A hole is made at the bottom of a tank filled with water. If the total pressure at the bottom of tank is 3 atmosphere and density of water is $1000 k g m^{- 3}$ , then the velocity of efflux is

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$10 \sqrt{5} m s^{- 1}$

$20 m s^{- 1}$

$10 \sqrt{2} m s^{- 1}$

$10 \sqrt{6} m s^{- 1}$

answer is A.

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Detailed Solution

Loss in pressure energy = Gain in kinetic energy

$Δ P = \frac{1}{2} ρ v^{2}$

$\Rightarrow$ $v = \sqrt{2 \frac{Δ P}{ρ}}$

$\Rightarrow$ $v = \sqrt{{\frac{2 \times (3 - 1) a t o m s}{10^{3}}}}$

$\Rightarrow$ $v = \sqrt{{\frac{2 \times 2 \times 10^{5}}{10^{3}}}} = 20 m s^{- 1}$

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