# hydrostatic force problem

• Dec 4th 2009, 03:46 PM
yoman360
hydrostatic force problem
I got this problem wrong and I need help because I don't know what I did wrong.

My answer: 2666.67 lb
Correct answer: 2133.3 lb

Here's the question:
A trough is filled with water and its vertical ends have the shape of the parabolic region in the figure. Find the hydrostatic force on one end of the trough.

http://i595.photobucket.com/albums/t...ceparabola.jpg

Here is my attempt:
When units are in feet, Force=δdA
Where δ=62.5 $lb/ft^3$
d= depth of the water
A= area

so I start of by finding the equation of the parabola by drawing axes on the picture.

http://i595.photobucket.com/albums/t...rabolaaxis.jpg

By looking at the graph I can tell the equation will look something like
$y=Cx^2+0$ //where C is a constant
using points on graph I get
$4=C(4)^2$
4=16C
C= $\frac{1}{4}$ or 0.25

I get $f(x)=0.25x^2$

Next what I did was find the area
$A= \int_{-4}^4 0.25x^2 dx$

I integrated and i got

$A=\frac{32}{3} ft^2$

Now that I have found A i can plug all into the Force formula
F=δdA
=(62.5 $lb/ft^3$)(4ft)( $\frac{32}{3} ft^2$)