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<br />e <br /> <br />.. <br /> <br />. <br /> <br />.. <br /> <br />e <br /> <br />. <br />... <br /> <br />" <br /> <br />e <br /> <br />6-7. Flow Regime <br /> <br />Water surface proftle computations begin at a cross sec- <br />tion with known or assumed starting conditions and <br />proceed upstream for subcritical flow or downstream for <br />supercritical flow. Subcritical profiles computed by a <br />program such as HEC-2 are constrained to critical depth <br />or above, and supercritical profiles are constrained to <br />critical depth and below. The program will not allow <br />proftle computations to cross critical depth except for <br />certain bridge-analysis problems. When flow passes <br />from one flow regime to the other, it is necessary 10 <br />compute the proftle twice, alternately assuming subcriti- <br />cal and supercritical flow (U.S. Army Corps of Engineers <br />199Ob). <br /> <br />6-8. Stanlng Conditions <br /> <br />If feasible, proftle computations should be started at a <br />point of control where the water surface elevation can be <br />definitely determined. This may be at a gaging station, a <br />dam, or a sectinn where flow is at critical depth. How- <br />ever, for practical reasons, it is often necessary 10 start <br />the computations at other locations. <br /> <br />a. Known elevation. When a proftle computation <br />begins at a dam or a gaging station on a river where the <br />water-surface elevation versus discharge relationship is <br />known and is applicable 10 the conditions for which a <br />proftle is desired, the starting elevation can be deter- <br />mined from a rating curve. A common situation of this <br />type involves the computation of a water surface profile <br />starting at a full-pool elevation of a reservoir with a <br />specified discharge through or over the darn. <br /> <br />b. Critical depth. In certain instances it may be <br />feasible to start computations from a point where it is <br />known that critical depth will occur. Critical depth in <br />rivers may occur where the channel slope steepens abrup- <br />tly, or at a natural constriction in the channel. Critical <br />depth may be produced artificially by structures that raise <br />the channel bottom or constrict the channel width. If a <br />critical depth location can be determined, the critical <br />depth option for determining the starting elevation can be <br />specified in input 10 a program like HEC-2, and it will <br />compute the critical depth and use it. <br /> <br />c. Un/form flow. If the assumption of uniform flow <br />is reasonable, the slope-area method may be used 10 fmd <br />a starting elevation based on the computation of normal <br />depth. If an estimate of the slope of the energy grade <br />line and an initial estimate of the starting water surface <br />elevation are input to HEC-2 at a given cross section, the <br /> <br />EM 1110-2.1416 <br />15 Oct 93 <br /> <br />program will do a normal-depth calculation autumati- <br />cally. It will compute the discharge for the initial condi- <br />tions, and compare it with the given discharge. If there <br />is a significant difference, it will adjust the depth and <br />repeat the computation in a series of iterations until a <br />I percent difference criterion is met for the computed <br />and given discharges. <br /> <br />d. Estimated slope. When the starting elevation for <br />a selected discharge cannot be determined readily, it is <br />necessary to derive a starting elevation using available <br />expedients. One method is 10 select a water-surface <br />slope on a similar stream(s), and solve Manning's Equa- <br />tion by trial-and-error or graphically for the water-surface <br />elevation necessary to give that slope. <br /> <br />e. Estimated stage. Another method is 10 begin <br />proftle computations using a trial starting elevation at a <br />location some distance downstream from the reach for <br />which the backwater curve is desired. The error resulting <br />from an incorrectly assumed trial starting elevation will <br />tend to diminish as the computation progresses upstream. <br />The distance downstream can be estimated from the <br />regression equations presented in "Accuracy of Computer <br />Water Surface Proftles" (U.S. Army Corps of Engineers <br />1986). Equations are presented for both critical and <br />normal depth starting assumptions. The impact of the <br />starting depth assumption can be tested by computing a <br />second profile beginning at the same downstream loca- <br />tion but at a different trial starting elevation. The start- <br />ing assumption is reasonable if the two corresponding <br />backwater curves merge into one before the computations <br />have progressed to the reach for which the backwater <br />curve is desired. In selecting the trial starting elevations, <br />one elevation should be below and the. other above the <br />true elevation. <br /> <br />f. Tidal conditions. When the proftle computation <br />begins at the outlet of a stream influenced by tidal fluctu- <br />ations, the maximum predicted high tide, including <br />wind-wave set up, is taken as the starting elevatinn at a <br />station usually located at the mouth of the stream. <br /> <br />Section 1lJ <br />Model Development <br /> <br />6-9. Data Sources <br /> <br />Data requirements for water surface profile computations <br />were discussed in the preceding section. To reiterate, the <br />following data are required: discharge, flow regime, <br />starting water surface elevation, roughness and other <br />energy loss coefficients, and the geometric data--cross <br /> <br />6-5 <br />