The following is the well established formula available in many books:

If ρ = f(x,y) is the pressure at (x,y)

The center of pressure:

x=  ∫∫ ρ.x dxdy   /   ∫∫ ρ dxdy  

      E                    E

and,

y=  ∫∫ ρ.y dxdy   /   ∫∫ ρ dxdy  

      E                    E

My question is, can this formula be extended in 3D, for example, if ρ = f(x,y,z) is the pressure at (x,y,z), is the following true, for center of pressure? If the following is correct, please send me a full ref where such a formula is stated.

x=  ∫∫∫ ρ.x dxdydz   /   ∫∫∫ ρ dxdydz  

      V                       V

y=  ∫∫∫ ρ.y dxdydz   /   ∫∫∫ ρ dxdydz  

      V                       V

and,

z=  ∫∫∫ ρ.z dxdydz   /   ∫∫∫ ρ dxdydz  

      V                        V

Thanks, Soumyajit Mukherjee