A simplified Lagrangian-based theory and practical computation of the longitudinal distribution of fertilizer injected into the inflow to a border strip, basin or furrow is presented as an adjunct to an existing surface-irrigation simulation model. The simplification consists primarily in the assumption that the chemicals are non-reactive and move by advection of the flowing water and that no mixing, dispersion, or diffusion of the chemical takes place. In a corollary calculation, the composition of runoff, in terms of water fractions selected for fertilizer injection, is also simulated. Comparisons of calculated post-irrigation longitudinal distribution of infiltrated chemical are made with the results of a complete advection-diffusion model that had already been validated in the field for injection of fertilizer pulses into the furrow inflow.