Abstract
This chapter begins with derivation of the governing equations. Instead of the ordinary differential equation with regard to depth, commonly used for prismatic channels, the ordinary differential energy equation is proposed. It is showed that the standard step method used for computation of the flow profiles in natural channel is in fact the differential energy equation integrated numerically with the implicit trapezoidal rule. Consequently this approach is applicable for solving the steady varied flow in both prismatic and non-prismatic channels. Analysis of the non-linear equations obtained while solving the energy equation showed that it can have one, two or even three roots. Appropriate choice of the root allows us to obtain all types of the flow profiles occurring in open channels. The same approach based on the energy equation is developed for a single channel as well as for a channel network of both branched and looped types. Several examples illustrate the possibilities of the method.
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Szymkiewicz, R. (2010). Steady Gradually Varied Flow in Open Channels. In: Numerical Modeling in Open Channel Hydraulics. Water Science and Technology Library, vol 83. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3674-2_4
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DOI: https://doi.org/10.1007/978-90-481-3674-2_4
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