Entropy generation in fluid flow
In the context of steady flow through a pipe with friction we learned that the entropy generation rate is directly proportional to the mechanical power needed to push the flow through the pipe. The mechanical power is proportional to the end-toend pressure drop AP and, in its tum, the pressure drop is proportional to the wall shear stress 'to acting over the wall-fluid interface. Because the pipe (control volume) shown in Figure 2.9 is stationary, a force balance in the longitudinal direction dictates
If, as in most engineering applications, the fluid is newtonian, the wall shear stress is
where (autay) 0 is the gradient of longitudinal velocity normal to the wall, evaluated at the wall, and Jl is the viscosity.