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A square plate of side 'a' ft is dipped in a liquid of weight density 'p' lb/ft^3. Find the fluid force on the plate if a vertex is at the surface and a diagonal is perpendicular to the surface.

I understand the surface has a diamond shape--I have tried dividing it into two triangles and finding the fluid force for each and adding them but have been unable to obtain the textbook's answer.

The two integrals I get are:

fluid force 1 = integral (limits: a*sqrt2/2 and 0) p * 2h^2 * dh

fluid force 2 = integral (limits: a*sqrt2 and a*sqrt2/2) p * ( h + (a*sqrt2)/2) * (2h) * dh

The book's answer is (a^3*p)/sqrt2.

Thanks,

Dean