JEE Main 2020 · Physics · Fluid Mechanics, Elasticity and Surface Tension · hard

A cylindrical tank of cross-sectional area 0.1 m^2 has a small circular hole of area 10 cm^2 in its base, and water drains out through it. The water…

Numerical answer

A cylindrical tank of cross-sectional area

0.1\ \mathrm{m^2}

has a small circular hole of area

10\ \mathrm{cm^2}

in its base, and water drains out through it. The water level falls from

1.8\ \mathrm{m}

0.45\ \mathrm{m}

. Taking

g = 10\ \mathrm{m\,s^{-2}}

, the time taken (in seconds) is

Show answer and solution

Answer: 30

Let the level be

h

. Torricelli: outflow speed

\sqrt{2gh}

, and continuity gives

A\,\dfrac{dh}{dt} = -a\sqrt{2gh}

. Integrating,

t = \dfrac{A}{a}\sqrt{\dfrac2g}\,(\sqrt{h_1} - \sqrt{h_2})

. With

A/a = 0.1/10^{-3} = 100

t = 100\times\sqrt{0.2}\times(\sqrt{1.8} - \sqrt{0.45}) = 100\times0.4472\times(1.3416 - 0.6708) = 30\ \mathrm{s}

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