Center of a pressure?

Question

Help me to solve this,

Find the depth of the center of pressure of a semicircular area of radius a with its base in the surface and vertex downwards.

I have the answer.( 3pi a)/(16)

pls give me the proof.

Answer 1

The center of pressure is the point on a body where the sum total of the aerodynamic pressure field acts, causing a force and no moment about that point. Mathematically it can be said that the net pressure force on the body acts through this point. The net force applied at the center of pressure point produces the equivalent moment as the pressure field about any arbitrary point. Typically the center of pressure is referenced to the nose of the vehicle but other points may be selected.