Fluid flow in the entrance region of a duct of circular sector

The laminar flow in the entrance region of a circular sector is investigated by linearizing the governing equation and considering the velocity as the fully developed velocity plus a difference velocity. The non-linear transformation is determined "after the fact" in that the axial coordinate is stretched, the problem solved in the transformed coordinate system and the "stretching factor" then determined by equating two expressions for the pressure gradient. There are no experimental results with which to compare, however, the results compare very favorably with similar analyses in a circular tube.