Developing flow in circular conduits: transition from plug flow to tube flow

A numerical solution of the complete Navier–Stokes equations of motion by means of an implicit finite-difference method is presented for the following developing-flow problem: a piston forced with constant speed through an infinitely long tube of circular cross-section. The transition of the velocity profile of an incompressible isothermal Newtonian fluid from the plug-flow profile in front of the piston to the parabolic profile of developed flow is analysed. Streamlines, vorticity distributions, velocity profiles, the excess pressure drop and the entrance length are given for Reynolds numbers from 0 to 800.