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(A) Let $a$ be the area of the hole,$v_e$ be the velocity of efflux,and $h$ be the height of the liquid above the hole. Let $v$ be the speed with whic

Vedclass · Accepted Answer

$50 \,m^2 \,s^{-2}$

Vedclass · Answer

(A) Let $a$ be the area of the hole,$v_e$ be the velocity of efflux,and $h$ be the height of the liquid above the hole. Let $v$ be the speed with which the level decreases in the container.From the equation of continuity,$a v_e = A v \Rightarrow v = \frac{a v_e}{A}$.Using Bernoulli's theorem at the top surface and the orifice:$p_0 + h ho g + \frac{1}{2} ho v^2 = p_0 + \frac{1}{2} ho v_e^2$$h ho g + \frac{1}{2} ho \left(\frac{a v_e}{A}ight)^2 = \frac{1}{2} ho v_e^2$$v_e^2 = \frac{2gh}{1 - (a/A)^2}$Given $h = 3 \,m - 0.525 \,m = 2.475 \,m$,$a/A = 0.1$,and $g = 10 \,ms^{-2}$:$v_e^2 = \frac{2 	imes 10 	imes 2.475}{1 - (0.1)^2} = \frac{49.5}{1 - 0.01} = \frac{49.5}{0.99} = 50 \,m^2 \,s^{-2}$.

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