Question

A cylinderical tank of cross–sectional area A has a hole O of cross–section a as shown in Fig. The tank is placed on a rigid horizontal plateform at a height H above ground. Initially tank is filled with a liquid up to a height h. The time taken by tank to empty itself on opening O is proportional to

(1) Hh

(2) √Hh

(3) √h

(4) √h/H

Answer 1

(3) √h

v = The instantaneous velocity of efflux of liquid from O

= √2gy

where y is the instantaneous height of liquid in tank above O.

The instantaneous rate of flow of liquid from O = av = -A dy/dt

where dy is change in level of liquid in tank in time interval t and t + dt