Fluid Mechanics

JEE Main level, numerical answer, medium

79 of 192

Question 79 of 192

The surface of water in a water tank of cross section area 750cm2750{cm}^{2} on the top of a house is hmhm. above the tap level. The speed of water coming out through the tap of cross section area 500mm2500{mm}^{2} is 30cms−130cm{s}^{-1}. At that instant, dhdt\dfrac{dh}{dt} is x×10−3ms−1x\times {10}^{-3}m{s}^{-1}. The value of xx will be ______.

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Answer: 2

Using continuity equation
A1v1=A2v2{A}_{1}{v}_{1}={A}_{2}{v}_{2}
We have,
750×10−4v1=500×10−6×0.3750\times {10}^{-4}{v}_{1}=500\times {10}^{-6}\times 0.3
v1=500×3×10−3750{v}_{1}=\dfrac{500\times 3\times {10}^{-3}}{750}
=2×10−3ms−1=2\times {10}^{-3}m{s}^{-1}
Thus, dhdt=−2×10−3ms−1\dfrac{dh}{dt}=-2\times {10}^{-3}m{s}^{-1}
Hence, the value of x=2x=2.

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