On the theoretical calculation of friction factors for laminar, transitional, and turbulent flow of newtonian fluids in pipes and between parallel plane walls



Various modifications of the Prandtl mixing-length model for turbulent momentum transport in pipes and between parallel plane walls are discussed. The most complete modification, due to Gill and Scher, is improved by replacing one of their two empirical constants by a theoretically calculable parameter. The new theory is compared with experimental data from the literature and found to reproduce frictional resistance data accurately for all values of the Reynolds number. It is somewhat in error for velocity profiles at high Reynolds numbers, but accurately reproduces velocity profile data in the transition region. The new theory represents the first accurate semi-theoretical calculation of frictional resistance coefficients for all regimes of flow (laminar, transitional, and turbulent) for both pipes and parallel plane ducts, and of velocity profiles in the transitional flow regime in either geometry.