This paper reports on a numerical study of the friction factor-modified Reynolds number product, f x Re-M, for fully developed, laminar flows of pseudoplastic and dilatant fluids in rectangular ducts. Constitutive equations for the apparent viscosity that span from the low shear rate Newtonian region through the high shear rate Newtonian region were utilized, and a shear rate parameter was defined that determines the flow regime where the duct is operating. Numerical results for f x Rem in all flow regimes are included along with correlation equations. Errors associated with applying power law solutions to flows of weakly non-Newtonian fluids are discussed. (C) 2007 Elsevier Ltd. All rights reserved.