A cylindrical vessel open at the top is 20 c | vedclass

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(D) In steady state,the volume flow rate entering the vessel is equal to the volume flow rate leaving the vessel through the hole.Let $Q$ be the inflo

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$5$

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(D) In steady state,the volume flow rate entering the vessel is equal to the volume flow rate leaving the vessel through the hole.Let $Q$ be the inflow rate,$a$ be the area of the hole,and $v$ be the velocity of efflux.$Q = a v$Using Torricelli's law,the velocity of efflux is $v = \sqrt{2gh}$,where $h$ is the height of the water column.Thus,$Q = a \sqrt{2gh}$.Squaring both sides,we get $Q^2 = a^2 (2gh)$.Solving for $h$,we get $h = \frac{Q^2}{2ga^2}$.Given $Q = 100 \ cm^3 s^{-1}$,$a = 1 \ cm^2$,and $g = 1000 \ cm s^{-2}$.Substituting the values: $h = \frac{(100)^2}{2 	imes 1000 	imes (1)^2} = \frac{10000}{2000} = 5 \ cm$.

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