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Nineteenth International Water Technology Conference, IWTC19 Sharm ElSheikh, 21-23 April 2016
194
FAIRNESS WATER DISTRIBUTION AT ON- FARM IRRIGATION
DEVELOPMENT PROJECTS IN EGYPT: CASE OF VARIABLE LAND LEVELS
Hany G. Radwan
Assistant professor, Irrigation and Hydraulics Department, Faculty of Engineering, Cairo University,
Giza, Egypt. Email: [email protected]
ABSTRACT
Water is a critical component of development in Egypt. 79% of the cultivated lands in Egypt are
considered old lands which are irrigated using traditional on-Farm Distribution System (FDS). FDS
refers to a network of small channels which usually serves areas ranging from 10 to 500 feddan with a
full responsibility by the farmers. Farm ditches serving plots belonging to usually more than one
farmer are called Mesqas which branched into small distributed ditches called Marwas. FDS at old
lands in Egypt contributes with about 40 to 60% of the total irrigation system losses. So, improved
irrigation projects in Egypt came to overcome this problem through increasing the irrigation
efficiency, and to enhance the quality of irrigated water at on-farm level by converting the earth cross
section of Mesqa, and Marwa channel into low pressure pipeline system. The main objective of this
paper is to detect the required operational conditions to achieve equity water distribution between
beneficiaries to achieve full satisfaction between farmers. An accepted and allowable limits for the
concept of equity water distribution are established with allowable difference in the discharge between
opened hydrants with four limits 5%, 10%, 15%, and 20%. This paper discuss the required operational
conditions to achieve equity water distribution between hydrants in case of varied land levels. Through
this paper, the critical downward slope for achieving exactly equal water distribution regardless of the
distance between opened hydrants has been determined. Such these slopes can be achieved during the
implementation of imbedded pipelines. Also the maximum distance between opened hydrants is
determined for random land slopes (upward, downward slopes) for achieving specified difference in
the discharge. Finally, this paper provides standard graphs and tables which can be used to achieve
equity water distribution between beneficiaries at on-farm distribution system.
Keywords : Irrigation System; Improved irrigation projects; Fairness water distribution, on-farm
Irrigation.
1. INTRODUCTION Egypt is unique among the nations of the world due to its main dependence upon a single water
source. Irrigation for agriculture consumes the bulk of the available water supplies [1]. So, a lot of
improvements have been achieved at off-farm and on-farm systems in order to reduce the water losses
in the irrigation network. Off-farm system (Owned by the Ministry of Water Resources and Irrigation)
consists of irrigation network, main, secondary, and branch canals including all control structures. On
the other hand, on-farm system (owned by the farmer) consists of existing small scale earth channels
called mesqa and marwa including several single lifting pumps distributed randomly along the branch
canals as shown in Fig. 1.
Nineteenth International Water Technology Conference, IWTC19 Sharm ElSheikh, 21-23 April 2016
195
Fig. 1a: On-farm irrigation system, Fig 1b: Several single lifting pumps basins at Qena
Governorate in Egypt.
At on-farm system, the improvement was done by replacing the existing open small channels Mesqa
and Marwa (owned by the farmer) into another alternative, in addition to reducing the multiple single
lifting pumps along the branch canals into main pump station. Low pressure pipeline is the most
common used alternative between other alternatives (Improved lined mesqa, and raised concrete mesqa)
[2] as shown in Fig. 2.
Fig. 2a: Improved on-farm irrigation system
Fig 2b: Main pump station instead of multiple single
lifting pumps.
The Improved Irrigation Projects (IIP) was started at 1989 by replacing the existing earth cross section
of Mesqa by low pressure pipeline. IIP started in eleven canal commands with the aim to improve almost
400,000 feddan at on-farm level [3]. Next in 1996, Egypt started with the World Bank/KfW to tackle
improvement of about 250,000 feddan in the northern part of the Nile Delta in Beheira Governorate , and
Kafr el Sheikh Governorate [4]. The main objectives of IIP can be summarized in improving the
efficiency of water uses at on-farm level, improving the quality of irrigated water, increasing the
cultivated lands by about 3% (occupied area by earth channel) [5], increasing the crop yield from 5 to
30% due to better irrigation condition, and decreasing the irrigation time due to continuous flow [6-8].
The Egyptian Government is planning to continue the improvement works to reach a target of more than 3
million feddan by the year 2017 [3,9,10]. Due to the importance of irrigation efficiency, Integrated
Irrigation Improvement and Management Project (IIIMP) comes to overcome some problems of IIP. In
Egypt, this project is financed by the World Bank, German Development Bank KfW, the Kingdom of the
Netherlands and the Government of Egypt (GoE) [4]. The IIIMP is expected to increase irrigation
efficiency and more sustainable use of land and water by replacing marwa from its earth cross section to
low pressure pipeline as improved mesqa. The main objectives of IIIMP are to study the environmental
contamination by diesel pumps used in IIP and converting them to electrical pumps, and study
unsatisfactory operation of the irrigation system under continuous flow conditions due to no systematic
planning of water scheduling [11, 12]. This unsatisfactory operation between farmers causes unequal
water distribution between opened outlets to the extent that some farmers suffer from water shortage
during their opening. The required operational conditions to achieve fairness water distribution between
beneficiaries in case of laser leveling have been determined in previous study [13]. Allowable limits for
Nineteenth International Water Technology Conference, IWTC19 Sharm ElSheikh, 21-23 April 2016
196
the concept of fairness water distribution are established with allowable difference in the discharge
between opened hydrants with four limits 5%,10%,15%, and 20%. The proposed distance between
opened hydrants was determined to achieve the various limits of the discharge differences. Finally,
standard graphs and tables are provided and can be used to control the operating cases between opened
hydrants in improved irrigation projects in Egypt. These graphs and tables are studied for the case of laser
leveling to achieve fairness water distribution between beneficiaries. The main objective of this paper is
how to achieve fairness water distribution between beneficiaries in the general case of varied ground
levels between opened hydrants.
2. DESIGN CONCEPT OF IMPROVED ON-FARM IRRIGATION SYSTEM The main components of Improved Irrigation Project in On- Farm System consists of three main
components as shown in Fig. 3. First component is improved mesqa or branch mesqa with low pressure
pipeline (IIP project), and the second is improved marwa with low pressure pipeline (IIIMP project). The
last component is pump station which takes its water from the branch canal through intake structure and
pump sump then injects its water directly to improved pipeline system of mesqa and marwa through
existing hydrants. The design of improved irrigation system is consisting of detecting the suitable
diameters for low pressure pipeline network for mesqa and marwa, and detecting the required pump
specifications to ensure extracting the designed water discharge from the far hydrant on the far marwa
pipeline. The design started by detecting the mesqa capacity from (1) considering the served area is
cultivated by Rice.
