First slide

Fluid dynamics

Question

A hole is made at the bottom of a tank filled with water (density= 10³ kg/m³). If the total pressure at the bottom of the tank is 3 atm (1 atm = 10⁵ N/m²), then the velocity
of efflux is

Moderate

A

$\sqrt{200} m / s$
B

$\sqrt{400} m / s$
C

$\sqrt{600} m / s$
D

$\sqrt{500} m / s$

Solution

Total pressure at the bottom = 3 atm
Pressure due to water in the tank = 3 atm - 1 atm = 2 atm = 20 m of water column
Height of water in the tank is h = 20 m
So, velocity of efflux $= \sqrt{2 g h} = \sqrt{2 \times 10 \times 20} = \sqrt{400} = 20 m / s$

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