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e ,. . ". . .. . '. e Chapter 6 Steady Flow. Water SUrface Profiles Section I Introduction 6-1. SCOpe This chapter is limited 10 a discussion of calculating rigid boundary, steady-flow, water-surface profiles. The assumptinns, equations, and general range of application are presented in U1is section; data requirements, model development, special problems, and an example calcula- tion follow in subsequent sections. 6-2. Assumptions of the Method Computer programs used to compute steady, gradually varied flow water surface profiles are based on a number of simplifying assumptions. A thorough understanding of these assumptions. is required before an adequate model of a study reach can be developed Considerable engi- neering judgment is required in locating cross sections and preparing input data. The assumptions and how they affect program application follow: a. Steady flow. Depth and velocity at a given loca- tion do not vary with time. This assumption requires that the flow remain constant for the length of time being considered. Of course, for natural rivers this condition does not hold true precisely. However, it is usually acceptable for general rainfall and snowmelt floods in which discharge changes slowly with time. For such floods, a person standing on the bank of a stream during a flood would most likely not perceive the vertical move- ment or curvature of the water surface. b. Gradually varied flow. The depth and velocity change gradually along the length of the watercourse. These conditions are valid for most river flows, including floods, and the assumption of a hydrostatic pressure distribution (associated with gradually varied flow) is reasonable as long as the flow changes are gradual enough so that the imaginary lines of flow are approxi- mately parallel. c. One-dimensional flow. Variation of flow charac- teristics other than in the direction of the main axis of flow may be neglected and a single elevation represents the water surface of a cross section perpendicular to the EM 1110-2-1416 15 Oct 93 flow. Thus, velocities in directions other than the direc- tinn of the main axis of flow and effects due 10 centrifu- gal force at curves, are not computed. A correction factor is applied to account for the burizontal velocity distribution. d. Small channel slope. The stream channel must have a slope of I in 10 or less. Small slopes are required because of the assumption that the hydrostatic pressure distribution is computed from the depth of water measured vertically. For a bed slope of 1:10, which is steep for a natural channel, measuring the depth verti- cally results in an error of only one percent. Most flood- plain studies are performed on streams that meet this requirement. e. Rigid boundary. The flow cross section does not change shape or roughness during the flood. While this assumption is generally used, many alluvial streams may undergo considerable change in the shape of the bed and banks during a major event f Constant (averaged) friction slope between adja- cent cross sections. Approximation of the friction loss between cross sections can be obtained by multiplying a representative friction slope by the reach length that separates them. Various approximating equations are used to determine the friction slope. For example, in HEC-2 four equations are available, designated as aver- age conveyance, average friction slope, geometric mean friction slope, and harmonic mean friction slope (U.S. Army Corps of Engineers 1990b). This assumption requires that cross section spacing and the selection of an appropriate friction-slope equation for computing the loss be governed by conditions in the reach. 6-3. Standard-step Solution In open channel flow, the potential energy, Z, is specified as the height of the solid boundary confming the flow above some datum. If the pressure distribution is hydro- static, the pressure energy, P/,y, is the depth of water above the solid boundary. These two energy terms can be added to obtain WS ~ Ply + Z (6-1) where WS is the water surface elevation above the datum, as shown in Figure 6-1. The equation can then be rewritten 6-1