Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

flumech2 Group Title

Are velocity components Vr=5rcos(theta), Vtheta = -5rsin(theta) irrotational?

  • one year ago
  • one year ago

  • This Question is Closed
  1. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Umm, irrotational? What do you mean?

    • one year ago
  2. flumech2 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Irrotational flow

    • one year ago
  3. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    LIke the curl is 0?

    • one year ago
  4. flumech2 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Ya....is that all I have to do?

    • one year ago
  5. flumech2 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    gradient X V....?

    • one year ago
  6. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Hold on, I'm not sure what irrotational is. Can you give me a definition?

    • one year ago
  7. flumech2 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Well my textbook it as flows for which no particle rotation occurs

    • one year ago
  8. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Okay so curl is 0... meaning we need to find if it has a potential function.

    • one year ago
  9. flumech2 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    This is impossible in reality because all fluids have viscosity, but flows can be assumed irrotational in certain cases

    • one year ago
  10. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    \[ \frac{\partial f}{\partial r} =5r\cos(\theta) \implies f = \frac{5}{2}r^2\cos(\theta) +g(\theta) \]

    • one year ago
  11. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    \[ \frac{\partial f}{\partial \theta} = -\frac{5}{2}r^2\sin(\theta) +g'(\theta)=-5r\sin(\theta) \]This let's us solve for \(g(\theta)\)

    • one year ago
  12. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    there might be another method, I'm not completely sure right now.

    • one year ago
  13. flumech2 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Okay. Well, I think it has to do with the gradient (del) cross velocity function (V)

    • one year ago
  14. flumech2 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    The only thing I am confused about is whether there is a different between the irrotational flow and the incompressible flow. It seems like if I find that there is an incompressible flow, it's automatically going to give me an irrotational flow

    • one year ago
  15. flumech2 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    My textbook defines the curl as (1/2)(del) X V.....but in rectangular coordinates it's simply defined as (1/2) (dv/dx - du/dx)

    • one year ago
  16. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    What's confusing me is if we take into consideration that it is in polar coordinates, and just treat it like Cartesian coordinates.

    • one year ago
  17. flumech2 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Ya. I mean every example I see in my book seems to look different ha....for example, for Vr = 0 and Vtheta = f(r) (1/r)* d/dr(r*Vtheta) = 0 for irrotational flow

    • one year ago
  18. flumech2 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    I feel like I kind of understand what is going on, but just not quite able to piece it together.

    • one year ago
  19. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    \[ \frac{\partial f}{\partial \theta} = -\frac{5}{2}r^2\sin(\theta) +g'(\theta)=-5r\sin(\theta)\\ g'(\theta) =(5r^2/2+r) (-\sin\theta)\implies g = (5r^2/2+r) (\cos\theta)+C \]

    • one year ago
  20. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    \[ \frac{\partial f}{\partial r} =5r\cos(\theta) \implies f = \frac{5}{2}r^2\cos(\theta) +g(\theta)\\ f = 5r^2\cos(\theta)+r\cos(\theta) \]

    • one year ago
  21. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    It has a potential function, that means it's curl is 0, it's conservative, irrotational, etc.

    • one year ago
  22. flumech2 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Another example my prof. gave in class was this: Given: velocity field V= \[\frac{ -q }{2 \Pi r } e _{r} + \frac{ K }{ 2 \Pi r } e _{}\] is it irrotational

    • one year ago
  23. flumech2 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    and what he did was gradient x V

    • one year ago
  24. flumech2 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    and got 0.....so I guess that is the same thing as you are saying essentially, right?

    • one year ago
  25. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Whoops, did a bit of algebra wrong there.

    • one year ago
  26. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    \[ \frac{\partial f}{\partial \theta} = -\frac{5}{2}r^2\sin(\theta) +g'(\theta)=-5r\sin(\theta)\\ g'(\theta) =(5r^2/2-5r) (\sin\theta)\implies g(\theta) = -(5r^2/2+r) (\cos\theta)+C \]

    • one year ago
  27. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    I keep messing up trying to find the damn potential function. Maybe it doesn't have one.

    • one year ago
  28. flumech2 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    I think it is \[del = e _{_{r}} \frac{\partial}{\partial r} + e _{_{\theta}} \frac{ 1 }{ r } \frac{\partial}{\partial \theta} \]

    • one year ago
  29. flumech2 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    and then that cross the the velocity vector of vr and vtheta

    • one year ago
  30. flumech2 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    \[e _{_{r}} \frac{\partial}{\partial r} + e _{_{\theta}} \frac{ 1 }{ r } \frac{\partial}{\partial \theta} X [ e _{_{r}} 5\cos(\theta) + e _{_{\theta}} -5\sin(\theta)]\]

    • one year ago
  31. flumech2 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    = 0

    • one year ago
  32. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    yeah, I don't know those formula unfortunately. The fact you bring them up makes me think we're dealing with polar coords though.

    • one year ago
  33. flumech2 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    We are definitely dealing with polar coordinates, but I think it's still the curl

    • one year ago
  34. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    \[ \frac{dx}{dt} = \frac{dx}{dr}\frac{dr}{dt} \]

    • one year ago
  35. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    anyway I'm going to bed.

    • one year ago
  36. flumech2 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Okay, thanks for your help

    • one year ago
    • Attachments:

See more questions >>>

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.