We previously developed a new, coupled‐source–sink modeling approach for evaluating an upper bound to the relative water uptake rate (water use efficiency) for two‐ and three‐dimensional geometries. Because the formulated water‐flow problem is linear, the relative water uptake rate for any given collection of point (or line) sources and point (or line) sinks is determined by superposing the appropriate solutions while assuming maximum suction at the soil–sink interfaces. In this study, analytical expressions for the maximum possible water uptake rates were determined for various two‐ and three‐dimensional configurations of surface water sources (emitters) and subsurface point (or line) sinks that represent plant roots. Relative water uptake rates were computed for cases of interacting source–sink couples and also for cases of unequal numbers of sources (emitters) and sinks (plants). The water uptake rate can be determined by using as few as three system parameters: the depth and radius of the conceived rooting zone, the soil sorptive number, and design parameters that represent the distances between sources and sinks within rows or between drip lines. Sample computations demonstrate and elucidate the effects of these parameters on the relative water uptake rate of plant roots beneath various configurations of on‐surface water sources. For all scenarios, the water uptake rates increased monotonically with increasing radius of the conceived rooting zone or with decreasing separation between emitters or drip lines. We suggest that the calculated relative water uptake rate be used as a design criterion for trickle irrigation systems.