A garden hose having an internal diameter 2.0 cm is connected to a lawn sprinkle that consists of an enclosure with 24 holes , each 0.125 cm in diameter. If water in the hose has a speed of `90.0 cm s^(-1)` , find the speed of of `90.0 cm s^(-1)`, find the speed of the water having the sprinkler hole.

Explanation

Here, diameter of the hose,
`D= 2.0 cm,`
Speed of water in the hose, `V=90.0 cms^(-1)`,
Diameter of each hole, `d= 0.125 cm`,
number of holes, `n=24` ltbr. Let `upsilon` be the velocity of water flowing out of each hole. Volume of the water crossing hose per second is equal to the volume of the water leaving out per second through holes : so,
`(pi D^2)/(4) xx V = npi d^(2)/(4) xx upsilon`
or `upsilon = (D^(2)V)/(nd^2) = ((2)^(2)xx 90.0)/(24 xx (0.125)^(2)) = 960 cm//s`.