A large open tank has two holes in the wall. | vedclass

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Question

(A) The volume flow rate (quantity of water per second) is given by $Q = A v$,where $A$ is the area of the hole and $v$ is the velocity of efflux.Acco

Vedclass · Accepted Answer

$\frac{L}{\sqrt{2 \pi}}$

Vedclass · Answer

(A) The volume flow rate (quantity of water per second) is given by $Q = A v$,where $A$ is the area of the hole and $v$ is the velocity of efflux.According to Torricelli's law,the velocity of efflux at a depth $h$ is $v = \sqrt{2gh}$.For the square hole: $A_1 = L^2$ and $v_1 = \sqrt{2gy}$.Thus,$Q_1 = L^2 \sqrt{2gy}$.For the circular hole: $A_2 = \pi R^2$ and $v_2 = \sqrt{2g(4y)} = 2\sqrt{2gy}$.Thus,$Q_2 = \pi R^2 (2\sqrt{2gy})$.Given that $Q_1 = Q_2$,we have:$L^2 \sqrt{2gy} = \pi R^2 (2\sqrt{2gy})$$L^2 = 2\pi R^2$$R^2 = \frac{L^2}{2\pi}$$R = \frac{L}{\sqrt{2\pi}}$.

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