TR-21 : Development of a variable parameter simplified hydraulic flood routing model or trapezoidal channels

Abstract

A variable parameter simplified hydraulic method based on the approximation of the St.Venant's equations which describe the one dimensional flow in a channel or river has developed for routing floods in channels having uniform trapezoidal cross section and constant bed slope. The governing equations of this method are same as that of Muskingum flood routing method and it has been demonstrated that these equations can directly account for flood wave attenuation without attributing to it the numerical property of the method as stated by some researchers. The parameters o and K viz., the weighting parameter and the travel time respectively, have been related to the channel and flow characteristics. Using this method the nonlinear behaviour of flood wave movement may be modelled by varying the parameters o and K at every routing time level, but still adopting the linear form of solution equation.

The developed method has been applied for routing floods in four different channels having prismatic trapezoidal cross-section with different constant bed slopes and Manning's roughness coefficients, and the results were compared with the corresponding St.Venant's solutions. Three different solution approaches have been used for routing floods in each channel corresponding to a reach length of 40 km. These approaches consists of considering the entire 40 km. length as a single reach and obtaining the solution by varying ø and K; considering the entire 40 Km. length as a single reach but obtaining the solution by varying K and keeping 9 constant; and considering the 40 Km. reach consists of 8 equal sub-reaches and obtaining the solution by successively routing through these reaches by varying both ø and K. It has been found from this study in general, the last solution approach is able to reproduce more closely the St.Venant's solution for both stage and discharge hydrographs, when compared with the other two approaches.

The theoretical reason for the reduced outflow in the beginning of the Muskingum solution has been brought out and the needed remedial measure to avoid it is suggested. Also it has been brought out from theoretical considerations that for Muskingum method, the maximum value of & is 0.5 and its negative value is admissible.