# Computation of Rapidly Varied Flow

Typical examples of natural and man-made open channels having rapidly varied flows are mountainous streams, rivers during periods of high floods, spillway chutes, conveyance channels, sewer systems, and outlet works. Unlike the case of gradually varied flows, a number of difficulties, such as the formation of roll waves, air entrainment, and cavitation, are encountered in the analysis of these flows. In addition, instabilities may develop if the Froude number exceeds a critical value, giving rise to roll waves or slug flow. Standing wave and large surface disturbances, commonly referred to as shocks or standing waves, are important aspects of rapidly varied flows and need to be considered in the analysis and design.

In this chapter, we present finite-difference methods for the computation of rapidly varied flows. These are shock-capturing methods and do not require any special treatment if a shock develops in the solution. Three different formulations are discussed. The St. Venant equation, also referred to as the shallow-water equations, are assumed to describe these flows in the first two formulations and Boussinesq terms are included in the third to account for nonhydrostatic pressure distribution. The validity of these computational procedures is verified by comparing the computed results with the analytical solutions and with the experimental measurements.

## Keywords

Froude Number Boussinesq Equation Hydraulic Jump Bottom Slope Courant Number

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