How Is the Resultant Force on a Submerged Plane Calculated?

[Stacyg]

Prove that the resultant force F on a plane surface of area A immersed vertically in a liquid of density (rho) is given by the equation:
F=rho.g.A.z
Where 'z' is the depth to the centroid of the plane area below the liquid surface level.


I under stand how F is found using this equation and how the force changes depending on the z value. But I don't know how to put this answer in a suitable way for my assignment.

Thanks

 

[dirk_mec1]

The pressure is given by $$p= \rho g \Delta h$$. The force F is given by $$F = pA$$. It's that easy!