Δm/Δt=ρAv
Since fluid has both mass and velocity in the tube, it is easy to relate it to the idea of momentum. So in real life, scientists use the motion of water to make a very useful technique---water jet cutter. It is an industrial tool capable of cutting aside variety of materials using a very high pressure jet of water.
Check the video below:
https://www.youtube.com/watch?v=crgujRcyhhE
Here are the parameters I found:
Diameter of the cross section area: 0.2 mm
Velocity of water: 800 m/s
And I want to calculate the pressure of water as it leaves the tube by using the equations we learned in class
Δm/Δt=ρAv
Δm=ρAvΔt
F=mΔv/Δt=ρA(v^2)Δt/Δt=ρA(v^2)
P=F/A=ρA(v^2)/A=ρ(v^2)=1*10^3*800^2=(6.4*10^8)Pa
I also searched the maximum pressure that some materials can bear:
rubber: 5*10^7 Pa
granite: 2*10^8 Pa
cast iron: 8.8*10^8 Pa
Compared with the pressure generated by water jet cutter, I can conclude that for this type of water jet cutter, rubber and granite can be cut. However, in order to cut harder material like cast iron, higher velocity is required.
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