Solved: Hydrostatic Force Calculation of Vertical Tank

[trekie4ever]

[SOLVED] Hydrostatic Forces

Any Help would be GREATLY appreciated. My grade depends on me understanding this.

Homework Statement

A tank contains freshwater. The end of a tank containing water is vertical and has the indicated shape. Explain how to approximate the hydrostatic force against the end of the tank by a Riemann sum. Then express the force as an integral and evaluate it.

Homework Equations

F=pgAd
A=wdx

The Attempt at a Solution

F= int 0->5 1000(9.8)2sqrt(100-y^2)(5)
98000*int 0->5 sqrt(100-y^2)
u=100-y^2
-1/2*du=dy
98000*int 75->100 u^(.5)
98000{(2/3)u^(3/2)} 75->100
64171414.85 N

 

[trekie4ever]

I figured it out finally...
The right answer should be 2.29x10^6. I actually did it right another way the first time.

F=(1000)(9.8)*int 0->5 (100-x^2)^.5(-2x)dx
=-9800{(2/3)(75^(2/3)-1000}0->5

U substitution works too... that's what I did hours ago, but I doubted my answer.


F=(1000)(9.8)(2)(5)*int 0->5 (100-x^2)^.5
=98000 int 0->5 sqrt(100-x^2)
u=100-x^2
-2dx=du
dx=-.5du
98000 int 75->100 u^.5
98000{(2/3)u^(3/2)}75->100