A stream of water flowing horizontally with a speed of
Question.
A stream of water flowing horizontally with a speed of $15 \mathrm{~m} \mathrm{~s}^{-1}$ gushes out of a tube of cross-sectional area $10^{-2} \mathrm{~m}^{2}$, and hits a vertical wall nearby. What is the force exerted on the wall by the impact of water, assuming it does not rebound?

solution:

Speed of the water stream, $v=15 \mathrm{~m} / \mathrm{s}$

Cross-sectional area of the tube, $A=10^{-2} \mathrm{~m}^{2}$

Volume of water coming out from the pipe per second,

$V=A v=15 \times 10^{-2} \mathrm{~m}^{3} / \mathrm{s}$

Density of water, $\rho=10^{3} \mathrm{~kg} / \mathrm{m}^{3}$

Mass of water flowing out through the pipe per second $=\rho \times V=150 \mathrm{~kg} / \mathrm{s}$

The water strikes the wall and does not rebound. Therefore, the force exerted by the water on the wall is given by Newton’s second law of motion as:

$F=$ Rate of change of momentum $=\frac{\Delta P}{\Delta t}$

$=\frac{m v}{t}$

$=150 \times 15=2250 \mathrm{~N}$
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