FLOOD00680 - Laserfiche WebLink

Home Browse Search

e - ;. COMPUTATION OF WATER.SURFACE PROFILES IN OPEN CHANNELS 3 SUPERCRITICAL FLOWS Y,,<Yc - ~ - ~ ~ ~ A Tranquil flow Supercritical flow ~Tr8nQuil flow -- -- -- -- S B VERTICAL SCALE IS GREATLY EXAGGERATED Figure 2.-Water-surface profiles on steep slopes. A, Supercritical flows. showing relations among 82,83. YII and YI' curves; B. Sketch showing typical instances of S curves. the no-backwater condition on the mild slope; and that the lowest S2 and highest S3 curves will each similarly coincide with the no-back- water. normal-depth line on the steep .slope. Because most natural streamflow is subcrit- ical. with only occasional stretches of super- critical-flow conditions. this manual empha- sizes M 1 and M2 curves. refers to the S2 and S3 curves where appropriate. and briefly men- tions the rare M3 and SI curves, Water-surface elevations along Ml and M2 curves should be computed only in an upstream direction. away from a control. to ensure that successive points on the computed curve will asymptotically approach. or converge toward, the normal-depth line. Similarly. water-surface elevations along S2 and S3 curves should be computed only in a downstream direction, away from a control. to ensure that the com- ~ puted curves will converge toward the normal- depth line. Computations in the wrong direc- tion will define profiles that diverge from the normal-depth line. and they are, therefore. erroneous. It is possible. however, to make a few computations in the wrong direction with- out introducing large errors if the velocity head is small. The small errors locally intro- duced and reflected in the computed profiles in such instances are quickly dissipated if further computations of the water-surface pro- files are in the correct direction for the re- mainder of the reach being investigated. It should be noted that the description of a reach as mild or steep. or as subcritical. or critical. or supercritical refers not to the nu- merical value of the slope of the reach, but, rather. to the regime of the discharge flowing through the reach, Whether the numerical value ofthe slope is small or large, a reach could be considered "mild" because of the subcritical flow it carries. but it could later be considered "steep" because a different discharge is super- critical during the passage of a flood wave through the reach. -- Transition curves Figures 3-8 show some backwater transition curves for flow passing from one reach into another. In figure 3. the normal-depth lines are at different depths; the Ml curve of the mild slope. therefore. smoothly joins the normal- depth line of the milder slope. In figure 4. a change in roughness (n) on a mild slope will result in different normal depths. The transition curve is. therefore. very similar to that of figure 3. In figures 5 and 6. the normal depths on mild slopes are high in the upstream reach for a very mild slope or a very high roughness. and they are low in the downstream reach for a steeper slope or a low\lr roughness. The water- surface profile in the transition is, therefore. an M2 curve which smoothly joins the down- stream normal-depth line. Figure 7 shows a break in channel bed slope from mild to steep. The tranquil flow upstream from the control point has a normal depth higher than the critical depth; the supercritical flow downstream from the control point has a