A gardening pipe having an internal radius 'R | vedclass

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(B) According to the equation of continuity,the mass flow rate of water remains constant throughout the system.$A_1 v_1 = A_2 v_2$Here,$A_1 = \pi R^2$

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$\frac{R^2 v}{n r^2}$

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(B) According to the equation of continuity,the mass flow rate of water remains constant throughout the system.$A_1 v_1 = A_2 v_2$Here,$A_1 = \pi R^2$ is the cross-sectional area of the pipe and $v_1 = v$ is the speed of water in the pipe.The sprinkler has $n$ holes,each of radius $r$. The total cross-sectional area of the holes is $A_2 = n \pi r^2$.Let $v'$ be the speed of water leaving the sprinkler.Substituting these values into the continuity equation:$\pi R^2 v = (n \pi r^2) v'$Solving for $v'$:$v' = \frac{\pi R^2 v}{n \pi r^2} = \frac{R^2 v}{n r^2}$

$A$ gardening pipe having an internal radius '$R$' is connected to a water sprinkler having '$n$' holes each of radius '$r$'. The water in the pipe has a speed '$v$'. The speed of water leaving the sprinkler is

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