Question 8.21: 600 litres/s of water at 320 K is pumped in a 40 mm i.d. pip...
600 litres/s of water at 320 K is pumped in a 40 mm i.d. pipe through a length of 150 m in a horizontal direction and up through a vertical height of 10 m. In the pipe there is a control valve which may be taken as equivalent to 200 pipe diameters and other pipe fittings equivalent to 60 pipe diameters. Also in the line there is a heat exchanger across which there is a loss in head of 1.5 m of water. If the main pipe has a roughness of 0.0002 m, what power must be delivered to the pump if the unit is 60% efficient?
Mass flowrate of water = (600 × 10^{-6} × 1000) = 0.6 kg/s.
Cross-sectional area of pipe = (π/4)0.042 = 0.00126 m².
Velocity of water in the pipe = (600 × 10^{-6}/0.00126) = 0.476 m/s.
Re = ρud/μ = (1000 × 0.476 × 0.04)/(1 × 10^{-3}) = 1.9 × 10^{4}.
If e = 0.0002 m, e/d = 0.005, and from Fig. 3.7, R/ρu² = 0.0042.
The valve and fittings are equivalent to 260 pipe diameters which is equal to (260 × 0.04) = 10.4 m of pipe.
The equivalent length of pipe is therefore (150 + 10.4) = 160.4 m.
The head loss due to friction is:
h_{f} = 4(R/ρu² )(l/d)(u²/g) (equation 3.20)
= (4 × 0.0042)(160.4/0.04)(0.476²/9.81) = 1.56 m
∴ total head = (1.56 + 1.5 + 10) = 13.06 m.
and: power required = (13.06 × 0.6 × 9.81)/0.6 = 128 W
