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