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Q.

A hole is made at the bottom of the tank filled with water (density = 1000 ${kgm}^{- 3}$ ). If the total pressure at the bottom of the tank is three atmospheres (1 atmosphere= 10⁵ ${Nm}^{- 2}$ ), then the velocity of efflux is nearest to

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a

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

b

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

c

$\sqrt{500} {ms}^{- 1}$

d

$\sqrt{200} {ms}^{- 1}$

answer is A.

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Detailed Solution

Neglecting gravitational head, difference in pressure energy = difference in kinetic energy

$∴ (3 p_{0} - p_{0}) = \frac{1}{2} ρ v^{2}$

or $v = 2 \sqrt{\frac{p_{0}}{ρ}} = 2 \sqrt{\frac{10^{5}}{10^{3}}} = 20 {ms}^{- 1} or \sqrt{400} {ms}^{- 1}$

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A hole is made at the bottom of the tank filled with water (density = 1000 kgm-3). If the total pressure at the bottom of the tank is three atmospheres (1 atmosphere= 105 Nm-2 ), then the velocity of efflux is nearest to