Fluid Mechanics

A closed water tank has cross-sectional area \(A\). It has a small hole at a depth of \(h\) from the free surface of water. The radius of the hole is \(r\) so that \(r \ll \sqrt{\frac{A}{\pi}}\). If \(p_o\) is the pressure inside the tank above water level and \(p_a\) is the atmospheric pressure, the rate of flow of the water coming out of the hole is ( \(\rho\) is density of water)