shell balance
Storyboard Text
- Ohhh! This is a nice water gun
- Yes Grandpa!!!
- Pass the ball to me Sarah!
- Oh No
- Nice pass isn't it Granpa?
- Watch out Sarah!
- Sorry! I wasn't aiming at you. It was an accident
- Why are you shooting at me?
- Calm down Sarah! It's only water
- Do you think you are the only one with a gun here?
- Don't shoot me. I don't want to get wet!
- Grandpa, why doesn't the water from my gun reach that guy?
- Let's come inside! I will teach you how fluid flow in your gun and you can tell me why it doesn't reach him
- This rectangle is what holds water inside your gun. Now tell me what do you think is driving the flow of the water inside the gun
- It's the pressure generated when I pulled the trigger
- Don't Worry! I will write on the board for you
- We are assuming that the pressure is driving the fluid forward, so what other things contribute to the flow?
- hmmm.
- Instead of analyzing the force for the whole rectangle, we should only analyze a shell of it. You can see how I cut a shell out of the whole rectangle on the board
- Ahhh. I got it, and then we can integrate it, so that we can know the profile of the whole rectangle
- But before we can analyze a shell, I will show you the momentum balance equation
- That's right. In this situation, we are using cartesian coordinates. So, stress is exerting in x direction and imparting in Y direction. Try draw how the stress is imparted in the shell on the board.
- So tell me what is stress.
- Stress is internal forces exerted by parallel particles to each other
- You also need the Stress equation on top of that as well.
- That is correct. Good job Sarah!!
- You mentioned convective force, so how does it help the water flow inside the gun?
- So, the convective forces will cancel out when we plug in the momentum balance equation
- That is the convective equation. However, the velocity of the gun will be the same in x - direction
- That is the momentum balance equation after I plugged in the stress and pressure.
- What is the area that you multiply with the stress force mean?
- Ahh! This looks very similar to the limit definition that I learned in Calc 1
- You will substitute the stress equation that I mentioned before for stress.
- To get to the equation of stress, you need to take the integral for both side.
- Wait, but that doesn't tell me why the water reach that guy on the beach.
- Now use these boundary conditions to solve for C1 and C2.
- But where does these B.C come from?
- When you pull the trigger, the bottom plate will move with V velocity, which makes the fluid moves with V velocity at the interference at the bottom plate. This is called the no-slip condition. However, the top plate will not move for this gun.
- So, because the top plate doesn't work, the velocity on the upper half is less than the velocity on bottom. So, the overall water velocity is not as high.
- The area is where the stress exerted force on, in this case it is (LxW). You can also see that I divided by the volume of the shell. I also take the limit of it as Delta Y goes to 0.
- That's right. I will fix your water gun, so that when you pull the trigger, both plates will move. The velocity profile will look like this after I fixed your gun.
- When both plates moves, it will generate higher overall velocity, so that water will reach that guy.
- I just fixed it. Now go out there and try another shot at that guy and see what happen
- Ahh. How did you get your gun to shoot so far?
- Take transport processes with me and then you will know
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