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July 17th, 2013, 09:12 AM   #1
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Integrate vectors along part of the circle

Hello!
I hope someone can help me out because I'm a little bit rusty with my math.

I have the following problem: the cylindric surface is under pressure. I know that the total resultant force in "horizontal" direction needs to be "N". So, basically, I would need to integrate all the "p*cos theta" along the curve from "-theta" to "theta" if I'm not wrong. Then, when multiplied with "L" and "s" where "s" would be arc length, I would get "N". Right?
But, am I doing something wrong?

http://tinypic.com/r/bfqo7m/5
No img codes? Really?
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July 17th, 2013, 03:54 PM   #2
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Re: Integrate vectors along part of the circle

Quote:
Originally Posted by rujan
No img codes? Really?
No. Post it as an attachment.

Welcome to the forum, rujan.
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July 17th, 2013, 04:15 PM   #3
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Re: Integrate vectors along part of the circle

Quote:
Originally Posted by rujan
Hello!
I hope someone can help me out because I'm a little bit rusty with my math.

I have the following problem: the cylindric surface is under pressure. I know that the total resultant force in "horizontal" direction needs to be "N". So, basically, I would need to integrate all the "p*cos theta" along the curve from "-theta" to "theta" if I'm not wrong. Then, when multiplied with "L" and "s" where "s" would be arc length, I would get "N". Right?
But, am I doing something wrong?

http://tinypic.com/r/bfqo7m/5
No img codes? Really?
Perhaps I am misunderstanding this. Are you saying that the pressure, P, is constant on the surface of the surface? If not you need to give the pressure function. If it is, then the total (vector) force is 0 because the force in one direction cancels the force in the opposite direction. The total (scalar) force is P times the total area the pressure is applied to. For the whole cylinder that is P times where r is the radius of the cylinder and h is the height of the cylinder.
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July 17th, 2013, 08:58 PM   #4
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Re: Integrate vectors along part of the circle

Hi and thanks.

Yes, the pressure is constant . It is applied on cylindrical surface as on the sketch. The force is not 0 because while p*sin theta components cancel each other, sum of p*cos theta should give N. What I need is, if I'm not wrong is double integral first integral from 0 to theta of p*cos(theta) then the along length of the surface (cylinder height) from 0 to L which is constant anyway. Correct?
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