Quadratic approximations for pipe friction

This paper develops quadratic approximations to the classical models of Darcy–Weisbach and Hazen–Williams for frictional head loss in water pipes. Key elements of the technique are selecting the approximation domain and minimizing the relative error. A comparison for individual pipes over a range of diameter, roughness, and Reynolds number showed that the approximation provides accuracy consistent with the experimental error in the classical equations. Two benchmark water distribution networks are also considered. In these systems, flows and pressures computed using the approximation were consistent with simulations using the classical models. Applications of the approximation include mathematical optimization problems where polynomial expressions are desirable.