Calculating Forces on a Tank with Flat Ends Using Integration

[Jason03]

I am working on the problem below that is confusing me. I am not sure of how to approach the center of pressure and resultant force. I attempted the problem using the formulas for a rectangular wall but I am not sure if its right. The problem asks for the pressure acting against the FLAT ends of the tank. It wants the diagram labled from the side view so that's why I would think this problem would be approached as if it were a rectangle plus a circle for the ends. Any suggestions would be great.

http://i674.photobucket.com/albums/vv106/jason03_2009/prob1-1-1.jpg

http://i674.photobucket.com/albums/vv106/jason03_2009/1-1-1.jpg

 

[Jason03]

any ideas?

 

[Dr.D]

I think the best way to attack this problem is to draw a differential area element on the end of the tank, and integrate the pressure over that area find the force. You will also need to find the moment of that force so that you can determine where the net force acts.

This is going to be a bit of integration, and it may work best to break it into parts. I would use rectangular coordinates to do the integration over the rectangular part of the end, and I would use polar coordinates to do the integration over the half circles to either side. With that, it will be a bit of dog work, but nothing really too difficult.

I would not try to use canned formulas, but rather I would suggest that you simply do the integrations. You will learn a lot more that way.