In the figure shown water is filled in the cylindrical tank of cross-sectional area 100 cm 2 up to a height of 10 cm . The mass of the thin, tight fitting and frictionless piston is 100 kg. The small

Question

In the figure shown water is filled in the cylindrical tank of cross-sectional area $100 cm^{2}$ up to a height of 10 cm . The mass of the thin, tight fitting and frictionless piston is 100 kg. The small hole in the piston has area $22 mm^{2}$ . Due to weight of the piston water spurts upwards in a jet from the hole. Find the time (in sec) in which the tank becomes empty. If your answer is n fill value of n/5. (Assume that spurted water does not fall back on piston)

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TestHub · Accepted Answer

The piston adds a constant excess pressure.

$P_{p} = \frac{m g}{A} = 1 0^{5} Pa$

Apply Bernoulli between points just inside and just outside the small hole. Atmospheric pressure cancels.

$P_{p} + P_{0} = P_{0} + \frac{1}{2} ρ v^{2}$

$v = \frac{2 P _{p}}{ρ}$

$v = 102 m s^{- 1}$

Let a be the area of the hole. The flow rate is constant while the piston descends.

$\dot{V} = a v = 4 \times 1 0^{- 5} m^{3} s^{- 1}$

A is the tank cross-sectional area, so the liquid volume is A h.

$V = A h = 1 0^{- 3} m^{3}$

$t = \frac{V}{a v} = 25 s$

$n = 25, \frac{n}{5} = 5$

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