Find the hydrostatic force on one end of the tank if it is filled to a depth of 8 ft.

  1. 1. The problem statement, all variables and given/known data
    A large tank is designed with ends in the shape of the region between the curves y =(1/2)x^2 and y = 12, measured in feet. Find the hydrostatic force on one end of the tank if it is filled to a depth of 8 ft with gasoline. (Assume the gasoline's density is 42.0 lb/ft^3).

    This is a section on applications.

    2. Relevant equations

    I'm not sure if this is precisely all I need.

    Force F = ρgdA (g gravity, d depth, A area)

    3. The attempt at a solution

    (42.0)(9.8) ∫ sqrt(2y) (8-y) dy on [0,8]

    823.2 ∫ 8 sqrt(2y) - ysqrt(2y) dy on [0,8]

    823.2 [ 16sqrt(2)/3 y^(3/2) - 2sqrt(2)/5 y^(5/2)] on [0,8]

    which evaluates to 56, 197.12 lb

    I always get scared when I deal with word problems and end up with such large answers.
     
    Last edited: Mar 23, 2012
  2. jcsd
  3. tiny-tim

    tiny-tim 26,054
    Science Advisor
    Homework Helper

    hi sushifan! :smile:
    yes, that looks ok :smile:, except

    i] you've only included half the tank (the x > 0 side)

    ii] erm … feet, lbs, 9.8 ? :redface:

    iii] i'm not familiar with these units, but i wonder, do you need g at all if you're using lbs ? :confused:
     
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