Question

A cylindrical vessel open at the top is $20cm$ high and $10cm$ in diameter. A circular hole whose cross-sectional is area $1{\text{cm}}^2$ is cut at the centre of the bottom of the vessel. Water flows from a tube above it into the vessel at the rate $100{\text{cm}}^3{s}^{-1}$. The height of water (in $cm$) in the vessel under steady state is (Take ${\text{g = 1000 cm s}}^{-2})$

Answer 1

At steady state,
Rate of inflow of water = Rate of outflow of water
$\Rightarrow A_1{V}_1=A_2{V}_2$
Given $A_1{V}_1=100c{m}^3{s}^{-1}$
$V_2=\sqrt{2gh}cm/s$, $A_2=1c{m}^2$
$\Rightarrow 100=\sqrt{2\times 1000\times h}\times 1$
squaring on both side
$10,000=2\times 1000\times h$
$h=\frac{10}{2}$
$\Rightarrow h=5cm$