Fully developed pressure driving flow in a duct with EPR

1 Fully developed pressure driving flow in a duct with EPR 

the complete Navier—Stokes equations with the discontinuous force (1.7) can be reduced to two ordinary differential equations each valid on adjoining intervals  

The problem thus formulated generalizes the textbook problem of the Poiseuille flow and so gives a parabolic velocity distribution and a linear shear distribution for h = 0, [380, 566]  

Maximum values of the velocity (taking place on the axis z = H) and that of shear (on the wall) 

The auxiliary parameters r0 = r(0), rh = t(S) (the shear on the duct wall and on the roughness interface), Uh = U(S), and Uh = U( 1) (the slip velocity on the EPR level and the maximum velocity on the flow axis) have been found as follows  

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