Calculating Fluid Force of Triangle Submerged in Water

[Blonde1551]

Homework Statement

Find the fluid force of a triangle with base of 6 ft and height of 4 ft submerged vertically into a body of water,vertex down, to a depth of 3 feet.

Homework Equations

from c to d W ∫ h(y) L(y)

The Attempt at a Solution

I set up the triangle on an x and y axis, splitting it down the middle. I made h(y) = -y and
L(y)= 2 (3/4(y+7)) (I found the equation of the line for the side of the triangle and multiplied it by 2). W is equal to 62.4

I set the problem up like this -6/4 x 62.4 times the integral from -7 to -3 of y(y+7).
When I integrated this I got 3244.8 lbs. I just want to know if I did this correctly. If not, please explain where I went wrong.

 

[paisiello2]

Looks like you got it to me.

The only thing unconventional to me is using -ve y in your set up. Usually in hydrostatic problems y is just taken as +ve in the down direction. Using your convention the force should have come out -ve mathematically. But as long as you are consistent it didn't matter.