𝑄 =4200𝐴𝑊𝐷
𝑇, (1)
Where 𝑄,𝐴,𝑊𝐷 ,𝑎𝑛𝑑 𝑇 are mesqa capacity (l/sec.), total served area (feddan), water duty requirement
(mm/d), and working time per day (seconds); respectively. The calculated discharge is approximated to
multiples of 20 𝑙/𝑠 or 30 𝑙/𝑠 according to the designed hydrant discharge to detect the number of
opened hydrants at the same time. Then the suitable pipeline diameter (bearing head pressure of
4 𝑏𝑎𝑟𝑠) is selected from the available commercial diameters. The maximum design velocity is 1.5 𝑚/𝑠
according to the last design criteria to decrease the total project cost. The suitable pump is selected to
overcome the total head losses through the critical operating path. Head losses are divided into losses at
hydrants and losses through reaches. Total hydraulic head at hydrants is calculated from the following
Equation [14]:-
𝐻𝑇 = 𝐿𝐿 + 𝐻𝑅𝑖𝑠𝑒𝑟 + 𝑂𝑃 + 𝐶𝑄2 (2)
Where 𝐻𝑇 , 𝐿𝐿 ,𝐻𝑅𝑖𝑠𝑒𝑟 ,𝑂𝑃 ,𝑄 are total hydraulic head at hydrant (𝑚), land level at hydrant, height of the
riser above land level, required outlet pressure at hydrant (𝑚), and actual extracting discharge (𝑚3/𝑠𝑒𝑐.); respectively. Parameter 𝐶 is depending on the friction coefficients, and it can be calculated from
the following equation 𝐶 = 𝐾𝑇/(2𝑔 𝐴𝑅𝑖𝑠𝑒𝑟2 ). Where 𝐾𝑇 is the summation of total friction coefficients
at hydrant location (taken 4). Parameters 𝑔 ,𝑎𝑛𝑑 𝐴𝑅𝑖𝑠𝑒𝑟 are the gravity acceleration (9.8 𝑚/ sec2 ), and cross section area of the riser pipe (𝑚2); respectively. Head losses through reaches are divided into
minor and main losses, for more details about minor losses see [15]. Main friction losses through
improved mesqa or marwa pipelines (𝑓 ) are calculated using Hazen-William equation:-
𝑓 = 3.59 𝑄
𝐶𝐻
1.852
𝐿
𝐷4.87 (3)
Nineteenth International Water Technology Conference, IWTC19 Sharm ElSheikh, 21-23 April 2016
197
Fig. 3: Main components of Improved Irrigation system at on-farm level.
Where 𝐻𝑓 ,𝐶𝐻,𝐷, 𝐿 are friction losses in pipeline (𝑚), coefficient taken 150 for 𝑃𝑉𝐶 pipe, diameter
of pipeline reach (𝑚) , and length of pipeline reach (𝑚); respectively. The previous design steps have
been programmed using Matlab software [16,17]. There was concern about the high cost of the IIP
improvements (civil works and associated equipment), which has increased from about 2,300 𝐿𝐸/𝑓𝑒𝑑
at the time of mid-term review in May 2000 to about 5,600 𝐿𝐸/𝑓𝑒𝑑 in 2004 [18]. To repay the costs
of improvements, farmers would have to make annual payments per feddan per year over several years
ranges from 10 to 20 year. So any reduction in the total improved system can relief something from
the farmer’s problem [1]. The new developed program has helped in discussing the available methods
to reduce the total improvement's costs [19,20].
3. THE REQUIRED CONDITIONS FOR EQUITABLE WATER DISTRIBUTION BETWEEN
OPENED HYDRANTS. This section deals with the conditions that should be achieved at operation scenarios to ensure
equity water distribution between opened hydrants. The total hydraulic head (𝐻𝑇) along pipeline
system between two hydrants (𝑖 ,𝑎𝑛𝑑 𝑗) is governed by the following equations (neglecting the
difference in the velocity head between the two hydrants), see Fig. (4).
𝐻𝑇𝑖 = 𝐿𝐿𝑖 + 𝐻𝑟𝑖𝑠𝑒𝑟 𝑖 + 𝑂𝑃𝑖 + 𝐶𝑄𝑖2 (4𝑎)
𝐻𝑇𝑗 = 𝐿𝐿𝑗 + 𝐻𝑟𝑖𝑠𝑒𝑟𝑗 + 𝑂𝑃𝑗 + 𝐶𝑄𝑗2 4𝑏
𝐻𝑇𝑗 = 𝐻𝑇𝑖 − 𝑙𝑖𝑗 (4𝑐)
Nineteenth International Water Technology Conference, IWTC19 Sharm ElSheikh, 21-23 April 2016
198
Fig. 4: Illustrated figure for improved mesqa pipeline with earth marwa (IIP).
Where 𝑙𝑖𝑗 is the friction losses between hydrants (𝑖 ,𝑎𝑛𝑑 𝑗) .The previous equations can be rewritten to
get the following relationship between the discharge of any two hydrants.
