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BIE 5110/
Sprinkle & Trickle Irrigation
Fall Semester, 2004
Assignment #3 (100 pts)
Set Sprinkler Lateral Design
Given:
- Sprinkler spacing, Se, of 12 m
- Lateral length of 252 m
- Riser height of 1.30 m
- Lateral will run downhill along a ground slope of 0.38%
- Nominal sprinkler discharge of 22 lpm at 2.08 atm pressure
- Nominal aluminum pipes sizes of 2, 3, 4 and 5 inches are available
- Assume a constant value of qa for each sprinkler along the lateral
- See Table 8.1 in the textbook (Keller & Bliesner) for pipe inside diameters
Required:
- Calculate the required aluminum lateral pipe size
- Round up to the nearest available pipe size
- Calculate the required lateral inlet pressure
- Calculate the location of minimum pressure in the pipe
- Calculate the pressure in the lateral pipe at the downstream end
- Calculate the percent pressure variation in the lateral pipe (%)
Solution:
If Hazen-Williams equation is used, the C value will be 130.
The number of sprinklers on the lateral is:
n e
L 252 m N 2 S 12 m
There will be 21 sprinklers per lateral. The multiple-outlet friction loss factor for 21
sprinklers is:
F 0.351 1 0.
The lateral inflow rate is:
l n a
(21)(22 lpm) Q N q 7.70 lp 60 s / min
= = = s
The elevation change along the length of the lateral is:
e
h (252 m) 0.958 m 100
The nominal sprinkler pressure is ha = 2.08 atm, or,
h a = (2.08 atm)(10.34 m/atm) =21.5 m
The allowable friction loss gradient is:
a e a
0.20h h J 100 FL
0.2(21.5 m) ( 0.958 m) 100 (0.38)(252 m)
5.49 m/100m
The minimum pipe ID is:
Sprinkler Distance Q hf head Position (m) (lps) (m) (m) 0 0 7.70 0.0000 26. 1 12 7.33 0.6262 25. 2 24 6.97 0.5721 24. 3 36 6.60 0.5203 24. 4 48 6.23 0.4707 24. 5 60 5.87 0.4234 23. 6 72 5.50 0.3785 23. 7 84 5.13 0.3358 23. 8 96 4.77 0.2955 22. 9 108 4.40 0.2576 22. 10 120 4.03 0.2221 22. 11 132 3.67 0.1891 22. 12 144 3.30 0.1585 22. 13 156 2.93 0.1304 22. 14 168 2.57 0.1048 22. 15 180 2.20 0.0819 22. 16 192 1.83 0.0615 22. 17 204 1.47 0.0439 22. 18 216 1.10 0.0290 22. 19 228 0.73 0.0170 22. 20 240 0.37 0.0080 22. 21 252 0.00 0.0022 22.
whereby the minimum head is found somewhere between 192 and 204 m from the lateral
inlet. The difference in the calculations are due to the F-factor for multiple outlets. It is also
seen that the maximum pressure head is at the lateral inlet (hmax = 26.1 m), which might
have been expected because the ground slope is very small.
Thus, the minimum pressure is at a distance of approximately 190 m from the lateral inlet,
which is nearest sprinkler number 190/12 ≈ 16.
The pressure in the pipe at the downstream end will be:
h end hl hf ( h )e
26.1 5.0 0.958 22.1 m
The head loss due to friction from sprinkler 16 to the end of the lateral is estimated as (from
Table 8.7, F = 0.46 for 21 – 16 = 5 outlets):
6 4. x end
(0.367)(5) lps J 16.42(10) (7.37 cm) 0.366 m/100m 130
− −
where the pipe length is 5(12 m) = 60 m,
( f )
x end
JFL (0.366)(0.46)(60 m) h 0.101 m 100 100
−
The friction loss from the inlet to distance x = 190 m is, then, 5.00 – 0.101 m = 4.90 m. The
elevation change from the inlet to 190 m is (-0.0038)(12)(16) = -0.730 m. Finally, the
minimum pressure head in the lateral pipe is:
h min = 26.1 − 4.90 − −( 0.730) =21.9 m
The pressure (or head) variation is:
max min
a
h h 26.1 21. P 0 h 21.
which is 20%. This just meets our design criterion.
