First slide

Fluid dynamics

Question

A large tank is partially filled with water. The tank has a small orifice at the bottom and water is coming out of the orifice. When height of water above the orifice is 2 m, rate of flow of water through the orifice is $0.5 m^{3} / s .$ when height of water above the orifice is 0.5 m rate of flow of water through the orifice will be

Moderate

A

0.5 $m^{3} / s$
B

0.125 $m^{3} / s$
C

0.25 $m^{3} / s$
D

0.4 $m^{3} / s$

Solution

(3)
Rate of flow through the orifice $Q α \sqrt{h}$
$∴ \frac{Q^{'}}{Q} = \frac{\sqrt{h^{'}}}{\sqrt{h}} \Rightarrow \frac{Q}{0.5} = \sqrt{\frac{0.5}{2}} = \frac{1}{2}$
$∴ Q^{'} = \frac{Q}{2} = \frac{0.5}{2} = 0.25 m^{3} / s .$

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