Equation 11-47:

we make the following claim for the last term on the right of equation (1147) : S(n^)dA=0 for flow across an open surface when the cross sectional area is symmetrical around the flow axis. Consider a cylindrical pipe with radius R and some velocity profile vz(r) for an incompressible fluid, where the pipe is aligned along the z axis. Prove the claim is true. Sin^iTidA=Si(n^i)PidA+typicallyzeroSi(n^i)idA