DESIGN OF OPENCHANNEL TRANSITIONS

Abstract

An open-channel transition involving an expansion and/or contraction of width is a common feature of canals and flumes. Depending upon the geometry of the inlet and outlet channels, there can be various types of such transitions. In the present study, the following four types of transitions were considered in formulating design problems: (i) a rectangular expansion with constant bed slope, (ii) a trapezoidal expansion with constant bed slope, (iii) a general expansion transition connecting a rectangular channel to a trapezoidal channel with variable bedelevation, and (iv) a variable-bed-elevation general contraction transition from a trapezoidal channel to a rectangular channel. As expansive transitions involve considerable head loss, any reduction of head loss will mean more power generation at the downstream end for power channels and increase in command area for irrigation canals. Furthermore, the minimum head-loss design will increase the life of both expansion and contraction structures. Present status of study and research on these types of transitions are not adequate. This is on account of complexities of the problem. Very little information is available regarding design of such transitions. The available information is mostly empirical, with no attention paid to minimizing the energy loss. I Thus there was a necessity to develop rational methodology for open-channel transition design. In all the transitions mentioned above, the design for subcritical state of flow primarily involves determination of bed-width, side-slope and bed-elevation profiles of the transition, such that, for given expansion/contraction ratio and transition length, the flow changes with the minimum-energy loss. To achieve above mentioned objective, one has to obtain expressions for total head loss and water-surface profiles. In the present study, applying the continuity, momentum and energy equations, head-loss equation for an expansion transition was found out. Using the available experimental data another head-loss equation for a contracting transition was obtained. Using these head-loss equations, the differential equations of gradually varied flow were found out for both expansion and contraction transitions. The problem under consideration involves minimization of an integral subjected to differential constraints and is defined as an optimal-contro1 problem in space domain. This requires solution of state equations and adjoint equations along with the optimality conditions. The optimality conditions can be satisfied by various search methods. In the present case steepest-descent method was adopted. A large number of expansion and contraction transition designs for various input data were obtained. Based on these designs, empirical equations of high accuracy were obtained for bed-width, side-slope and bed-elevation profiles. These equations can directly be used by a design engineer.