First slide

Fluid dynamics

Question

A container of large cross-sectional area has a small orifice at its bottom. The container is filled with water upto a height of ‘h’ above the orifice and mass flow rate of water through the orifice is 2 Kg/sec. If the height of water surface above the orifice is made 4h and cross-sectional area of the orifice is doubled, then mass flow rate of water will be

Moderate

A

12 Kg
B

16 Kg
C

4 Kg
D

8 Kg

Solution

If ‘a’ be the cross sectional area of the orifice, then mass flow rate $m = ρ . a . \sqrt{2 gh}$
$\begin{array}{l} ∴ \frac{{(\overset{•}{m})}^{1}}{\overset{•}{m}} = (\frac{a^{1}}{a}) \sqrt{\frac{h^{1}}{h}} \Rightarrow \frac{{(\overset{•}{m})}^{1}}{2} = (2) \sqrt{4} \\ \Rightarrow {(\overset{•}{m})}^{1} = 8 Kg \end{array}$

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