Question

If a hemispherical tank of radius R has an orifice of area a, at its base,determine the time required to empty the tank assuming the tank was initially full.

Answer 1

$$dV=\pi (2Rh-h^2)dh\\-\frac{dV}{dt}=a\sqrt{2gh}\\t=\frac{14\pi R^{2.5}}{15\sqrt{18}a}$$