Flow around a cylinder - potential theory/Fluid mechanics

[Nikitin]

Homework Statement

https://fbcdn-sphotos-g-a.akamaihd.net/hphotos-ak-prn2/p526x296/960031_10201604348407190_1235705166_n.jpg

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?

 

[Chestermiller]

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 textbooks, 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.

Chet

 

[Nikitin]

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.

 

[Chestermiller]

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.

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.

 

[Nikitin]

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?

 

[Chestermiller]

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?

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?

Chet

 

[Nikitin]

Yeah! Thanks for your help!