Question

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

1. 1.8
2. 17.4
3. 20.5
4. 41.0

Answer 1

Correct Answer - Option 2 : 17.4

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