Force Main Operating Point and Surge After Valve Closure
A 600 m long, 400 mm inside diameter HDPE force main conveys 120 L/s from a wet well to a treatment plant. Static lift is 18 m. Minor-loss coefficient sum K=4.5; Hazen-Williams C=140. The pump curve is approximately H_p = 26 - 0.00045 Q^2, with H in m and Q in L/s. The discharge check valve closes in 4 s during a power failure; pressure-wave speed is 350 m/s. The pipe is rated PN 10 (100 m head), and the low point is at the pump discharge. The operator wants to know whether the existing pump will operate near design flow and whether the check-valve closure needs surge protection.
1. Compute velocity, friction and minor head losses at 120 L/s, the system head, and estimate the operating flow.
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At Q=0.12 m3/s: A=pi(0.4)^2/4=0.1257 m2; V=0.12/0.1257=0.955 m/s. Hazen-Williams hf=10.67 L Q^1.852/(C^1.852 D^4.87). With L=600 m, C=140, D=0.4 m, hf is about 1.16 m. Minor loss=K V^2/(2g)=4.5(0.955)^2/(19.62)=0.21 m. System head at 120 L/s=18+1.16+0.21=19.37 m. Pump curve at 120 L/s: H=26-0.00045(120)^2=19.52 m. Pump head is slightly above system head, so the operating point is just above 120 L/s, about 121 L/s. The pump is near design flow; runout is not a concern at this point.
2. Evaluate the surge from a 4 s check-valve closure. Is the PN 10 rating sufficient, and what surge protection would you recommend?
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2L/a=2(600)/350=3.43 s; the 4 s closure is only slightly slower than the pipe period. Joukowsky instantaneous rise=aV/g=350(0.955)/9.81=34.1 m. For slow closure, Michaud gives delta-H about 2LV/(gT)=2(600)(0.955)/(9.81*4)=29.2 m. Initial pressure at the pump discharge is about 19 m; a 29 m downsurge would drive it to about -10 m gauge, causing cavitation and possible column separation, even though the positive surge (about 48 m) is below the PN 10 rating. The check valve also may slam near the end of closure. Recommend a method-of-characteristics surge analysis, an air vessel or surge tank, controlled valve closure, and air/vacuum valves; do not rely on the pipe pressure rating alone.