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A 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.

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A generalized equation describing the flow of any time-independent purely viscous non-Newtonian fluid in packed beds and porous media is proposed. The equation, which is expressed in terms of the Kozeny constant k i and the bed tortuosity T, unifies the three well-known packed bed models due to Blake, Blake-Kozeny and Kozeny-Carman within a general framework which also brings out their differences. The accuracy of each of the three bed models is assessed by comparing the predictions with existing experimental results, and is found to depend on the rheological properties of the fluid. The Kozeny-Carman model appears to give the best overall description of the flow of pseudoplastic (shear-thinning) fluids in packed beds and porous media although the Blake-Kozeny model gives a better representation for the high shear-thinning fluids. consistency index defined for circular pipe flow L length of packed bed; subscript e denotes equivalent length n flow behaviour index in power-law model n* index defined by eq. (25) n' index defined for circular pipe flow P = P + Q 9 h, hydrostatic potential q = e (u), superficial average velocity qw = e ~7~, superficial effective velocity at the wall R h hydraulic radius