Hydraulic

Friction lossHazen-Williams Equation

Q=Flow rate (gpm)

D=Pipe diameter (in)

L= Pivot length (ft)

hf =Friction loss (ft)

h 𝑓 =10.47𝐿(𝑄𝐶 )1.852

𝐷− 4.87

C factorPipe 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 130

Epoxy-coated steel 145-150

Polyethylene lined steel 135-145

Steel (new) 130

Steel (15 years old) 100

Butyl rubber drop tubes 150

Rigid drop tubes 145

Multiple outlet factorChristiansen'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 factorN= number of sprinklersM= 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 rectangular system eachsprinkler applies water to an Identically sized Area (A)

In a circular system the areaincreases as the radius increasesHence, each sprinkler applies water to a differently sized Area (A)

1 432

A1 = A2 = A3 = A4 A1 < A2 < A3 < A4

1 2 43

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 lossHazen-Williams Equation

Q=Flow rate (gpm)

D=Pipe diameter (in)

L= Pivot length (ft)

F = Friction Reduction factor

hf =Friction loss (ft)

h 𝑓 =10.47𝐹𝐿(𝑄𝐶 )1.852

𝐷− 4.87

Hydraulic lengthNo 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)

𝐿h=𝐿√𝑄𝑏+𝑄𝑔

𝑄𝑏

Friction lossHazen-Williams Equation

Q=Flow rate (gpm)

D=Pipe diameter (in)

Lh= Pivot length (ft)

F = Friction Reduction factor

hf =Friction loss (ft)

h 𝑓 =10.47 h𝐹𝐿 (𝑄𝐶 )1.852

𝐷− 4.87

© Irrigation Association

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

Hand out – problem set

Energy BalanceBernoulli

Equation

=

At the pivot point

𝑃𝑝=𝑃𝑛+0.433 (h 𝑓+𝑍𝑛𝑜𝑧𝑧𝑙𝑒+∆ 𝑍𝑝 )