Total energy loss assessment for trickle lateral lines equipped with integrated in-line and on-line emitters

The accurate evaluation for the pressure head distribution along a trickle (drip) irrigation lateral, which can be operated under low-pressure head, dictates to precisely determine the total energy (head) losses that incorporate the combined friction losses due to pipe and emitters and, the additional local losses, sometimes called minor losses, due to the protrusion of emitter barbs into the flow. In routine design applications, assessment of total energy losses is usually carried out by assuming the hypothesis that minor losses can be neglected, even if the previous experimental studies indicated that minor losses can become a significant percentage of total energy losses as a consequence of the high number of emitters (with reducing the emitter spacing) installed along the lateral line. In this study, first, simple mathematical expressions for computing three energy loss components—minor friction losses through the path of an integrated in-line emitter, the local pressure losses due to emitter connections, and the major friction losses along the pipe—are deduced based on the backward stepwise procedure, which are quickly implemented in a simple Excel spreadsheet, to rapidly evaluate the relative contribution of each energy loss component to the amount of total energy losses. An approximate combination formulation is finally proposed to evaluate total energy drop at the end of the lateral line. For practical purpose, two design figures were also prepared to demonstrate the variation of total friction losses (due to pipe and emitters) with emitter local losses, and the variation of pipe friction losses with emitter minor friction losses, versus different emitter spacing ranging from 0.2 to 1.5 m, and various total number of emitters, regarding two kinds of the integrated in-line emitters. Comprehensive comparison test covering two design applications for different kinds of integrated in-line and on-line emitters indicated that the present mathematical model is simple, can be easily adaptable, but sufficiently accurate in all design cases examined, in comparison with the alternative procedures available in the literature.