Radial water infiltration–advance–evaporation processes during irrigation using point source emitters in rigid and swelling soils

SummaryIn this paper we investigate the dynamic water balance of radial flows during irrigation using point source emitters. The components of radial flows of this kind include infiltration simultaneously coupled to the storage and advance on the soil surface, and evaporation into the air while the source continuously supplies water. The soils we consider here can be rigid or swelling. Because the infiltration equations reported for both rigid and swelling soils have an identical mathematical structure, the analysis for rigid soils using Philip’s two-term infiltration equation applies to both swelling and rigid soils. As such, we emphasise that our analysis is applicable to both rigid and swelling soils. We first extend the radial Lewis–Milne equation (RLME) given by Rasmussen to analyse the radial flow mechanics by incorporating evaporation as a key component in the radial dynamic water balance. Then we present a set of four solutions of the RLME using Philip’s two-parameter infiltration equation and two-term and three-term equations for cumulative evaporation. With the two-term cumulative evaporation equation, we show that the three solutions yield a simple identical asymptotic formulae at large times, which can be used to design the area to be irrigated, or to derive the final infiltration rate, A, and the final evaporation rate, E2. Analyses show that evaporation plays an important role in the radial dynamic water balance at large times, and as expected it plays a minor role during the early stage of irrigation (small time solutions).