)5()( 22 ahLLOOQQCijlLiLjPiPjji
Where:
)5(59.3
87.4
852.1
bD
L
CH
Qh
ij
ijjlij
)5(,,,)( ,22 cDLQLOfQQC ijijjLPji
Where Lij , and Dij are distance and diameter between opened hydrants. From (5a), there are several
scenarios that can represent the actual field situation. According to each actual scenario, the required
conditions that should be achieved to ensure fairness water distribution between opened hydrants can
be determined. The required operational conditions to achieve fairness water distribution between
beneficiaries in case of laser leveling, and constant outlet pressure (OP) have been determined [13].
This paper concerns with the case of constant outlet pressure (OP) for opened hydrants i & j (OPi =Opj)
and variable land levels. So Eq.(5a) can be rewritten as follows:
𝐶 𝑄𝑖2 − 𝑄𝑗
2 = 𝐿𝑖𝑗 𝑆 + 3.59𝑄𝑗
𝐶𝐻
1.852
𝐿𝑖𝑗
𝐷𝑖𝑗4.87 (6)
The friction term is always a positive value. But, the term of the difference between land levels
(𝐿𝑖𝑗 ∗ 𝑆 ) can be positive and negative according to the slope direction (S) (upward or downward) as
shown in Fig. 5. For upward slope, the right hand side of (6) is always positive, which means that the
nearest opened outlet 𝑄𝑖 is always extracts flow larger than the far opened outlet 𝑄𝑗 . For downward
slope, the relationship between the flow of opened hydrants depends on the net result sign of the right
hand side of (6).
(a)
Nineteenth International Water Technology Conference, IWTC19 Sharm ElSheikh, 21-23 April 2016
199
(b)
Fig.5. Illustrated figure for (a) Upward slope, and b) Downward slope.
3.1 Upward Slope For upward slope, the expected discharge for the nearest opened hydrant will be always larger
than the discharge of the far one. Due to the larger number of unknowns in (6), the discharge for the
far hydrant will be assumed with two default values of designed discharge of 20 𝑙/𝑠𝑒𝑐., and 30 𝑙/𝑠𝑒𝑐. Then the expected discharge at the near opened hydrant will be calculated taking into consideration
the effect of other different variables such as distance between opened hydrants, upward slope,
diameter of the reach between the two opened hydrants. Table 1 illustrates the accepted distance along
mesqa pipeline between selected opened hydrants (Marwas) for different upward land slopes to
achieve certain differences in the discharges between opened hydrants ∆𝑄%. Four different limits for
∆𝑄% are assumed and the final decision is left to the decision maker. Table 1 can be used to select the
hydrants (Marwas) that should be opened at the same time depending on the maximum accepted
distance between opened hydrants illustrated in the table. The selection of opened hydrants (Marwas)
depends also on the actual land slope along mesqa pipeline, and the required difference in the
extracted discharge between opened hydrants.
Table 1: Maximum accepted distance between selected opened hydrants ( ijL ) in meter for various
percentages of the difference in the flows (∆𝑸%)- Upward slope.
