Simple Relationships for the Optimal Design of Paired Drip Laterals on Uniform Slopes

Abstract

Microirrigation plants, if properly designed, allow water use efficiency to be optimized and quite high values of emission uniformity to be obtained in the field. It is known that disposing paired laterals, in which two distribution pipes extend in opposite directions from a common manifold, contribute to increasing water use efficiency. Recently, an analytical procedure has been proposed to optimally design paired drip laterals on uniform slopes under the assumption of neglect: (1) the variations of the emitters’ flow rate along the lateral, and (2) the local losses due to the emitters’ insertions. However, this procedure is not readily usable for every geometric and hydraulic characteristic of the lateral and slope fields because it requires solving a system of implicit equations. This study derives simple explicit relationships, reproducing the proposed approach, allowing derivation of the design variables that are required for the optimal design. Moreover, an easy method to determine the best position of the manifold associated to the optimal lateral length on uniform slopes is proposed, making evident a very moderate influence of the geometric and hydraulic characteristics of the lateral. The proposed procedure was successful compared with that derived by the analytical solution. Applications of the proposed relationships, considering different design parameters, are presented and discussed

Minor Losses and Best Manifold Position in the Optimal Design of Paired Sloped Drip Laterals

“…Relative errors, RE, calculated by assuming that the corresponding analytical values were true, resulted less than ±2%, demonstrating the applicability of the proposed procedure. Moreover Baiamonte () detected, for any slope of the lateral, the exact position of the manifold (BMP = 0.24), which is necessary to fix for an optimal design. The BMP was defined as the ratio between the number of emitters in the uphill lateral, n u , and the number of emitters in the uphill lateral and in the downhill lateral ( n opt = n u + n d ).…”

“…These equations are rewritten here by introducing the minor losses terms, expressed according to the classic formula that considers a friction coefficient αmultiplied by a kinetic energy term (De Marchi, ; Jeppson, ; Juana et al, ; Yıldırım, , ), and by highlighting the scale role of the emitter spacing S , for the pressure head, already observed in Baiamonte (). Thus, in the following, the normalized pressure head with respect to the emitter spacing S [m] will be indicated with h * (dimensionless): in which r denotes the flow rate exponent of the flow resistance equation, is the generalized harmonic number of order − r , truncated at n corresponding to …”

“…Before illustrating the optimal design of a paired drip lateral system when accounting for minor losses, for the simple case in which minor losses are neglected, a comparison between designing paired sloped drip laterals by fixing BMP = 0.24, suggested by Baiamonte () and designing according to the best submain position derived by Jiang and Kang (), was performed.…”

“…By maintaining the hypothesis of negligible minor losses and by assuming the Blasius resistance equation, so that the discharge exponent in the resistance equation equals 1.75, Baiamonte (, , ) simplified the analytical solution previously described to design paired drip laterals in sloping fields. The author used exponential laws and power functions that approximate the analytical solution well.…”

“…It should be observed that the ‘optimal’ design defined in Baiamonte et al . () and Baiamonte (, ) only refers to an ‘optimal’ distribution of the emitters’ pressure head along the laterals, and does not lead to the minimum annual operation cost since no economic analysis associated with the above procedures was carried out. The latter feature, although based on an iterative method and on a step‐by‐step (SBS) procedure, was well addressed by Carrión et al .…”