Question

A cylindrical container of cross-section area, A is filled up with water upto height 'h'. Water may exit through a tap of cross section area 'a' in the bottom of container. Find out :

(a) Velocity of water just after opening of tap.

(b) The area of cross-section of water stream coming out of tape at depth h₀ below tap in terms of 'a' just after opening of tap.

(c) Time in which container becomes empty.

(Given :(a/A)^1/2=0.02,h=20 cm, h₀=20 cm)

Answer 1

Applying Bernoulli's equation between (1) and (2) -

(c) From (1) at any height 'h' of liquid level in container, the velocity through tap,

we know, volume of liquid coming out of tap = decrease in volume of liquid in container.

For any small time interval 'dt'

av₂dt = -A · dx