Kinematic Wave Parameters for Trapezoidal and Rectangular Channels

Abstract

Essential to the application of the kinematic wave theory to open channel flow is the kinematic wave parameters which relate the discharge to the flow area in the channel. Earlier works have developed the kinematic wave parameters for a variety of channel shapes, but none for the trapezoidal channel. This paper unveils the kinematic wave parameters for four channel types: (1) trapezoidal channel with unequal side slopes; (2) trapezoidal channel with equal side slopes; (3) trapezoidal channel with one side vertical; and (4) rectangular channel. However, in the application of these parameters, all of them require the determination of flow area which is quite troublesome as the expression is not explicit. For the purpose of developing explicit analytical solutions, for channel types (2) and (3), it is shown that they can be approximated by a wide and a deep trapezoidal channels. For channel type (4), it can be approximated by a wide rectangular, a square and a deep rectangular channel. Further, for cases where the above approximations are not appropriate, alternative kinematic wave parameters have been established by mathematical fitting. The limits of applicability for all these approximations, and the maximum differences in discharge between the approximations and the “true” values have also been determined.