1. Hydraulic

2. Friction loss Hazen-Williams Equation Q=Flow rate (gpm)
D=Pipe diameter (in)
L= Pivot length (ft)
hf =Friction loss (ft)
ℎ𝑓=10.47 𝐿 𝑄 𝐶 𝐷 −4.87

3. C factor Pipe Material C Plastic (4-in diameter or larger) 150
Plastic (2- to 3-in diameter)
140
Aluminum (with couplers every 30 ft)
130
Galvanized steel
Epoxy-coated steel
Polyethylene lined steel
Steel (new)
Steel (15 years old)
100
Butyl rubber drop tubes
Rigid drop tubes
145

5. Multiple outlet factor
Christiansen's equation for computing the reduction coefficient (F) for pipes with multiple, equally spaced outlets where the first outlet is Sl from the mainline is:
F = Reduction factor
N= number of sprinklers
M= exponent depends on which friction equation is used

6. Caveats For pipes that have no flow past the last outlet (sprinkler)
Cannot be directly applied to the estimation of friction losses only partway down the lateral pipe.
Assumes that each outlet has a constant discharge,
Equations are for use with laterals having nearly constant discharge per outlet, such as for hand lines, wheel-lines, solid set (fixed), and linear-move systems.
The value of F approaches 0.36 when N > 35, which is often the case with sprinkler laterals.

7. Applying Irrigation Water in Circles (vs. squares)
Why it’s a little trickier?
In a circular system the area
increases as the radius increases
Hence, each sprinkler applies
water to a differently sized Area (A)
In a rectangular system each
sprinkler applies water to an
Identically sized Area (A) 1 2 4 3
Explain how area considerations affect nozzle sizing, spacing and possibly throw diameter 1 2 3 4
A1 = A2 = A3 = A4
A1 < A2 < A3 < A4

8. Center pivot reduction factor
Outlet discharge varies with distance from the center pivot
Flow rate in the pipe decreases more slowly at the upstream end
Average velocity along the length of the lateral is higher.
F value is higher on a center-pivot lateral than on laterals for other types of sprinkler systems
For center pivot F = (> than 35 sprinklers)

9. Friction loss Hazen-Williams Equation Q=Flow rate (gpm)
D=Pipe diameter (in)
L= Pivot length (ft)
F = Friction Reduction factor
hf =Friction loss (ft)
ℎ𝑓=10.47𝐹𝐿 𝑄 𝐶 𝐷 −4.87

10. Hydraulic length No flow past the last outlet End gun?
Lh = Hydraulic length (ft)
L = Base pivot length (ft)
Qb = base pivot flow rate (gpm)
Qg = end gun flow rate (gpm)
𝐿 ℎ =𝐿 𝑄 𝑏 + 𝑄 𝑔 𝑄 𝑏

11. Friction loss Hazen-Williams Equation Q=Flow rate (gpm)
D=Pipe diameter (in)
Lh= Pivot length (ft)
F = Friction Reduction factor
hf =Friction loss (ft)
ℎ𝑓=10.47𝐹𝐿ℎ 𝑄 𝐶 𝐷 −4.87

12. 1,000 gpm total – 125 gpm end gun – sprinklers at 20’ 8” (approx) pipe
© Irrigation Association

13. Hand out – problem set

14. Energy Balance Bernoulli Equation
𝑃 𝑍 𝑉 𝑔 = 𝑃 𝑍 𝑉 𝑔 ℎ 𝑓1−2

15. At the pivot point
𝑃 𝑝 = 𝑃 𝑛 ℎ 𝑓 + 𝑍 𝑛𝑜𝑧𝑧𝑙𝑒 +∆ 𝑍 𝑝