Irrigation and Drainage Systems 16: 53–68, 2002. © 2002 Kluwer Academic Publishers. Printed in the Netherlands. Numerical analysis to solve the hydraulics of trickle irrigation units NUMAN MIZYED Faculty of Agriculture, An-Najah National University, P.O. Box 7, Nablus, Palestine Authority Accepted 23 January 2002 Abstract. A model to solve the hydraulics of trickle irrigation units is developed in this study. This model is based on utilizing Newton Raphson technique. The model converts laterals into equivalent outlets through utilizing a simple power relation between inlet lateral discharge and hydraulic head. This relation is obtained through least squares analysis between inlet lateral discharge and hydraulic head. This study showed that this relation with only two coefficients is sufficient to describe the relation between inlet lateral discharge and hydraulic head. Based on this relation, the model converts manifold lines into equivalent laterals and solves their hydraulics by Newton Raphson technique. After that solution, the model evaluates trickle ir- rigation units by estimating statistical uniformity and Christiansen uniformity coefficients and checks the solution obtained through forward step method for each lateral. Several numerical examples for utilizing the model are presented in this paper. Key words: hydraulics, laterals, manifold, trickle irrigation Abbreviations: C H (j) – Hazen-Williams coefficient for lateral segment # j; C(j) – lateral line coefficient for segment #j; d(j) – Diameter of lateral segment # j in mm; E(j) – Elevation of outlet # j; f ′ (H m ) – First derivative of f(H) evaluated at H m ; H(j) – Total hydraulic head at outlet # j; H m – Hydraulic head vector (H) as determined (or assumed) from iteration # m; H m+1 – Improved estimate of vector H for the following iteration (m+1); H o – Inlet pressure at inlet point of the lateral/manifold line; h f (j) – Head loss in lateral segment number j; K&x – Outlet pressure-discharge coefficients; L(j) – Length of lateral segment j in meters; q – Outlet discharge; q(j) – Discharge from outlet number j; Q(j) – Flow rate in lateral segment number j Introduction Hydraulic analysis of trickle irrigation units is based on the hydraulics of pipelines with multiple outlets. Well known, Christiansen’s F factor was introduced to estimate the friction head losses along a pipe with multiple outlets, equally spaced with constant discharge (Christiansen 1942). Wu & Gitlin (1974) introduced a method to describe the pressure distribution along a lateral line assuming that discharge is uniformly distributed along that line. As the distance between the first outlet and the beginning of the lateral line is some times equal to half the spacing between other outlets, Christiansen’s