Fig. 1. Contrast between the classic solution to the pipe entrance problem (top left and middle panels) invoking uniform velocity at the entrance as boundary condition, with the more realistic boundary condition of constant volumetric outflow rate (bottom left and right-most panels). Plotted are isopleths of flow speed at two different Reynolds numbers (Re). Both the axial coordinate (z) and the radial coordinate (r) are scaled by the pipe inner diameter (D). With the more realistic boundary condition, substantial flow adjustment occurs upstream of the pipe entrance (Jumars 2013).
Peter A. (Pete) Jumars, Last Updated 12 April 2013