Hydrostatic Force

[HanRam]

Here's my problem:

Find hydrostatic force on the vertical side of the tank that has the shape of the region bounded by the curves y=2x[sup:2c5ebr4v]2[/sup:2c5ebr4v], y=8. Assume that the tank is full of water.

My problem is I can't come up with the integral that needs to be evaluated. Here's the best I could come up with (I integrated from 0 to 2):

My final answer was 313600 N. I really do not feel confident that I did it right though, so any help would be appreciated.

 

[galactus]

The depth is \(\displaystyle h(y)=8-y\).

From \(\displaystyle y=2x^{2}\Rightarrow x=\sqrt{y/2}\)

The length of the region is then \(\displaystyle L(y)=2\sqrt{\frac{y}{2}}\)

\(\displaystyle F=\int_{0}^{8}(8-y)2\sqrt{\frac{y}{2}}dy\)

Multiply by the weight density.