Design Emission Uniformity of Horizontal Tapered Drip Laterals from the Normalized Pressure Head Distribution Approach

A new analytical solution is developed to calculate the hydraulic emission uniformity ($E{U}_h$) of horizontal tapered drip laterals. Our methodology builds upon normalizing the pressure head profiles along each segment of the lateral. Results indicated that the $E{U}_h$ remains fairly consistent regardless of the total lateral length if a fixed pressure head tolerance ($\delta$) is assigned in the design process. Instead, the $E{U}_h$ is primarily influenced by the number of emitters on each segment, their diameter ratio, and the emitter exponent $x$. Employing tapered laterals for any given values of $\delta$ and $x$ enhances energy conservation compared to using single diameter laterals. However, it may lead to a reduction in the $E{U}_h$, particularly when the number of emitters in the smaller diameter segment is low relative to the total number of outlets. It was concluded that the coefficient of variation in emitter pressure heads $CV$ and $E{U}_h$ exhibit a nonlinear behavior in the case of tapered laterals, whereas it has been previously established as linear for single diameter laterals. Interestingly, when applying the newly formulated relationships for $E{U}_h$ and $CV$ while keeping the same diameter for both segments, the results align with those previously obtained for single diameter laterals. Validation of the proposed $E{U}_h$ model against the precise stepwise solution revealed a maximum absolute relative error of $\approx 1\%$. When excluding the fully laminar flow condition ($x=1$), relative errors typically remained below 0.5%. The proposed model could serve as a foundational framework for designing tapered laterals to achieve a targeted uniformity level in future studies.