A cylindrical tank of constant cross-sectional area drains through a small hole at the bottom. Its total ideal emptying time from initial water depth H is 100 s. The time required for the water level to fall from H to H/4 is N s. Find N.
Physics · Fluid Mechanics · equation of continuity and bornullie theorem
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Question

A cylindrical tank of constant cross-sectional area drains through a small hole at the bottom. Its total ideal emptying time from initial water depth H is 100 s. The time required for the water level to fall from H to H/4 is N s. Find N.

Physics · Fluid Mechanics · equation of continuity and bornullie theorem

G1 Physics · Accepted Answer

For a cylindrical tank draining through a small hole, time for level to fall from H₁ to H₂ is proportional to √H₁−√H₂. Total emptying time is proportional to √H−0 = √H. For fall from H to H/4, t ∝ √H−√(H/4) = √H−√H/2 = √H/2. Thus this time is one-half of the total emptying time. Therefore, t = 100/2 = 50 s. Hence, N = 50.