Modelling the Darcy–Weisbach friction factor and the energy gradient of the lateral line*

Abstract

The objective was to adjust explicit mathematical models to determine the friction factor ( f ). Besides, an adaptation of the Blasius model is presented and an application of the Darcy-Weisbach equation to estimate the energy loss along the lateral line for four types of microsprinklers. f was determined by the model of Offor and Alabi and the model of Blasius for velocities between 0.5 to 3.0 m s À1 and internal pipe diameters of 0.0130, 0.0161, 0.0206, 0.0270, 0.0288, and 0.0368 m. The friction factor determined by Offor and Alabi was associated with the pipe diameters utilizing regression, and based on that an adaptation to the Blasius model was proposed. From the results of f, the energy and flow gradient along the lateral line for four NaanDanJain microsprinklers was simulated. The models of Offor and Alabi, Blasius, and Adapted Blasius showed excellent precision in determining f. The results of unit head loss, determined by the three mathematical models, showed dispersion close to zero among the pairs, showing a high correlation between the models (R 2 = 0.99).The Blasius equation is the most suitable to be inserted into the Darcy-Weisbach model to determine the maximum length of the lateral line.