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Math Help - Fluid Force Problem

  1. #1
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    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.
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  2. #2
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    Quote Originally Posted by vReaction View Post
    "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.
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