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(D) According to the equation of continuity,the volume flow rate of water remains constant.Let $A_1$ be the cross-sectional area of the pipe and $v_1$

Vedclass · Accepted Answer

$48$

Vedclass · Answer

(D) According to the equation of continuity,the volume flow rate of water remains constant.Let $A_1$ be the cross-sectional area of the pipe and $v_1$ be the velocity of water in the pipe.Let $A_2$ be the total cross-sectional area of the $100$ holes and $v_2$ be the velocity of water coming out of the holes.$A_1 v_1 = 100 	imes A_{hole} 	imes v_2$Given:Diameter of pipe $D_1 = 2 \ cm = 2 	imes 10^{-2} \ m$,so radius $r_1 = 1 	imes 10^{-2} \ m$.Velocity $v_1 = 3 \ ms^{-1}$.Diameter of each hole $d = 0.05 \ cm = 0.05 	imes 10^{-2} \ m$,so radius $r = 0.025 	imes 10^{-2} \ m$.Substituting the values:$\pi (1 	imes 10^{-2})^2 	imes 3 = 100 	imes \pi (0.025 	imes 10^{-2})^2 	imes v_2$$10^{-4} 	imes 3 = 100 	imes (2.5 	imes 10^{-4})^2 	imes v_2$$3 	imes 10^{-4} = 100 	imes 6.25 	imes 10^{-8} 	imes v_2$$3 	imes 10^{-4} = 6.25 	imes 10^{-6} 	imes v_2$$v_2 = \frac{3 	imes 10^{-4}}{6.25 	imes 10^{-6}} = \frac{300}{6.25} = 48 \ ms^{-1}$.

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