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Question

(A) According to the equation of continuity, the volume flow rate of water entering the first pipe must equal the total volume flow rate of water exit

Vedclass · Accepted Answer

$\frac{D^2 v}{n d^2}$

Vedclass · Answer

(A) According to the equation of continuity, the volume flow rate of water entering the first pipe must equal the total volume flow rate of water exiting through the $n$ holes in the second pipe.Let $A_1$ be the cross-sectional area of the first pipe and $v$ be the speed of water in it.$A_1 = \pi \left(\frac{D}{2}ight)^2$Let $A_2$ be the area of each hole and $v'$ be the speed of water leaving each hole.$A_2 = \pi \left(\frac{d}{2}ight)^2$The total flow rate out is $n 	imes A_2 	imes v'$.Equating the flow rates: $A_1 v = n A_2 v'$$\pi \left(\frac{D}{2}ight)^2 v = n \pi \left(\frac{d}{2}ight)^2 v'$$\frac{D^2}{4} v = n \frac{d^2}{4} v'$$v' = \frac{D^2 v}{n d^2}$

$A$ pipe having an internal diameter $D$ is connected to another pipe of the same size. Water flows into the second pipe through $n$ holes, each of diameter $d$. If the water in the first pipe has speed $v$, what is the speed of water leaving the second pipe?

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