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.

A

t = 23.5 s

B

t = 47.3 s

C

t = 19.02 s

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=r2√2gh ⇒−dh√h=r2R2√2g.dt. Integrating we get,−∫00.16dh√h=(0.0050.08)2√2×9.8∫t0dt Therefore, t = 46.26 sec.

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