Water at 20◦C is pumped through 1000 ft of 0.425 ft diameter pipe at a volumetric flowrate of 1 ft3/s through a cast iron pipe that connects to connects two reservoirs. The elevation difference between the two reserviors is 120 ft. Find the pumping power delivered to the water. The minor losses only include a wide-open globe valve with KL = 10. Use a density of 1.94 slug/ft3 and a dynamic viscosity of 2.32 × 10−5 lbf·s/ft2 .

7582.9 ft.Ibf/s

Explanation:

Given

L=1000ft,d=0.425ft,Q=1ft^3/s,z2-z1=120ft,Kl=10,d=1.94slug/ft^3, vicosity u= 2.32*10-5ibf.s/ft2

Reynold Re= Density*diameter*velocity/ viscosity

But Q=AV

V= 4/3.142*0.425=2.99ft/s

Re= 1.94*0.425*2.99/2.32*10-5)=106455.3

Friction factor=1/√f=-1.8log[((e/d)/3.7)^1.11+6.9/Re] is very neglible hence equals 0

Pump head Hp= z2-z1+v^2/2g[FL/f+KL]

Hp=120+2.99^2/2*32.2(0+10)=121.4ft

Pump power = density*g*Q*hp

1.94*32.2*121.4=7582.9 ft.Ibf/s

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