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

by sushifan
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sushifan
#1
Mar23-12, 03:45 PM
P: 27
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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tiny-tim
#2
Mar24-12, 04:40 AM
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tiny-tim's Avatar
P: 26,157
hi sushifan!
Quote Quote by sushifan View Post
(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
yes, that looks ok , except

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

ii] erm feet, lbs, 9.8 ?

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


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