Thread: Fluid force on a submerged vertical plate

"Find the total force against the rectangular plate submerged vertically in a tank of water. The plate is 2' (vertical) by 5' (horizontal) and is touching the bottom of a tank of water that is 6 feet deep."

The formula for this is the integral from a to b of (strip depth)(strip length)dy, and for water multiply this by 62.4 lb/ft^3.

I put the strip depth is -y and the limits of integration are from -6 to -4 for the integral of (-y)(5)dy. This is incorrect. What am I doing wrong?

That should be correct except you get a negative answer.

$\displaystyle 62.4\int_{4}^{6}5xdx=3120 \;\ lbs$

But
$\displaystyle 62.4\int_{4}^{6}5xdx=3120 \;\ lbs$ is the same as

$\displaystyle 62.4\int_{-6}^{-4}-5xdx=3120 \;\ lbs$, both positive.

I missed this question on a test, but the question only asked to set up the integral. Maybe my teacher set up the integral a different way, but both ways give the same answer. I'll ask her about it the next time I see her.