1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Flow around a cylinder - potential theory/Fluid mechanics

  1. Oct 17, 2013 #1
    1. The problem statement, all variables and given/known data


    3. The attempt at a solution

    Hey! Well, I don't really know where to start, even.. Heck, I think the problem is formulated pretty badly (with width, I assume they mean length of the cylinder?)..

    Anyway, I think I can solve the problem with the following steps:

    1) I can probably assume inviscid flow.
    2) I need to figure out the velocity-distribution around the cylinder, and then the pressure distribution. I think I will somehow need to superimpose a vortex and linear-flow?
    3) Calculate the difference in pressure between the outside and the inside.
    4) Calculate the force on each bolt.

    My problem is 2: I simply have no clue what to do. Please help?
    Last edited: Oct 17, 2013
  2. jcsd
  3. Oct 17, 2013 #2
    You have it doped out pretty well. Yes, you do have to assume inviscid flow. Yes, you do need to determine the surface pressure distribution for inviscid flow over a cylinder. This will be a function of the polar angle. Then, you integrate the pressure force over the top of the cylinder (taking into account the fact that the pressure is everywhere normal to the surface, so you need to take into account its directionality). The solution for inviscid flow over a cylinder can be found in many text books, like Transport Phenomena by Bird, Stewart, and Lightfoot. The outside force, of course, will be less than atmospheric; the latter is the pressure far from the cylinder.

  4. Oct 18, 2013 #3
    thanks for reply :), however the problem is, I'm not supposed to just find the distribution from a book, I'm supposed to use the concepts of potential theory to calculate it... I.e. superimposing sinks, sources, line streams, dipoles, vortexes etc. on each other so that you get a correct field.
    Last edited: Oct 18, 2013
  5. Oct 18, 2013 #4
    No problemo. Use a dipole at the center of the cylinder, and uniform flow in the far field. Have the dipole aligned with the direction of the uniform flow. This will give you what you want in the flow region outside the cylinder.
  6. Oct 18, 2013 #5
    Why would that work? I see that it's a good idea just by knowing dipoles have "curvy" stream-lines, so the streamlines go around the cylinder, but do you have any formal reasoning?
  7. Oct 18, 2013 #6
    No formal reasoning. But I do know that if you just have a source and no sink in a uniform flow, you will get a long torpedo shape for the inner region. So, if you also include the sink part of the dipole, it closes down the tail end of the torpedo, and forms a cylindrical region. Otherwise, I don't remember how I came to know that this is the correct setup. Have you solved it yet for the dipole and shown that the boundary is a circle?

  8. Oct 19, 2013 #7
    Yeah! Thanks for your help!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted