Maximum Lateral Expansion of Wetting Bulbs from Buried and Surface Point Sources: Implications for Drip Irrigation Design

In surface and subsurface drip irrigation systems, predicting the size expansion of the wetting bulb and the irrigation time is mandatory for water saving, and helps drive their design and scheduling, which cannot ignore the soil hydraulic properties. Toward this aim, different hydrological models that consider the soil hydraulic properties, highly affecting the design choices, have been suggested. In this paper, we focused on the model presented by Philip, who provided dimensionless analytical solutions for bulb geometry. The equations presented in the Philip model, for special cases, i.e., for the horizontal size at the burial plane and along the vertical direction, are very simple and were applied by many researchers. However, for an accurate design of emitters’ spacing, the maximum lateral expansion of the bulb, which is below the burial plane and was not provided by Philip, is required. In this paper, the Philip model was revisited, and the maximum lateral expansion of the wetted bulb for both buried and surface point sources was addressed. The new but long solutions were also approximated by simpler equations that fit the analytical ones well. Important implications in drip irrigation engineering arose. Design relationships that make it possible to calculate the irrigation time, the spacing, and the burial depth of emitters to wet a desired rooting depth were derived. Applications showing the important effect of the soil hydraulic parameters were performed, and the results were tested by using the analytical solutions of the bulb considered in the Philip model and by applying the exact but numerical demanding Richards equation via Hydrus 2D/3D.

This paper aims to provide an easy-to-apply tool for surface and subsurface drip irrigation, to design the emitters’ spacing, their depth (in the case of buried emitters), and the irrigation time. The latter is particularly important because exceeding the irrigation time determines wastewater as deep percolation, whereas low values of the irrigation times determine the underwatering of the root zone. Compared to other design procedures, the work is based on the analytical solutions first introduced by Philip; thus, no calibration coefficients are required, but physical parameters that describe the soil hydrological properties on which the design parameters depend. Because simplifying assumptions are adopted, errors are expected that more sophisticated design methodologies do not commit, but the latter are not easy to apply for practical use. Further research is needed to investigate this issue and to provide correction factors that hopefully would improve the results of this work.