S %
∆𝑸%
𝑫𝒊𝒋(𝒎𝒎)
𝑄𝑗 = 20 𝑙/𝑠𝑒𝑐 𝑄𝑗 = 30 𝑙/𝑠𝑒𝑐
200 225 250 280 225 250 280 315
0.0
5 11.72 20.76 34.66 60.18 9.06 15.07 26.19 46.46
10
25.39 45.04 75.24
130.6
7 19.60 32.75 56.84
100.8
6
15
41.59 73.77
123.2
1
213.9
5 32.12 53.60 93.07
165.1
4
20
60.88
108.0
3
180.4
4
313.3
4 47.01 78.49
136.2
9
241.8
5
0.05
5 9.53 14.76 20.67 27.67 7.63 11.45 16.86 23.41
10 20.68 32.07 44.86 60.03 16.49 24.80 36.56 50.81
15 33.86 52.50 73.46 98.31 26.97 40.62 59.84 83.19
20
49.55 76.87
107.5
8
143.9
7 39.45 59.47 87.65
121.8
3
0.1 5 8.08 11.49 14.72 17.97 6.58 9.22 12.44 15.65
10 17.47 24.87 31.98 38.98 14.20 19.96 26.96 33.97
Nineteenth International Water Technology Conference, IWTC19 Sharm ElSheikh, 21-23 April 2016
200
15 28.56 40.74 52.34 63.82 23.25 32.72 44.11 55.60
20 41.81 59.65 76.64 93.46 34.01 47.90 64.58 81.43
0.15
5 7.00 9.38 11.46 13.32 5.77 7.752 9.83 11.78
10 15.06 20.33 24.82 28.87 12.52 16.75 21.35 25.51
15 24.67 33.31 40.64 47.26 20.40 27.40 34.91 41.77
20 36.14 48.75 59.51 69.19 29.85 40.06 51.15 61.15
0.2
5 6.16 7.97 9.36 10.56 5.12 6.67 8.18 9.42
10 13.32 17.23 20.29 22.94 11.15 14.39 17.69 20.42
15 21.77 28.17 33.24 37.53 18.24 23.56 28.92 33.45
20 31.85 41.22 48.66 54.91 26.66 34.46 42.35 48.97
0.25
5 5.48 6.91 7.95 8.78 < 5.0 5.84 7.00 7.90
10 11.92 14.88 17.20 19.02 10.01 12.66 15.05 17.07
15 19.42 24.38 28.12 31.11 16.46 20.65 24.66 27.91
20 28.46 35.70 41.15 45.54 24.05 30.21 36.12 40.83
0.3
5 < 5.0 6.09 6.90 7.53 < 5.0 5.18 6.09 6.78
10 10.74 13.18 14.86 16.25 9.18 11.27 13.18 14.61
15 17.60 21.53 24.35 26.59 14.94 18.42 21.53 23.93
20 25.70 31.50 35.64 38.91 21.94 26.95 31.51 34.99
0.35
5 < 5.0 5.43 6.08 6.58 < 5.0 < 5.0 5.38 5.93
10 9.78 11.80 13.17 14.18 8.47 10.11 11.70 12.84
15 16.04 19.25 21.50 23.22 13.78 16.62 19.09 20.95
20 23.47 28.19 31.46 33.96 20.08 24.27 27.95 30.65
0.4
5 < 5.0 < 5.0 5.42 5.82 < 5.0 < 5.0 < 5.0 5.24
10 9.04 10.65 11.79 12.62 7.85 9.25 10.47 11.42
15 14.71 17.45 19.23 20.57 12.78 15.07 17.17 18.65
20 21.59 25.47 28.16 30.10 18.63 22.13 25.05 27.29
3.2 Downward Slope
For downward slope (negative slope), the relationship between the extracted discharge of near
and far hydrants in the network depends on the summation of the two parts on the right hand side in
(6) as follows:-
)7(
)(..:3
)(..:2
)(0.0..:1
)7(59.3
*.. 87.4
852.1852.1
b
QQveSHRSSCase
QQveSHRSSCase
QQSHRSSCase
aD
LQ
CHSLSHR
jic
jic
jic
ij
ijjij
From the previous equations, there are three different operating cases that can be happened with
different characteristics in the system as shown in Fig.6. These cases will be discussed in details in the
following sections.
Nineteenth International Water Technology Conference, IWTC19 Sharm ElSheikh, 21-23 April 2016
201
Fig.6: Illustrated figure for the three cases of downward slope.
Case (1): Calculation of the critical downward slope for equal discharges.
In this case, the critical downward slope that is needed to achieve exactly equal water
distribution between opened hydrants will be determined. The critical downward slope for exactly
equal water distribution (𝑄𝑖 = 𝑄𝑗 = 𝑄) can be determined from (7a) as follows:
)8(1
*59.3
87.4
852.1
ijc DCH
QS
Where 𝑆𝑐 ,𝑄,𝐷𝑖𝑗 are critical downward slope for equal water distribution between opened hydrants,
designed discharge for the near and far hydrant (𝑄𝑖 = 𝑄𝑗 ) in (𝑚3/sec), and reach's diameter between
opened hydrant (m); respectively. The critical slopes illustrated in Table (2) can be achieved by two
methods; first method by changing the land level and keep imbedded pipelines horizontally, and
second method by changing the slope of the imbedded pipelines and keep land level horizontally as
shown in the Fig.7. From the practical point of view, second method is preferred and applicable rather
than first one.
