Tapered drip laterals for sloping agricultural fields

Tapered drip laterals offer a promising solution to enhance hydraulic performance and reduce energy consumption in horizontal or sloping agricultural fields. However, their design typically relies on iterative numerical procedures, which limit their practical implementation. This study develops a fully analytical framework for the hydraulic design of dual-diameter tapered drip laterals installed on downhill slopes. The methodology is based on a normalised pressure head formulation that enables the explicit derivation of pressure head distribution and directly embeds pressure head tolerance criteria to limit emitter flow-rate variability across the entire lateral, without requiring iterative computations. A new pressure head tolerance is introduced at the diameter-change point, DCP, leading to three distinct pressure head distribution patterns and providing a systematic basis for selecting DCP and upstream diameter. The analytical procedure is validated against the exact step-by-step numerical method that relaxes the assumption of uniform emitter discharge. Relative errors in characteristic pressure heads remained below 0.81 %, while deviations in hydraulic performance indicators were negligible for practical design purposes. Application to representative case studies demonstrates that properly designed tapered laterals can reduce the required inlet pressure head by more than 60 % compared with equivalent one-diameter configurations, resulting in substantial energy savings and reduced pumping requirements. The analytical framework provides a practical and reliable tool for optimising the hydraulic and energetic performance of tapered drip laterals on sloping terrain.