Question

A garden hose having an internal diameter of 0.710 in. ( 1.8034 cm ) is connected to a lawn sprinkler that consists merely of an enclosure with 30 holes, each 0.055 in. ( 0.1397 cm ) in diameter. If the water in the hose has a speed of 3.33 ft/s ( 101.600 cm/s ), at what speed does it leave the sprinkler holes?

Answer 1

Looking into the problem, we find that the volume of water passing through the hose must equal the volume of water leaving the sprinkler.

Consider, s = speed of the water from sprinkler

Now, use the volume of a cylinder -

Vh = 1.016 * pi * (1.8034 / 2) ^ 2 = 0.826 * pi

And -

Vs = s * 30 * pi * (0.1397 / 2) ^ 2 = 0.1464 * s * pi

Equalize the tw o -

Vh = Vs

0.826 * pi = 0.1464 * s * pi

=> 0.826 = 0.1464 * s

=> s = 0.826 / 0.1464 = 5.64
Therefore, the speed of water when it leaves the sprinkler = 5.64 m/s