Question

A garden hose with an internal diameter of 2.9 cm is connected to a (stationary) lawn sprinkler that consists merely of a container with 24 holes, each 0.36 cm in diameter. If the water in the hose has a speed of 0.98 m/s, at what speed does it leave the sprinkler holes?

Answer 1

Answer:

Water leaves the holes with a speed of 2.65 m/sec    

Explanation:

It is given internal diameter of garden hose = 2.9 cm

So internal radius $r_1=\frac{2.9}{2}=1.45cm$

Number of holes n = 24

Diameter of holes d = 0.36 cm

So radius of holes $r_2=\frac{0.36}{2}=0.18cm$

Velocity of water in hose  $v_1=0.98m/sec$

According to continuity equation

$A_1v_1=nA_2v_2$

$\pi r_1^2\times 0.98=24\times \pi r_2^2\times \times v_2$

$1.45^2\times 0.98=24\times 0.18^2\times \times v_2$

$v_2=2.65m/sec$

Therefore water leaves the holes with a speed of 2.65 m/sec