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e . . .. ie , ... " e a. Steady flow. This assumption generally is not a significant problem. For most naturally occurring floods on major streams, flow changes slowly enough with time that steady flow is a fair assumptinn. Even when it is not, the assumptinn would seldom cause any computa- tional problems. Three conditions under which a steady- flow model may not be applicable are: (I) A rapidly moving flood wave, as from a darn breach, for which the time-dependent term of the full unsteady-flow Equation has a significant effect. (2) Backwater effects from a downstream. boundary condition, such as a tidal flow, are significant. (3) A flat chatmel slope resulting in a pronounced loop effect in the relationship between discharge and elevation. See Chapter 5 for more information. b. Gradually varied flow. This is a reasonable assumption in most river reaches that are free of struc- tures and severe changes in channel geometry; however, this may not be a valid assumption in the vicinity of structures such as bridges and chatmel controls. The estimation of energy losses and the computation of water surface elevations in rapidly changing flow become more uncertain. Under these conditions, the estimated energy loss may be too high or too low, or the computational process may not be able 10 determine a water surface elevation based on computed energy losses, and a critical depth is assumed. For most floodplain studies, the criti- cal depth solution is not valid. A critical depth solution at a cross section will not provide a basis for computing a floodway encroachment based on a change of water surface elevation. c. One-dimensional flow. This may not always be a valid assumption. Two major problems that violate the assumption of one-dimensional flow are multiple water surface elevations and flow in multiple directions. (I) Multiple water surface elevations within one cross sectinn usually result from multiple flow paths. When the flow in each path is physically separated from the other paths, the distribution of flow in each path is a function of the conveyance (or energy loss) through the length of that path. Because the one-dimensionai model distributes flow in each cross section based on the con- veyance in that cross sectinn, the flow distribution in the model is free to shift from cross section 10 cross section in the computational process. The traditional solution to the problem is to divide the model into the separate flow EM 1110-2.1416 15 Oct 93 paths and compute a proft1e for each (see Chow 1959, Sec. 11-9). (2) Flow in multiple directions cannot easily be modeled with a single cross section perpendicular to the flow. In cases where the flow is gradually expanding, contracting, or bending, a cross section generally can be defined that will reasonably meet the requirement, but it does take special care. When flow takes a separate path, . as in the case of a levee overflow or a side diversion, the flow lost from the main channel must be separatelyesti- mated and subtracted from the main channel flow. The HEC-2 program bas a split flow option 10 compute lateral flow losses and the resulting profile in the main channel (U.S. Anny Corps of Engineers 19813). d. Small channel slope. This condition is common in natural streams. A slope less than I in 10 means that the pressure correction factor is close to I and not required. Also, the depth of flow is essentially the same whether measured vertically or perpendicular to the chan- nel bottom (Chow 1959). For most valley streams where floodway computations are performed, a I in 10 slope would be considered steep. Channel slopes are usually less than I in 100. e. Rigid boundaries. This assumption requires that the channel shape and alignment be considered constant for the period of analysis. The concern is not with long term changing boundaries, like those on meandering rivers, but with local scour and deposition that can occur in a stream during a flood event. The problem is more pronounced at major contractions, such as bridge cross- ings, because there is an increase in velocity with the potential for increased scour. Guidelines for determining critical scour velocities can be found in design criteria for stable channels of EM 1110-2-1610. 6-5. Example of Steady Flow Water Surface Profile Study a. Study objective. The overall objective was a comprehensive reaualysis of water surface profiles for a reach of the Tug Fork River in the Williamson, West Virginia, flood protection project area (Williams 1988a, 1988c). b. Description of the study reach. The Tug Furl< River originates in the southern part of West Virginia and flows for 155 miles in a northeasterly direction to Louisa, Kentucky, where it joins the Big Sandy River. 6-3