Non‐newtonian flow through open channels

Abstract

AbstractA general method is proposed for prediction of the flow rate and maximum velocity in the isothermal, steady, uniform, laminar flow of any incompressible, time‐independent non‐Newtonian fluid in straight open channels of arbitrary cross section. The method requires only a knowledge of two geometric coefficients and a function of shear stress, used to characterize the behavior of the fluid model. The slip effect at the solid boundary has been taken into consideration. Numerical values of the geometric parameters have been determined for flow through an inclined plane of infinite width, semi‐circular, semi‐elliptical, rectangular, and 90° and 60° symmetric triangular open channels. Applications have been made to various non‐Newtonian fluid models such as the power‐law, Bingham, Ellis, Meter and the Reiner‐Rivlin general model. Numerical examples are presented.A generalization of the Fanning friction factor — Reynolds number is also presented. The problem of determining the point of transition from laminar to turbulent flow in the general case is examined, as is the problem of prediction of the friction factor in turbulent flow.