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Find the hydrostatic force on one end of the tank if it is filled to a depth of 8 ft.
Tags: force distance
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Mar23-12, 03:45 PM
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.
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