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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 :

Cricetus

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,

[tex] A_1v_1 = A_2v_2 [/tex]

Rewrite the expression for v₂.

[tex] v_2 =(\frac{A_1}{A_2}  )(v_1) [/tex]

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

[tex] v_2 =(\frac{A_1}{A_2}  )(v_1) =\frac{10 cm^2}{2 cm^2}  (3m/s) =15 m/s [/tex]

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

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