First slide

Fluid dynamics

Question

A hole is in the bottom of the tank having water. If total pressure at the bottom is 3 atm (1 atm·= 105 Nm^-2), then velocity of water flowing from hole is:

Moderate

A

$\sqrt{400} {ms}^{- 1}$
B

$\sqrt{600} {ms}^{- 1}$
C

$\sqrt{60} {ms}^{- 1}$
D

none of these

Solution

Pressure at bottom
$= P_{0} + {hρ}_{w} g = 3 ρ_{0} \Rightarrow h \times 10^{3} \times 10 = 2 \times 10^{5} \Rightarrow h = 20 m$
Velocity of efflux $= \sqrt{2 gh} = \sqrt{2 \times 10 \times 20} = \sqrt{400} {ms}^{- 1}$ =20 m $s^{- 1}$

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