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The author presented a methodology for calculating the hydraulics of trail tubes for center-pivot irrigation systems. While he mentioned several possible difficulties with trail tube irrigation, and stated that they have potential benefits in energy saving and improvements in water-use efficiency, additional clarification and analysis are required before the procedures he presented can be used for the rational design of such systems.
First and most importantly, a potential error in the analysis should be mentioned and discussed. The author used the two-term infiltration model of Philip to describe the water intake beneath a center-pivot irrigation system. The assumption of one-dimensional infiltration with surface saturation at time zero is implicit in the application of this infiltration model, though not stated by the author. Thus, for this equation to be satisfactorily used for the case of parallel trail tubes described in the paper, the tubes must be close enough together to provide sufficient lateral water movement from the tubes to simulate one-dimensional flow. The trail tube spacing necessary to insure the one-dimensional conditions is, of course, a function of the flow rate of the trail tubes and the depth of irrigation to be applied (or speed of the system), as well as the soil properties. The flow conditions existing in trail tube irrigation, while not precisely the same, are similar to the unsteady flow from parallel line source trickle irrigation systems. An analysis of these types of irrigation systems, at least under time-dependent linearized conditions, has been described by Lomen and Warrick (11).