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

The correct option is C $5.1cm$
Given, water inflows rate in the larger tank, $Q_{in}={10}^{-4}{m}^3/s$

Area of the hole from which water is leaking, $A=1c{m}^2={10}^{-4}{m}^2$

Since height of water column is constant therefore,

Water inflow rate $\left(Q_{in}\right)=$ water outflow rate $\left(Q_{out}\right)$

From continuity equation,

$Q_{out}=Au={10}^{-4}\times \sqrt{2gh}$

${10}^{-4}={10}^{-4}\sqrt{2\times 9.81\times h}$

$h=0.0509m\approx 5.1cm$