Question

A boy is playing with a water hose, which has an exit area of 10 cm2 and has water flowing at a rate of 3 m/s. If he covers the opening of the hose with his thumb so that it now has an open area of 2 cm2, what will be the new exit velocity of the water?

A. 20 m/s
B. 15 m/s
C. 5 m/s
D. 10 m/s

Answer 1

The exit velocity of water is B. 15 m/s.

According to equation of continuity, for a steady flow of water, the volume of liquid entering a pipe in 1 second is equal to the volume that leaves per second.

If the initial exit area of the pipe is A₁ and the speed of exit is v₁ and the final exit area is A₂ and its corresponding exit velocity is v₂, then,

`A_1v_1 = A_2v_2`

Rewrite the expression for v₂.

`v_2 =((A_1)/(A_2)  )(v_1)`

Substitute 10 cm² for A₁, 2 cm² for A₂ and 3 m/s for v₁.

`v_2 =((A_1)/(A_2)  )(v_1) =(10 cm^2)/(2 cm^2)  (3m/s) =15 m/s`

The exit speed of water from the hose is 15 m/s.