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Physics · MECHANICAL PROPERTIES OF FLUIDS
हिन्दीA large cylindrical tank open at the top has a small orifice of area \( A_1 \) at a depth \( h \) below the water surface. The cross-sectional area of the tank is \( A_2 \). If \( A_1 / A_2 = \alpha \), taking the motion of the upper liquid surface into account, the speed of efflux \( v_1 \) is given by:
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Correct answer · Option A
\( \sqrt{\frac{2gh}{1 - \alpha^2}} \)
Explanation
Applying Bernoulli's equation between surface and hole: \( P_a + \frac{1}{2}\rho v_2^2 + \rho gh = P_a + \frac{1}{2}\rho v_1^2 \). Using continuity \( A_2 v_2 = A_1 v_1 \implies v_2 = \alpha v_1 \), we get \( v_1^2 (1 - \alpha^2) = 2gh \implies v_1 = \sqrt{\frac{2gh}{1 - \alpha^2}} \).
