LAMINAR FLOW IN A HELICALLY COILED PIPE.

Abstract

The governing equations for a steady fully developed laminar flow in a helically coiled pipe are derived and the solutions are obtained for small values of a*/R*, where a* is the radius of the pipe cross-section and R* is the radius of the circular cylinder on which the pipe center-line is helically coiled. The torsion of the pipe center-line causes asymmetry of the flow pattern in a pipe cross-section, an example of which appears in the inclination of the flow pattern at large values of the parameter D//1. Here, D//1 equals (C*a***3/v***2 rho *)(2a*cos**2 beta /R*)**1**/**2, where C* is a constant pressure drop along the pipe center-line, v* is the kinematic viscosity, p* is the density of the fluid and beta is a constant angle which the normal to the helix makes with the generating line of the cylinder. It is concluded that the resistance formula for a toroidally curved pipe is also applicable to a coiled pipe, if the curvature of the coiled pipe is used instead of that of the toroidally curved one.