In the last chapter, we discussed how to qualitatively sketch water-surface profiles in channels having gradually varied flows. For engineering applications, however, it is necessary to compute the flow conditions in these flows. These computations, generally referred to as water-surface profile calculations, determine the water-surface elevations along the channel length for a specified discharge. The water-surface elevations are required for the planning, design, and operation of open channels to assess the effects of various engineering works and channel modifications. The addition of a dam, for example, raises water levels upstream of the dam and it is necessary to know the flow depths in the upstream area to determine the extent of flooding.
In addition, steady-state flow conditions are needed to specify proper initial conditions for the computation of unsteady flows. Improper initial conditions introduce false transients into the simulation, which may lead to incorrect results. Unsteady-flow algorithms may be used directly to determine the initial conditions by continuing the computations until the flow conditions become steady. However, such a procedure is computationally inefficient and may not converge to the proper steady-state solution if the finite-difference scheme is not consistent.
In this chapter, methods to compute gradually varied flows are presented. Preference is given to the methods suitable for a computer solution. Two traditional methods – commonly referred to as the direct and standard step methods – are first presented. The computations progress step by step from one section to the next in these methods. Then, numerical methods to integrate the governing differential equation are introduced. A procedure is then presented that computes the flow conditions at all specified locations of a channel system simultaneously instead of computing them from one section to the next.
KeywordsEuler Method Channel Network Head Loss Channel Cross Section Bottom Slope
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