Abstract
For a viscous fluid flowing very slowly near a pipe inlet and exit when the mass forces of Navier-Stokes equations are negligible, the author solved strictly the equations of motion and obtained the stream function, the velocity distribution, the coefficient of skin friction and the pressure gradient. The results are as follows. (1) When the radius of a rounded pipe is large, the velocity distributions at a straight pipe entrance are near-parabolic. When it is small, they are close to the mean velocity profile. Also, when it is zero, i.e. the entrance is square-edge, the streamlines and the velocity distribution agree with Sampson's solution for a thin orifice. (2) The pressure gradient on the rounded pipe surface is large near a straight pipe inlet, and is small at a large distance from it. Either for inflow or for outflow, separation can not occur as the pressure continues to decrease due to viscosity.
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