Hydraulics of Center-Pivot Laterals: Complete Analysis of Friction Head Loss

The classical expressions obtained through the mathematical theory of friction head loss along the center-pivot lateral are adequate for many existing center-pivots. Nevertheless, several important aspects are not accounted for in the classic approaches, such as the presence of closed outlets at the beginning of the center-pivot and the friction head loss that occurs between the last sprinkler and the end gun. Furthermore, the irrigated radius and area considered in classical approaches are different from those used in this study. To address the previously mentioned important aspects, in addition to more standard situations, this paper develops closed-form expressions characterizing the friction head loss of center-pivot laterals with and without end-gun sprinklers and with and without closed outlets at the beginning of the center-pivot lateral. The friction head loss is computed by using two methods: continuous outflow distribution along the lateral using a different formulation from that in the literature, and discrete outflow distribution. Several applications are included that use the Chézy equation and the Hazen-Williams equation for both discrete and continuous distributions. The method of the discrete outflow distribution provides a closer description of the physical phenomenon and is used to validate the classical approaches. The formulas developed in this study validate the classical formulas for several practical applications. However, for a more accurate and general description of head losses, the approach developed in this paper is preferable because it produces more accurate results. These expressions, after small changes, can also be applied in multidiameter center-pivots, for laterals in which the spacing between outlets changes, and with ground slope.