Table 2: Critical downward slope (m/m) for exactly equal water distribution between opened hydrants.
Designed hydrant
discharge (𝒍/𝒔𝒆𝒄)
Reach diameter ijD (mm)
200 225 250 280 315
20 0.2188 0.1233 0.0738 0.0425 0.0240
30 0.4630 0.2612 0.156 0.090 0.051
40 0.7900 0.4450 0.27 0.150 0.087
50 1.1940 0.6730 0.4 0.232 0.131
Fig.7: Achieving the critical slope by inclined imbedded pipelines.
Nineteenth International Water Technology Conference, IWTC19 Sharm ElSheikh, 21-23 April 2016
202
Case (2): When cSS0.0
As the land slope decreases from the horizontal situation to the critical downward slope (Sc), as the
difference in the discharge between nearest opened hydrant and far opened hydrant disappeared
(∆𝑄 = 𝑄𝑖 − 𝑄𝑗 ) until reaching zero at the critical slope (Sc). By assuming constant discharge for the
nearest opened hydrant, the discharge for far opened outlet be determined from (6) as follows:
)9(059.3
* 87.4
852.1852.122
cij
ijjijij SS
D
LQ
CHSLQCQC
Due to non-linearity of (9) in calculating(𝑄𝑗 ),so Newton Raphson method is used for solving the
previous equation as follows [21]:
)10()(
)(
)10(852.12)(
:
)10(0.0)(
)10(0*,59.3
)(\
)(
)()1(
852.0
)()()(\
852.12
287.4
852.1
dQf
QfQQ
cQyQCQf
kiterationFor
bWQyQCQf
aSSwhereSLQCWD
L
CHyLet
kj
kj
kjkj
kjkjkj
jjj
cijiij
ij
In addition to the non-linearity of (10) in determining the flow for far opened hydrant, also it depends
on several variables. These variables are the designed hydrant discharge for nearest outlet (𝑄𝑖), slope
(𝑆), distance between opened hydrants (𝐿𝑖𝑗 ), and reach's diameter between opened hydrants (𝐷𝑖𝑗 ).
Figure 8 illustrates an example for the variation of the discharge for the far opened hydrant as a
function of 𝑆 and 𝐿𝑖𝑗 for different 𝑄𝑖 and 𝐷𝑖𝑗 . Table 3 illustrates the maximum distance between
opened hydrants to achieve accepted difference in the flow (∆𝑄).
