 1 represent comparison of the average values of the wetted perimeter that were acquired by Den ken
test through difference measuring procedures.
For more investigation, the the results of regression lines fitting, the results the fitted line equation and their
correlation coefficient for the average values of the wetted perimeter were assessed the results were based on
both cross- section method and the ellipsoid equation procedures. The results showed that the correlation
coefficient of the wetted perimeter was almost equal to 1 for all the furrows in both procedures.
In addition the results containing regression line fitting, the fitted line equation and their coefficient of
correlation for the average of water flow cross section were assessed through both cross- section method and the
ellipsoid equation procedures. The results showed that, in both measurement procedures, the highest value of the
coefficient of correlation in the case of the water flow cross section belonged to the equal to 0.9909 and
belonged to the furrow No 4 (Table 4). Nasserites found that in the case of a creation a simple correlation
between the cumulative permeation and the dependant permeation variables there would be significant effect by
both water flow cross section and the wetted perimeter on the cumulative permeation.

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Average values of the weteed 48.37 a b
perimeter(Cm) 48.36
48.35 Cross- se ction me thod Ellipsoid e quation
48.34
48.33
48.32
48.31

48.3
48.29
48.28
48.27

Fig. 1: The comparison between the average values of the wetted perimeter indifferent measuring procedures
based on Den ken testing. The results of variance analysis for the tested data also showed that there was
a significant difference between the average values of the water flow cross section in measurement
blocks (furrows 1 to 5) and the ones by measurement procedures (cross- section method and the
ellipsoid equation). There was a signification difference at the level of 1% and the data variation
coefficient was equal to 2.18% the average values of the water flow cross section in both cross- section
method and ellipsoid equation procedures were equal to 306.279 and 347.426 in order figure 2
represents the comparison of the average value of the water flow cross section in different
measurement procedures based on Den ken testing.

Averagevalues of 350 b a
thecross section 340
330 Cross- section method Ellipsoid equation
320
310
300
290
280

Fig. 2: The comparison of average values of water flow cross section in different measurement procedures
based on Den ken testing.

For more investigation, using both cross- section method and the ellipsoid procedures, the results of
regression lines fitting the fitted line equation and their correlation value for the average values of the wetted
perimeter were assessed in all furrows. The results showed that, using both procedures, the acquired values of
the coefficient of correlation were almost equal to 1 the for all furrows while it was equal to 0.9879 for the water
flow cross section. In Table 5, the relations between the wetted perimeter values and the ones for the water flow
cross section have been represented for both measurement procedures of cross- section method and the ellipsoid
equation.

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Table 3: The fitted line equation and the correlation coefficient of the wetted perimeter in different procedures.

Number Furrow Measurement procedure Line equation R

1 cross- section WP  1.0013WP  0.1449 1
Wetted perimeter. 1
1
2 cross- section WP  1.0007WP  0.0835 1
Wetted perimeter. 1

3 cross- section WP  0.9989WP  0.0103
Wetted perimeter.

4 cross- section WP  1.0023WP  0.1652
Wetted perimeter.

5 cross- section WP  0.999WP  0.0235
Wetted perimeter.

WP = the wetted perimeter cross- section procedures

WP = the wetted perimeter (ellipsoid equation)

StreKoff and Souza (1984) and behzad (1315) Found that the wetted perimeter was the best variable for the
configuration of the two – dimensional permeation of water in the soil in furrow irrigation. There is a positive
correlation between the ratio of water permeation velocity to the wetted perimeter of the furrow some of the
researcher hers believe that the variation of the wetted perimeter of the furrow is equal to ⅓of the permeation
varieties.

Table 4: The fitted line equation and the coefficient of correlation for the water flow cross section in different procedures.

Number Furrow Measurement procedure Line equation R

1 cross- section A  1.2501A  43.073 0.992
Wetted perimeter. A  1.2818A  27.978 0.9965
A  1.2789 A  33.642 0.9932
2 cross- section A  1.2064 A  45.529 0.9909
Wetted perimeter. 0.9918
A  1.269 A  34.418
3 cross- section
Wetted perimeter.

4 cross- section
Wetted perimeter.

5 cross- section
Wetted perimeter.

A = the water flow cross section procedure)

A = the water flow cross section (the ellipsoid equation)

Table 5: The fitted line equation and the coefficient of correlation for both the wetted perimeter and the water flow cross section in different

measurement procedures (furrows 1 to 5)

Number Furrow Description Measurement procedure Line equation R

1 Wetted perimeter cross- section WP  1.0006WP  0.0796 1
Wetted perimeter.

2 cross- section cross- section A  1.1912 A  21.439 0.9879

Wetted perimeter.

WP = the wetted perimeter cross- section procedures

WP = the wetted perimeter (ellipsoid equation)
A = the water flow cross section procedure)

A = the water flow cross section (the ellipsoid equation)

In this research, significant differences were observed among the results of the wetted perimeter and those
of the water flow cross section in the furrows while implementing cross- section method, the ellipsoid equation,
Manning equation and the SCS procedure. These results can have a significant effect upon the configuration the
water permeation value in surface irrigation procedures and specially the furrow irrigation procedure. Since the
determination of the wetted perimeter, using both Manning equation and the SCS procedure, requires the
expensive, time consuming configuration of the intensivityof the input flow, the slope value of the furrows,
Mainegs roughness coefficient, and the shape coefficients of the furrows, these methods can be only used to
determine the values of the wetted perimeter and the water flow cross section at the beginning of the furrows. It
is also because of the facet that the value of Maninegs coefficient is mostly vague and should be guessed and
this makes the precision level decreased. In the furrow irrigation the permeation of water is a two – dimensional
process so the geometric effect of the furrows cross section should be paid attention to through the simulation of
the water How and the configuration of the permeation value.

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100.00

Weteed perimeter-ellipsoid equation(Cm) 80.00

60.00

40.00

20.00

0.00 20.00 40.00 60.00 80.00 100.00
0.00

Weteed perimeter-Cross- section(Cm)

Fig 3: The comparison of the wetted perimeter values by both cross- section method and the ellipsoid equation
procedures in the furrows 1 to 5.

Cross section-ellipsoid equation 1050.00
900.00
750.00
600.00
450.00
300.00
150.00

0.00
0.00 150.00 300.00 450.00 600.00 750.00 900.00 1050.00
Cross section -Cross- section method

Fig 4: The comparison of the wetted flow cross section values by both cross- section method and the ellipsoid
equation procedures in the furrows 1 to 5.

In 1375, Behzad performed a series of permeability tests so as to study the effect of the wetted perimeter on
the permeation of water through input – output rotating penetrometer, and the block furrows procedures with
both fixed and variable depths. Paying attention to the permeation value of all equations, the results of variant
analysis for the previewed values showed that the equations which had paid no attention to the effects of the

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wetted perimeter and the water flow cross section had the highest value of error. In contras the equations which
had paid attention to the parameters of the wetted perimeter and the water flow cross section not only had less
error value but also were more flexible in the case of corresponding to the hydraulic variations of the furrows
comparing with the previous equations. At the end it is recommended that the equations of both the wetted
perimeter and the water flow how cross section is used to determine the permeation value of water in the
furrows, because it maximizes the precision of the configurations and the efficiency.

ACKNOWLEDGMENTS

This artical was the product of a research which was financially supported by IAUS, therefore it is highly
appreciated.

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