Question

A cylindrical vessel of height h and base area S is filled with water. An orifice of area s << S is opened in vessel. Neglecting the viscosity of water, determine how soon all the water will pour out of the vessel.

Answer 1

Let at any moment of time, water level in the vessel be H then speed of' flow of water through the orifice, at that moment will be 

v=√2gh   ....(1) 

In the time interval dt, the volume of water ejected through orifice, 

dv=svdt    ..........(2) 

On the other hand, the volume of water in the vessel at time t equals

V=SH  .....(3) 

Differentiating (3) with respect to time,

dV/dt=s dH/dt or dV=SdH    ............(4)

Eqs. (2) and (4)