A garden pipe has an internal diameter of 4 cm. It is connected to a lawn sprinkler that consists of 24 holes at the other end. Each hole is of radius 0.06 cm. If the water in the pipe has a speed of 80 cm `s^(-1)`, find its speed through sprinkler holes.

Explanation

Given that
speed of water through pipe, `v_(1) = 80 cm s^(-1)`
Area of cross-section of pipe, `A_(1) = (pi xx (4)^(2))/(4)`
`= 4 pi cm^(2)`
Let the speed of water through hole = `v_(2)`
Area of cross- section available to water through sprinkler `A_(2) = 24 xx` (Area of one hole)
= `24 xx (pi xx (0.06)^(2))`
`= 24 pi xx 36 xx 10^(-4) cm^(2)`
From the equation of continuity
`A_(1)v_(1) = A_(2) v_(2)`
`rArr 80 xx 4 pi = (24 pi xx 36 xx 10^(-4)) xx (v_(2))`
`rArr (80 xx 4 pi)/(24 pi xx 36 xx 10^(-4)) = v_(2)`
= `0.3703 xx 10^(4) cm s^(-1) = v_(2)`
`rArr v_(2) = 37 m s^(-1)`