A cylindrical vessel of cross-section A contains water to a height h . There is a hole in the bottom of radius ' a '. The time in which it will be emptied is:

Step-by-step solution

Let the rate of falling water level be - d h d t Initially at t=0 ; h=h t=t ; h=0 Then, A (- d h d t )= a^2 v d t=- A a^2 2 g h d h [ velocity of efflux of liquid v= 2 g h ] Integrating both sides ₀^t d t=- A 2 g a^2 _h^0 h^ -1 / 2 d h [t]₀^t=- A 2 g a^2 [ h^ 1 / 2 1 / 2 ]_h^0 t= 2 A a^2 h g