Modified Hazen–Williams and Darcy–Weisbach Equations for Friction and Local Head Losses along Irrigation Laterals

Abstract

In previous analytical approaches, the direct calculation of friction loss along a lateral is usually based on empirical power-form flow resistance equations, such as the Hazen–Williams and Blasius equations. The more generalized Darcy–Weisbach resistance equation is not usually applied since its friction coefficient varies along the lateral. In this paper, initially, the Darcy–Weisbach and Hazen–Williams equations are systematically compared, leading to a correction form for the Hazen–Williams coefficient. In addition, a more accurate procedure assuming a power function form for the Darcy–Weisbach equation along irrigation laterals is also proposed. The systematic analysis of various typical flow pipe irrigation situations (e.g., sprinkler irrigation laterals of linear or radial-center pivot displacement, trickle irrigation laterals, and manifolds) indicates that the friction loss along laterals calculated using the Darcy–Weisbach equation closely follows a discharge-power form function. The two empirical parameters of the power function depend on the specific pipe characteristics as well as the specific range of discharge values along the lateral. The proposed analytical solution is extended to incorporate the local head loss, the velocity head variation, and the outflow nonuniformity along sprinkler and trickle irrigation laterals. The suggested direct computation solution is demonstrated in two application examples of sprinkler and trickle irrigation laterals and compared with accurate numerical solutions.