A large vessel completely filled with water h | vedclass

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Question

(C) According to Torricelli's law,the velocity of efflux is given by $v = \sqrt{2gh}$.For hole '$A$' at depth '$h$',the velocity is $V_A = \sqrt{2gh}$

Vedclass · Accepted Answer

$\sqrt{2 \pi} \cdot R$

Vedclass · Answer

(C) According to Torricelli's law,the velocity of efflux is given by $v = \sqrt{2gh}$.For hole '$A$' at depth '$h$',the velocity is $V_A = \sqrt{2gh}$.For hole '$B$' at depth '$4h$',the velocity is $V_B = \sqrt{2g(4h)} = 2\sqrt{2gh} = 2V_A$.The volume flow rate $(Q)$ is given by $Q = A \cdot v$,where '$A$' is the area of the hole.Given that the flow rate is the same for both holes: $Q_A = Q_B$.$A_A \cdot V_A = A_B \cdot V_B$.Since hole '$A$' is a square of side '$L$',$A_A = L^2$.Since hole '$B$' is a circle of radius '$R$',$A_B = \pi R^2$.Substituting the values: $L^2 \cdot V_A = (\pi R^2) \cdot (2V_A)$.$L^2 = 2\pi R^2$.$L = \sqrt{2\pi} \cdot R$.

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