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An analytical approach was developed to design a single uniformly sloping lateral in the micro-irrigation systems.Emission uniformity was used as the water application uniformity criterion.Energy relations based on the energy-gradient-line approach were revamped to account for the spatial variance of emitter outflow and the emitter connections local energy losses.Four pressure head grade line profiles were distinguished:uphill,horizontal,gentle downhill and steep downhill.Analytical expressions of emission uniformity by hydraulic variation for each pressure profile were developed based on the design variables:length and diameter of lateral,emitter spacing,emitter flow equation parameters,equivalent length characterizing local losses and ground slope.The design conditions for selecting emitter type,the number of emitters per plant and designing the diameter of the uphill and steep downhill laterals were also developed.The nonlinear equations for determining lateral diameter and lateral length were solved iteratively by using the built-in root-finding function of(Tools>Goal Seek…)in the calculation spreadsheet of Microsoft Excel.The procedures also provide the options to fix the design lateral diameter with the commercial standard size or fix the design lateral length based on the field size.The operating inlet pressure and maximum amplitude of the pressure head throughout the lateral could also be determined easily by the procedure.Two numerical applications with various slope combinations indicate that the proposed analytical approach produces results close to the accurate stepwise numerical solutions.In comparison with Keller method,the proposed approach could produce more appropriate designs.
An analytical approach was developed to a single uniformly sloping lateral in the micro-irrigation systems. Emission uniformity was used as the water application requires criterion. Energy Syndications based on the energy-gradient-line approach were revamped to account for the spatial variance of emitter outflow and the emitter connections local energy losses. Flow pressure grade grade line profiles were distinguished: uphill, horizontal, gentle downhill and steep downhill. Analytical expressions of emission uniformity by hydraulic variation for each pressure profile were developed based on the design variables: length and diameter of lateral, emitter spacing, emitter flow equation parameters, equivalent length characterizing local losses and ground slope. the design of conditions for selecting emitter type, the number of emitters per plant and designing the diameter of the uphill and steep downhill laterals were also developed The nonlinear equations determine the lateral diameter and lateral length was solved iteratively by using the built-in root-finding function of (Tools> Goal Seek ...) in the calculation spreadsheet of Microsoft Excel. procedures: provide the options to fix the design lateral diameter with the commercial standard size or fix the design lateral length based on the field size. the operating inlet pressure and maximum amplitude of the pressure head throughout the lateral could also be determined easily by the procedure. dual numerical applications with various slope combinations indicate that the proposed analytical approach produces results close to the accurate stepwise numerical solutions.In comparison with Keller method, the proposed approach could produce more appropriate designs.