Fig. 8: Relationship between the discharge of far opened hydrant and the distance between opened
hydrants for downward slopes cSS0.0
Nineteenth International Water Technology Conference, IWTC19 Sharm ElSheikh, 21-23 April 2016
203
Table 3: Maximum distance between selected opened hydrants (𝑳𝒊𝒋) in meter for various percentages
of the difference in the flows- Downward slope cSS0.0
Slo
pe
%
∆𝑸%
𝑫𝒊𝒋 (𝒎𝒎)
𝑄𝑗 = 20 𝑙/𝑠𝑒𝑐. 𝑄𝑗 = 30 𝑙/𝑠𝑒𝑐
200 225 250 280 225 250 280 315
-0.05
5 15.51 37.18 134.87 696.77 9.17 15.51 27.68 9.17
10 34.61 87.48 419.63 >1000 19.75 33.54 60.00 19.75
15 58.72 159.30 >1000 >1000 32.18 54.68 98.22 32.18
20 89.97 270.12 >1000 >1000 46.84 79.79 143.94 46.84
-0.1
5 23.36 190.59 126.26 45.37 15.48 50.40 >1000 50.30
10 56.25 >1000 415.99 100.85 36.10 144.64 >1000 116.12
15 106.11 >1000 >1000 169.86 64.87 384.73 >1000 205.34
20 190.56 >1000 >1000 257.64 107.91 >1000 >1000 332.47
-0.15
5 47.18 161.16 35.06 23.46 24.32 >1000 43.50 23.69
10 149.93 >1000 80.25 50.07 63.88 >1000 107.66 51.23
15 551.11 >1000 140.36 80.41 139.72 >1000 211.02 83.51
20 >1000 >1000 223.75 115.19 344.46 >1000 403.74 121.72
-0.2
5 >1000 37.33 20.36 15.82 56.67 77.60 22.07 15.49
10 >1000 93.96 44.42 33.31 277.80 341.20 49.51 32.87
15 >1000 189.47 73.15 52.69 >1000 >1000 84.43 52.42
20 >1000 382.98 107.89 74.18 >1000 >1000 130.12 74.49
-0.25
5 230.55 21.11 14.35 11.95 >1000 28.40 14.77 11.52
10 >1000 48.33 30.71 24.95 >1000 72.26 32.17 24.20
15 >1000 84.56 49.46 39.17 >1000 148.40 52.79 38.20
20 >1000 134.93 71.09 54.70 >1000 311.63 77.58 53.68
-0.3
5 40.09 14.71 11.09 9.58 159.02 17.40 11.13 9.16
10 127.57 32.54 23.48 19.94 >1000 40.40 23.82 19.15
15 460.46 54.43 37.38 31.18 >1000 72.26 38.40 30.04
20 >1000 81.91 53.02 43.34 >1000 118.82 55.25 41.96
-0.35
5 22.00 11.31 9.03 8.02 34.91 12.55 8.92 7.63
10 55.89 24.51 19.00 16.63 119.52 28.08 18.91 15.84
15 114.67 40.12 30.01 25.90 606.87 47.76 30.16 24.76
20 240.36 58.80 42.27 35.88 >1000 73.42 42.93 34.43
-0.4
5 15.12 9.18 7.64 6.89 19.62 9.78 7.46 6.52
10 35.79 19.67 15.96 14.25 51.91 21.51 15.68 13.52
15 65.50 31.80 25.08 22.16 114.25 35.66 24.84 21.07
20 111.62 45.86 35.13 30.61 283.68 53.13 35.07 29.20
Case (3): When cSS
As land slope decreases than the critical slope, the discharge of far opened hydrant will be larger than
the same of the nearest opened hydrant as in the following equation.
)11(,59.3
87.4
852.122 SSwhereLS
D
L
CH
QQCQC ij
ij
ijjji
Figure 9 illustrates an example for the variation of the discharge for the nearest opened hydrant with
respect to other parameters such as land slope, distance and diameter of the reach between opened
hydrants. Table 4 illustrates the accepted distance between opened hydrants for different four values of
discharge differences (∆𝑄). As seen from Fig.9, the discharge of the nearest opened hydrant will be
dissipated at certain conditions which can be calculated from the following equation:
Nineteenth International Water Technology Conference, IWTC19 Sharm ElSheikh, 21-23 April 2016
204
)12(159.3
87.4
852.1
2
ij
j
jij
DCH
QS
QCL
Fig. 9: Relationship between the discharge of far opened hydrant and the distance between opened hydrants for
downward slopes cSS0.0
Table 4: Maximum accepted distance between selected opened hydrants (𝑳𝒊𝒋) in meter for various
percentages of the difference in the flows - Downward slope cSS
Slo
pe
%
∆𝑸%
𝑫𝒊𝒋(𝒎𝒎)
𝑄𝑖 = 20 𝑙/𝑠𝑒𝑐 𝑄𝑖 = 30 𝑙/𝑠𝑒𝑐
200 225 250 280 225 250 280 315
-0.05
