Question

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

Answer 1

Figure shows a column of water of length $15m$ and cross - section area ${10}^{-2}{m}^2$ at rest. Let us calculate the mass of water flowing out per second and hitting the wall. When the stream of water has a speed of $15m/s$, the particle of water at section B would have travelled a distance of $15m$ in one second and arrived at the section A. The water contained in this column would have gone out in one second and hit the wall.

Thus, the volume of water coming out of A in one second = volume of water contained in a cylinder of length $15m$ and area of cross - section $0.01m^2$
= $\text{Length}\times \text{Area of cross - section}$
$=15\times {10}^{-2}=0.15m^3$
Mass of water gushing out per second
= $\text{Volume of water}\times \text{Density of water}$
$=0.15\times 1000=150kg$
[density of water $=1000kg/m^3]$
|Change in momentum| $=2250-0=2250N$
Since change in momentum per second is the force, hence
force exerted on the wall will be $2250N$.