Water at 25°C is flowing through a 1.0 km long GI pipe of 200 mm
Water at 25°C is flowing through a 1.0 km long GI pipe of 200 mm diameter at the rate of 0.07 m3/s. If value of Darcy friction factor for this pipe is 0.02 and density of water is 1000 kg/m3, the pumping power (in kW) required to maintain the flow is
A. 1.8
B. 17.4
C. 20.5
D. 41.0
Please scroll down to see the correct answer and solution guide.
Right Answer is: B
SOLUTION
Concept:
The pumping power fow water flowing required to pump is , P = ρgQH
and Head is, \(H=\frac{fLQ^2}{12D^5}\)
where, ρ = density of liquid, Q = discharge through pipe, H = required head, f = Darcy friction factor
Calculation:
Given:
L = 1 km = 1000 m, D = 200 mm = 0.2 m, Q = 0.07 m3/s, f = 0.02, ρ = 1000 kg/m3
\(∴ H=\frac{0.02~\times~1000~\times~0.07^2}{12~\times~0.2^5}\)
∴ H = 25.52 m
Pumping power = ρgQH
∴ 1000 × 9.81 × 0.07 × 25.52
∴ 17524.58 W = 17.52 kW