Fangmeier, D. D.; Abdel-Rahman, Hayder A. (The University of Arizona., 1981)
      A zero inertia mathematical model as described by Strelkoff and Katopodes (1977b) was used to simulate irrigations in blocked-end or ponded sloping borders. The model is based on the assumption that inertia is negligible. A linearization method was then used to decrease the difficulty and expense of the solution. The resulting mathematical expressions were solved with a double sweep technique. Border irrigations were simulated, using the model, for selected intake families (soil infiltration characteristics), required depths of infiltration, discharge rates, lengths, times of application, slopes, and roughness values. The output from the model, including the depth of infiltration, the maximum depth of flow at the upper end of the border, the maximum depth of ponding at the downstream end and the application efficiency, was used to develop the design charts for ponded sloping irrigation borders. These were combined with the operational input parameters to provide the design charts for a given intake family, slope and roughness. Since the same input parameters apply, the design charts developed can be used for ponded or free outflow borders. In cases of free outflow borders, ponding is replaced by runoff. Ponding can improve application efficiency over free outflow borders, provided that ponding affects a significant length of the border. Where runoff can not be reused, ponding or end-blocking a border strip is recommended. The maximum potential application efficiencies, on ponded borders, with adequate irrigation and minimum deep percolation were determined, with respect to intake family, required depth of infiltration, slope, roughness and length of run. A sensitivity analyses to evaluate the effect of infiltration showed that it is better to underestimate than to overestimate infiltration. The effects of roughness and slope on irrigation efficiencies and depth of ponding were also studied. A comparison of the Soil Conservation Service method for extended length, with blocked-end borders, and the maximum application efficiencies computed showed the SCS method to be satisfactory, provided that there is runoff adequate to irrigate the length extended.