Question

A garden hose with an internal diameter of 1.6 cm is connected to a (stationary) lawn sprinkler that consists merely of a container with 25 holes, each 0.30 cm in diameter. If the water in the hose has a speed of 0.96 m/s, at what speed does it leave the sprinkler holes?

Answer 1

s = 1.024 m/s

Step-by-step explanation:

The volume of water passing through the hose(Vh) must equal the volume of water leaving the sprinkler(Vs)

Thus, using the volume of a cylinder, we have;

Vh = 0.96 x π x (1.6/2)²

Vh = 0.576π

Let s be the speed from the sprinkler. Thus;

Vs = s x 25 x π x (0.3/2)²

Vs = 0.5625π(s)

Since the condition is ;Vh = Vs

Thus,

0.576π = 0.5625π(s)

π will cancel out to give ;

0.576/0.5625 = s

s = 1.024 m/s