A pipe having an internal diameter D is conne | vedclass

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Question

(A) According to the equation of continuity,the volume flow rate of water remains constant.For the first pipe,the area of cross-section is $A_1 = \pi

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 remains constant.For the first pipe,the area of cross-section is $A_1 = \pi (D/2)^2$ and the speed is $v$.For the second pipe,the water flows out through $n$ holes,each of area $a = \pi (d/2)^2$. Let the speed of water leaving these holes be $v'$.Equating the flow rates: $A_1 v = n 	imes a 	imes v'$.Substituting the values: $\pi (D/2)^2 v = n 	imes \pi (d/2)^2 v'$.Simplifying the equation: $(D^2/4) v = n (d^2/4) v'$.Solving for $v'$: $v' = \frac{D^2 v}{n d^2}$.

$A$ 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 $v$,the speed of water leaving the second pipe is

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