Momentum Transfer–Equivalent States Assumption of the Apparent Shear Stress in Compound Open-Channel Flow

The use of apparent shear stress at the interface between the adjacent subregions of a cross section to represent the effect of momentum transfer is a common method for the one-dimensional calculation of compound open-channel flow. The apparent shear stress of the dividing lines is affected by the compound geometry and boundary conditions. The expressions of the apparent shear stress established with previous studies are very different. Empirical treatment was proposed in this study to simplify the expressions based on a momentum transfer-equivalent states assumption, in which (1) the apparent shear stress was assumed to be the difference of the momentum transfer from two sides of a dividing line, and (2) two assumed equivalent states were employed to define the equivalent value of the momentum transfer. The apparent shear stress could be calculated based on the deviation of the momentum transfer from its equivalent value. The new expressions were used to calculate the discharges and the boundary shear force. Comparisons between the calculated results based on different methods and the measured data showed that the proposed method improved the calculation of the subregion boundary shear force and the discharges in the compound cross sections.