Turbulent flow of a viscoelastic fluid through smooth and rough pipes

In order to investigate the suitability of various models for explaining the Toms effect, the material equations of the Maxwell and the Walters models of viscoelastic fluid are used as the basis for describing the turbulent motion of a viscoelastic fluid in a smooth pipe. The equations of motion were numerically integrated with the aid of Van Driest's mixing length formula, and the results were compared with available experimental data. The variations of the pipe friction coefficient with Reynolds number and elasticity modulus obtained from the Maxwell model are in closer agreement with experimental data than those obtained from the Walters model. Corresponding results were obtained for a rough pipe, and a considerable drag decrease in a wide range of Reynolds numbers is also revealed here.