A small hole of cross-sectional area $5 \mathrm{~mm}^{2}$ is present near the bottom of a fully fill

Question

A small hole of cross-sectional area $5 \mathrm{~mm}^{2}$ is present near the bottom of a fully filled open tank of height $5 \mathrm{~m}$. Taking $g=10 \mathrm{~m} / \mathrm{s}^{2}$, the initial rate of flow of water through the hole would be

Professor PC Thomas Classes · Answer

(a) : According to Torricelli's theorem, the velocity of efflux is $v = \sqrt{2gh} = \sqrt{2 	imes 10 	imes 5} = \sqrt{100} = 10 \mathrm{~m/s}$. The area of the hole is $A = 5 \mathrm{~mm}^2 = 5 	imes 10^{-6} \mathrm{~m}^2$. The rate of volume flow is $Q = A 	imes v = (5 	imes 10^{-6} \mathrm{~m}^2) 	imes (10 \mathrm{~m/s}) = 50 	imes 10^{-6} \mathrm{~m}^3/\mathrm{s} = 5.0 	imes 10^{-5} \mathrm{~m}^3/\mathrm{s}$.