Question

A cylindrical vessel of height h and base area is filled with water. An orifice of area << * 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=* dH/dt or dV=SdH ............(4)

Eqs. (2) and (4)