Darcy Friction Factor Equations for Small-Diameter Pipes in Lateral Irrigation Systems: An Experimental Study

Highlights Polyethylene tubes for lateral lines present a smooth pipe flow. Blasius equation still presented high confidence estimates of the friction factor. A previous modification in the Blasius equation presented the best results of the study. ABSTRACT. The accurate determination of head loss is fundamental to the design of efficient pressurized piping systems, especially in the agricultural sector, where the performance of irrigation systems depends on precise hydraulic calculations. The Darcy-Weisbach equation is integral to the calculation of the Darcy friction factor (f) with numerous formulas for different scenarios. Given this context, this study sought to bridge the knowledge gap by experimentally investigating head loss in small-diameter polyethylene pipes commonly used in drip irrigation and critically evaluating the extant formulas for estimating f. A total of 18 equations were evaluated to determine the most accurate estimation of the f. We selected pipes with internal diameters of 14.2, 16.0, and 18.6 mm to represent a size range typical of irrigation systems. Here, we measured flow rate, temperature, and friction head loss for Reynolds numbers of 4000 and above, ensuring robust coverage of common operational ranges. Our findings revealed that these pipes behaved as hydraulically smooth tubes. All tested equations reliably estimated f, with RMSE values below 0.002 and only one formula exhibiting a relative error above 5% across its application range. Established equations such as Colebrook-White and Blasius each provided excellent f estimations. Additionally, the Jardim et al. equation demonstrated promising results, aligning closely with experimental data. This research validates established hydraulic principles in the context of modern irrigation technology and sets the stage for future advancements in computational fluid dynamics and its practical applications. The findings of this study could significantly influence the design and optimization of localized irrigation systems, potentially leading to resource conservation and improved agricultural productivity. Keywords: Drip irrigation, Head loss, Polyethylene, Turbulent flow.