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A mathematical question about preassure

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A mathematical question about preassure

Unread postAuthor: Tobin » Sun May 29, 2011 8:15 am

If we have a circle, the circle has an circumference at 10cm. Inside the circle we have a preassure at 10kg/cm. Does that mean that at the circle's side is exposed to a tractive force at 100kg? (10kg*10cm=100kg)

If not how do i calculate the tractive pressure the side are exposed to?
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Unread postAuthor: DYI » Sun May 29, 2011 8:37 am

Firstly, the term "tractive" is not applicable here as it is specifically for dealing with the force exerted by vehicles.

The total magnitude of the force exerted on the walls is, in this case, 100kg<sub>f</sub>. That's not particularly useful for anything though, is it?

A quantity more applicable to the engineering of a pressure vessel would be the longitudinal and circumferential stresses (or in your peculiar two dimensional example, only longitudinal...). The diameter of your circle is 10/π, giving a longitudinal stress (tending to split your infinite cylinder from end to end, as opposed to into two semi-infinite cylinders) of 100/2πt where t is the thickness of the wall, assuming that the wall is thin in comparison to the diameter. You shouldn't have any trouble deriving that for yourself.

If you're interested in more complex vessels, look into Von Mises and Tresca yield criteria, and FEM software (or learning how to write your own FEM code, if you're feeling ambitious). There's also a very useful formula for longitudinal yielding of any cylindrical pressure vessel derived by btrettel in this thread (my formula up at the top is very conservative, not of much use for high pressure design work).
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Unread postAuthor: Tobin » Sun May 29, 2011 10:54 am

Ok, thanks. Actually i dont know exactly what tractive means, i did just use the google translator :P
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