Irrigation by gravity from a water delivery system where the difference in elevation between the canal's source and the fields is small requires careful use of the limited head available. Drop structures normally used to control flow are not used in order to conserve head. Instead, a desired distribution of the flow is achieved by sizing canal and channel turnouts. Turnout size depends on the required discharge rate and on the differential head. This head, in turn, is determined by flow rates in the connected channels and their cross-sections, hydraulic roughness, and slopes. Because the flow rate and head are interdependent, an iterative procedure is required to solve the turnout size problem. Furthermore, a change in water level at a single point may be reflected throughout the entire system. A computer model solves the hydraulics of the integrated system. Application of the model is demonstrated in the design of the distribution system for the Abyuha region in Middle Egypt. Appended are a 16-item bibliography (1959-1984), computer programs, sample output, and extensive statistical data.