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A lawn sprinkler has 20 holes, each of c...

A lawn sprinkler has `20` holes, each of cross-sectional area `2.0 xx 10^(-2) cm^(2)`, and is connected to a hose pipe of cross sectional area `2.4 cm^(2)`. If the speed of water in the hose pipe is `1.5 ms^(-1)`, the speed of water as it emerges from the holes is

Text Solution

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D =Diameter of hose = 3 cm
d=Diameter of each hole = 0.12 cm
n = 20
V = 1000 cm/s
V = ?
According to equation of continuity
Amount of water crossing hole/sec.
= amount of water leaving through holes of sprinkler `(pi D^(2))/(4) .V =n. (pi d^(2))/(4) .v`
`V=. d^(2)/4 . (v xx 4)/D^(2)`
`=(nvd^(2))/(D^(2))=(20 xx 1000 xx (0.12)^(2))/((3)^(2))`
=32 cm/sec.
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