First slide

Fluid dynamics

Question

There is a hole of area A at the bottom of cylindrical vessel. Water is filled up to a height h and water flows out in t second. If water is filled to a height 4h, it will flow out in time equal to

Moderate

A

t
B

4t
C

2t
D

t/4

Solution

Time required to emptied the tank $t = \frac{A}{A_{0}} \sqrt{\frac{2 H}{g}}$
$∴ \frac{t_{2}}{t_{1}} = \sqrt{\frac{H_{2}}{H_{1}}} = \sqrt{\frac{4 h}{h}} = 2 ∴ t_{2} = 2 t$

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