Geometric overlapping coefficients for calculating the required emitters per plant in drip irrigation

Abstract

The designer of irrigation systems must consider a complex combination of emitter type, emitter uniformity, hydraulics, topography, desired water distribution, crop salt tolerance, water requirements, water quality, fertilizer injection, soil salinity, cultural practices, and other site-specific conditions. In contrast to the approaches applied for the hydraulic design of irrigation installations, there is not a clear, general and consolidated design criterion for calculating the number required emitters per plant. In most cases, given the wide spectrum of possible scenarios, only guideline recommendations can be found, and the final decision is often based on the subjective experience of the designer or grower. This paper aims at revising, clarifying and refining the existing published guidelines and methodologies for estimating the required emitters per plant in drip irrigation, focussing on the Montalvo approach. The agronomic design should satisfy, among others, two specific conditions: (i) the emitters should wet at least a minimum threshold of the soil area (or volume) corresponding to the plant for ensuring a proper development of the roots; (ii) overlapping between emitter bulbs is required for merging wetted volumes and avoiding salt concentration near the root zone. Relying on this basis, a thorough theoretical geometric analysis of the overlapping between wet bulbs of contiguous emitters is carried out. As a result, Montalvo's overlapping coefficients are deduced here. This author assumes an identical net wetted area for all emitters in the laterals, but it can be stated that the overlapping areas between emitters differ in extreme emitters and interior emitters, as well as in configurations with one lateral per plant row and two laterals per plant row. Therefore, this study proposes new formulations for the computation of the overlapping coefficient, which need to incorporate the number of emitters as an additional variable, as well as to distinguish between the presence of one or two laterals per plant row, and between grouped and non-grouped emitters. In one lateral per plant row, the original overlapping coefficient underestimates the net wetted area by one emitter and thus overestimates the theoretical number of required emitters. In the case of two laterals per plant row, the original overlapping coefficient overestimates the net wetted area in the interior emitters, and thus underestimates the theoretical number of required emitters per plant. The presented formulations are applied in different practical examples covering a wide range of scenarios. The results allow a general overview of the influence of the soil type, the emitter flow rate, and the selected overlapping ratio in the number of required emitters per plant. The revision of guidelines and methods presented here, complemented with other experimental results and models of soil water dynamics under drip irrigation, might contribute to a better decision making of designers and field engineers.