VISCOUS-FLOW IN AXISYMMETRICAL PIPES WITH SLOW VARIATIONS

A solution is developed for viscous flow in pipes with axisymmetric cross-sections possessing slow variations in the longitudinal direction. This solution is constructed by embedding the intuitive idea that-such a flow should locally resemble Poiseuille flow into a systematic scheme of recursively defined successive approximations. An approximate solution in powers of a small parameter epsilon characterizing the slow variations is generated from the first few iterates to yield useful perturbation solutions for small Values of the product epsilon Re. Problems with and without specific pipe geometries are considered.