## Fluid Force

A circular "pressure release gate" is located in the vertical face of a dam. The radius of the gate is 2 metres and the gate is positioned so that its top lies 5 metres below the surface of the water held in the reservoir behind the dam.Find the total fluid force acting on the door of the gate, when it is in a fully closed position.

My attempt to solution:

According to the solutions manual when l evaluate one of my integral l should be zero. But the problem is that when l evaluate my two integrals there isn't one which gives me a zero. Where did l make a mistake ?