Effects of rolling on laminar frictional resistance in tubes

The laminar velocity distribution in tubes in rolling motion is obtained by properly simplifying the laminar flow equations. The method of Sexl, 1930 and Uchida, 1956 for analyzing the effect of periodic pressure on laminar flow is partly adopted. The influence of initial velocity on the velocity in rolling motion fades away quickly, while the periodic pressure due to rolling motion controls the velocity variation gradually. The effects of several parameters on the velocity profile in the cross-section are investigated. The rolling radius and amplitude only affect the velocity in a specified proportion, and the velocity profile shape remains unchanged. The tube radius, rolling period and fluid viscosity not only affect the velocity peak, but also the profile shape. The tube radius and fluid viscosity could limit the effect of rolling motion on the flow. The laminar friction coefficient in rolling motion is also obtained. The laminar friction resistance and factor for two special cases are investigated.