Question

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

• A. $2250N$
• B. $2000N$
• C. $1500N$
• D. $1000N$

Answer 1

Answer: (A)

Area of the cross-section of the tube, $a=10^{- 2}m^{- 2}$
Speed of stream of water $=15ms^{- 1}$
$V=$ The volume of water coming out per second from the tube $=a\times v=15\times \, 10^{- 2}m^{3}s^{- 1}$
$ \, $ Also, we know that the density of water striking the wall per second, then
$m=pV=10^{3}\times 15\times 10^{- 2} \, kgs^{- 1}=150 \, kgs^{- 1}$
As on hitting the wall, water does not rebound, so
$F=$ change in momentum per second
$= \, \, $ mass of water flowing out per second $\times $ velocity
$=150\times 15=2250 \, N$