# Fluid Force Problem

• Mar 30th 2010, 06:14 PM
vReaction
Fluid Force Problem
"You plan to store mercury (weight-density 849 lb/cubic ft) in a vertical rectangular tank with a one foot square base side whose interior side wall can withstand a total fluid force of 40000 lbs. About how many cubic feet of mercury can you store in the tank at any one time?"

I start out with F=PA. I get P to be 849(9.8)x and A to be 1(delta x). I'm not sure where to introduce a coordinate axis though. After looking at it, it seems like the problem is easier than I'm making it but these problems are supposed to be complex. A push in the right direction would be appreciated. Thanks.
• Mar 31st 2010, 03:24 AM
HallsofIvy
Quote:

Originally Posted by vReaction
"You plan to store mercury (weight-density 849 lb/cubic ft) in a vertical rectangular tank with a one foot square base side whose interior side wall can withstand a total fluid force of 40000 lbs. About how many cubic feet of mercury can you store in the tank at any one time?"

I start out with F=PA. I get P to be 849(9.8)x and A to be 1(delta x). I'm not sure where to introduce a coordinate axis though. After looking at it, it seems like the problem is easier than I'm making it but these problems are supposed to be complex. A push in the right direction would be appreciated. Thanks.

If you set up you coordinate axes so that x= 0 at the top of the mercury and increases downward, then the pressure at depth x will be 849 x. The total force on that side will be $\int_0^D 849 x dx$ where D is the depth of the tank.