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

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(B) The velocity of efflux for a hole at depth $h$ is given by Torricelli's law: $v = \sqrt{2gh}$.The rate of flow of water (volume per second) is giv

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

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