Question

A garden hose having with an internal diameter of 2.5 cm is connected to a (stationary) lawn sprinkler that consists merely of an container with 22 holes, each 0.17 cm in diameter. If the water in the hose has a speed of 0.90 m/s, at what speed does it leave the sprinkler holes?

_______ m/s

Answer 1

According to continuity equation, or principle of continuity,  what flows into a defined volume in a defined time, will equal to what flows out of that volume in that time,

A₁V₁=A₂V₂

Area of inlet A₁=π(r₁)² = 3.14 × { (2.5×10^-2)/2 }²

A₁= 0.000490625m²

Velocity at hose V₁ =0.90m/s

So rate of inlet flow

A₁V₁= 0.000490625× 0.90 m³/s

= 0.000442m³/s

now there are 22 holes with diameter 0.17cm each ,so rate if out flow will be = 22× area of hole× velocity of flow in holes

A₂V₂= 22× π× {(0.17×10^-2)/2 }² V₂

. =4.99× 10^-5 V₂

_{so according to continuity equation}

A₁V₁=A₂V₂

V₂= 0.000442/ 4.99×10^-5

=8.85m/s