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 been developed for routing floods in channels having uniform rectangular 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 ()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 0 and K at every routing time level, but still adopting the linear form of solution equation. The situation for which the routing solution can not be obtained using this method has been brought out, and an alternative solution procedure is suggested for the same. It has been found from this study in general, that the method in which both a and K varying along with multiple routing reaches consideration is able to produce the true solution much closer than the method in Which both ø and K varying, but with the consideration of single routing reach, or the method in which only K varying and 0 remaining constant, but with the consideration of single routing reach. 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 the maximum value of ø is 0.5 and its negative value is possible. The said methodology has been verified using some hypothetical problems.
