Navier-Stokes Solutions for Accelerating Pipe Flow—A Review of Analytical Models

This paper reviews analytical solutions for the accelerated flow of an incompressible Newtonian fluid in a pipeline. problem can be solved one two ways according to (1) imposed pressure gradient or (2) rate. Laminar presented number publications concern cases where driving mechanisms are described by simple mathematical functions: (a) impulsive change; (b) constant (c) ramp change, etc. The adoption more complex and realistic description rate will associated with profound complexity final solution. is particularly visible help universal formula derived several researchers over years discussed this paper. In addition strictly defined laminar flow, interesting extension theory underlying analysis turbulent pipe flows (TULF model developed García Alvariño). TULF extends Pai than 60 ago, which has been previously used steady only. extend simplified two-dimensional Navier–Stokes equations not only study behavior liquids during accelerating but they also test accuracy commercial CFD codes.