Hydraulic

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 1.852 𝐷 −4.87

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 145-150 Polyethylene lined steel 135-145 Steel (new) Steel (15 years old) 100 Butyl rubber drop tubes Rigid drop tubes 145

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

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.

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

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 = 0.555 (> than 35 sprinklers)

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 1.852 𝐷 −4.87

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

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 1.852 𝐷 −4.87

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

Hand out – problem set

Energy Balance Bernoulli Equation 𝑃 1 +0.433 𝑍 1 + 𝑉 1 2 2𝑔 = 𝑃 2 +0.433 𝑍 2 + 𝑉 2 2 2𝑔 +0.433 ℎ 𝑓1−2

At the pivot point 𝑃 𝑝 = 𝑃 𝑛 +0.433 ℎ 𝑓 + 𝑍 𝑛𝑜𝑧𝑧𝑙𝑒 +∆ 𝑍 𝑝