Question

A cylinder containing a liquid of density p has a hole of cross–sectional area A at A depth h. The cylinder is counter poised on a balance. The hole is opened what is initial reading of the balance?

Answer 1

Let y be height of liquid above hole at t = t. The instantaneous velocity of efflux = √2gy. In time interval t, t + dt; as liquid emerges out of hole the weight of liquid in cylinder decreases. The decrease in weight equals instantaneous rate of change of linear momentum of liquid emerging out. The instantaenous force, F; is

where dV/dt is instantaneous rate of flow of liquid. Obvisouly

dV/dt = Av