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<br />EM 1110-2-1416 <br />15 Oct 93 <br /> <br />Boll..:::> <br />--- <br />~~ <br /> <br />High Elevation <br />Acceleration l Low Elevt'ltion <br />___ I" ____ ___ I ___ <br />... <br /> <br />~~ <br /> <br />u <br />- <br /> <br /> <br />Tranquil Flow, Alluvial Channel <br />(0) <br /> <br />Deceleration <br /> <br /> <br />Sond <br /> <br />Rapid Flow, Alluvial Channel <br />(e) <br /> <br />u <br />- <br /> <br />////l//A <br /> <br />Tranquil Flow <br />Rigid Boundary <br />(b) <br /> <br />~ <br />~ - <br />~ ///)'////A <br /> <br />Rapid rlow <br />Rigid Boundary <br />Cd> <br /> <br />Figure 2-3. Reletlon between weter surface and bed configuration for tranquil and rapid flow (from <br />Simons and SentOrk 1976) <br /> <br />phenomenon. Examples are the hydraulic jump and <br />hydraulic drop (see p. 6 of Chow 1959). <br /> <br />(2) Gradually varied. As a rule of thumb, if the <br />slope of the surface of a body of water is indiscernible 10 <br />the naked eye, the flow therein is gradually varied. <br />Unsteadiness of open channel flow (in contrast 10 the <br />case of a rigid closed conduit flowing full) implies non- <br />uniformity because disturbances (imposed flow changes) <br />are always propagated as waves. In principle, at any <br />instant, some portion of the flow is influenced by the <br />disturbance, other portions have not yet been reached, <br />and the requirements for varied, i.e., nonuniform flow are <br />met. Furthermore, any Il()_nilniformity of the channel <br />characteristics; e.g., expansions and contractions in cross <br />section shape or changes in slope or roughness, causes <br />the flow to accelerate and decelerate in response. The <br />relative sizes of these two contributions to the flow non- <br />uniformity, flow unsteadiness, and irregular cbannel <br />geometry, influence the applicability of various <br />techniques for simulating river flows. In general, the <br />flow in a river subject to variations in inflow, outflow, or <br />tidal action should be assumed to be unsteady and non- <br />uniform. Gradually varied flow implies that the stream <br /> <br />2.8 <br /> <br />lines are practically parallel (e.g., a hydrostatic pressure <br />distribution exists throughout the channel section). An <br />underlying assumption for gradually varied flow compu- <br />tations is that "The headloss for a specified reach is <br />equal to the headloss in the reach for a uniform flow <br />having the same hydraulic radius and average velocity <br />..... (French 1985, p. 196). This assumption allows uni- <br />form flow equations 10 be used to model the energy <br />slope of a gradually varied flow at a given channel sec- <br />tion. It also allows the coefficient of roughness <br />(Manning's n), developed for uniform flow, 10 be applied <br />to varied flows. These assumptions have never been <br />precisely confirmed by either experiment or theory, but <br />the errors resulting from them are known to be small <br />compared 10 other errors such as survey errors and <br />roughness estimation (U.S. Army Corps of Engineers <br />1986). If large errors are introduced by the use of <br />simplified gradually varied flow methods, or if the partic- <br />ular flow conditions violate the basic assumptions of <br />steadiness, one-dimensionality, or rigid boundaries, the <br />river engineer must consider use of more detailed analyti- <br />cal methods. Chapter 3 presents some simple procedures <br />for eliminating inappropriate methods and identifying <br /> <br />. <br /> <br />. <br />. <br /> <br />. <br />>> <br /> <br />e <br /> <br />t <br /> <br />i <br /> <br />e <br />