Correct Answer - Option 3 : 848.2
Concept:
Darcy’s friction factor is given by:
\({h_f} = \frac{{fl{v^2}}}{{2gd}}\)
where
hf = head loss, f = friction factor, l = length, v = velocity, d = diameter
Power required can be calculated by:
P = ρgQh
where
ρ = density, Q = discharge ⇒ AV
Calculation:
Given:
D = 100 mm ⇒ 0.1 m, L = 100 m, V = 2 m/s, ρ = 900 kg/m3, f = 0.03
\(Q\; = \frac{\pi }{{\;4}}{\left( {0.1} \right)^2} \times 2 \Rightarrow 0.0157\;{m^3}/s\)
Now
\({h_f} = \frac{{fl{v^2}}}{{2gd}}\)
\({h_f} = \frac{{0.03 \times 100 \times {2^2}}}{{2 \times 10 \times 0.1}}\)
hf = 6 m
Power is:
P = ρgQh
P = 900 × 10 × 0.0157 × 6
P = 847.5 W