First slide

Fluid dynamics

Question

A pump is delivering water at a rate of 0.05 $m^{3} / s$ through a pipe of cross-sectional area $10 c m^{2}$ . Ignoring all losses, find the power of the pump.

Moderate

A

54.5 KW
B

62.5 KW
C

36 KW
D

10 KW

Solution

Velocity of water in the pipe, $V = \frac{Q}{A}$
Mass flow rate of water m = $ρ$ Q
$∴$ Power of pump $= \frac{1}{2} m V^{2} = \frac{1}{2} (ρ Q) {(\frac{Q}{A})}^{2}$
$= \frac{ρ Q^{3}}{2 A^{2}} = \frac{10^{3} \times {(0.5)}^{3}}{2 \times {(10 \times 10^{- 4})}^{2}} W = 62.5 K W$

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