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Question

A cylindrical tank of height 0.4 m is open at the top and has a diameter of 0.16 m. It is filled with water upto a height of 0.16 m. Find the time taken to empty the tank through a hole of radius 5 x 10-3 m in its bottom.



Your Answer
A

t = 23.5 s

Your Answer
B

t = 47.3 s

Your Answer
C

t = 19.02 s

Correct Answer
D

t = 46.26 s


Solution

The correct option is D

t = 46.26 s


The velocity of efflux through a small hole at a depth h is given by
v=2gh.
According to the principle of continuity,
We get,
πR2dhdt=πr2v. Since the rate of fall of water level in the tank is - dhdt
R2dhdt=r22gh
dhh=r2R22g.dt.
Integrating we get,00.16dhh=(0.0050.08)22×9.8t0dt
Therefore, t = 46.26 sec.

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