Laminar Flow in a Helically Coiled Pipe

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 which appears in the inclination of the flow pattern at large values of the parameter D1. Here, D1 = (C*a*3/ v*2ρ*)(2a*cos2β/R*)1/2, where C* is a costant pressure drop along the pipe center-line, v* is the kinematic viscosity, ρ* is the density of the fluid and β 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.