5 15.16 34.90 107.46 307.69 11.19 22.18 58.85 >1000
10 32.93 75.78 233.31 599.60 24.25 48.12 127.78 >1000
15 53.89 124.08 382.02 875.74 39.68 78.78 209.22 >1000
20 78.91 181.72 559.47 >1000 58.13 115.36 306.41 >1000
-0.1
5 21.55 109.84 88.10 40.14 14.63 41.81 213.84 43.18
10 46.77 238.50 171.68 78.22 31.77 90.77 416.71 84.15
15 76.56 390.52 250.75 114.24 52.00 148.63 608.61 122.91
20 112.12 571.92 325.30 148.21 76.13 217.67 789.55 159.45
-0.15
5 37.19 86.39 30.29 21.46 21.21 369.32 35.48 21.42
10 80.74 168.35 59.03 41.83 46.02 801.90 69.15 41.76
15 132.20 245.89 86.21 61.10 75.34 >1000 100.99 60.99
20 193.60 318.99 111.84 79.27 110.33 >1000 131.01 79.12
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-0.2
5 136.15 30.09 18.28 14.65 38.50 48.77 19.34 14.25
10 295.61 58.63 35.64 28.55 83.59 95.04 37.69 27.76
15 484.04 85.63 52.04 41.70 136.86 138.80 55.06 40.56
20 708.88 111.08 67.52 54.10 200.43 180.07 71.43 52.61
-0.25
5 73.94 18.21 13.09 11.11 209.86 22.71 13.29 10.67
10 144.09 35.49 25.52 21.66 455.65 44.27 25.91 20.79
15 210.45 51.83 37.27 31.64 746.09 64.67 37.84 30.38
20 273.02 67.24 48.35 41.06 >1000 83.89 49.09 39.41
-0.3
5 28.41 13.05 10.20 8.95 54.87 14.81 10.13 8.52
10 55.38 25.45 19.88 17.45 106.92 28.85 19.74 16.61
15 80.88 37.16 29.03 25.50 156.16 42.14 28.82 24.28
20 104.94 48.21 37.65 33.07 202.59 54.68 37.39 31.49
-0.35
5 17.58 10.18 8.34 7.48 23.96 10.98 8.16 7.08
10 34.27 19.84 16.27 14.62 46.69 21.40 15.93 13.83
15 50.06 28.96 23.77 21.34 68.19 31.25 23.27 20.23
20 64.95 37.57 30.84 27.68 88.47 40.56 30.21 26.22
-0.4
5 12.72 8.32 7.05 6.43 15.33 8.72 6.84 6.07
10 24.82 16.24 13.77 12.55 29.87 16.99 13.35 11.84
15 36.24 23.72 20.14 18.35 43.62 24.85 19.52 17.30
20 47.01 30.78 26.10 23.81 56.59 32.21 25.33 22.45
4. CONCLUSIONS
This paper discussed the required operational conditions for opened hydrants on the improved on-
farm irrigation projects in Egypt to achieve fairness water distribution between beneficiaries. An
accepted and allowable limits for the concept of fairness water distribution have been established.Four
allowable limits for the difference in the discharge between opened hydrants with 5%, 10%, 15%, and
20% have been introduced. The required conditions for achieving each limit of the above limits were
developed, and the final decision for the used limit is left to the decision makers.This paper discussed
the variation of land levels along improved mesqa pipeline either for downword and upword slopes
through:-
Determining the maximum distance between opened hydrants for achieving various accepted
difference in the discharge for upward slope.
Determining the critical downward slope for exactlly equal water distribution between opend
hydrants regardless of the distance between opened hydrants. It is suggested that these slopes can
be achieved during the implementation of the imbeded pipeline network and not on the land level
(if available).
Determinig the accepted distance between opened hydrants for other downward slopes around
the critical downward slope for achieving certain difference in the discharge between opened
hydrants.
So, finally this paper presented guideline tables for the operational scenarios between hydrants at on-
farm irrigation development projects in Egypt in order to achieve fairness water distribution.
Nineteenth International Water Technology Conference, IWTC19 Sharm ElSheikh, 21-23 April 2016
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