Question

Water flows into a large tank with flat bottom at the rate of $10^{-4}\,m^{3}\, s^{-1}$ . Water is also leaking out of a hole of area $1 \,cm^{2}$ at its bottom. If the height of the water in the tank remains steady, then this height (in cm) is:

Answer 1

Since height of water column is constant therefore,
water inflow rate $\left(Q_{\text{in}}\right)$
= water outflow rate
$Q_{\text{in}} = 10^{-4} \,m^{3} s^{-1}$
$Q_{\text{out}} = Au =10^{-4} \times \sqrt{2gh}$
$\therefore 10^{-4} =10^{-4} \times \sqrt{20\times h}$
$\therefore h=\frac{1}{20} \,m = 5\,cm$