Water at 25°C is flowing through a 1 Km long pipe of 200 mm diameter at the rate of 0.07 m³/s. If the 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 

Concept:

Head Loss \({h_f} = \frac{{fl{V^2}}}{{2gD}} = \frac{{fL}}{{2gD}}{\left( {\frac{Q}{A}} \right)^2}\)

Calculation:

Given:

f = 0.02, L = 1000 kg/m³, Q = 0.07 m³/s, D = 200 mm.

\(\Rightarrow {h_f} = \frac{{0.02 \times 1000 \times {{\left( {0.07} \right)}^2}}}{{2 \times 9.81 \times 0.2 \times {{\left[ {\frac{\pi }{4}{{\left( {0.2} \right)}^2}} \right]}^2}}} = 25.30\ m\)

Then power P = ρgQ × h_f = 1000 × 9.81 × 0.07 × 25.30

P = 17.37 kW