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<br />undular wave. Also shown in this plate is a relation given <br />by Keulegan and Patterson (1940) for the height of the <br />first undulation <br /> <br />~ = 2. (Y2 - Yl ) <br />Yl 2 ~ Yl <br /> <br />(4-6) <br /> <br />Experiment and theory indicate that the undular wave will <br />begin to spill at the first crest when the Froude number <br />exceeds about 1.28. Undulations persist, however, until <br />the Fronde number exceeds about 1'3 (- 1.7). This is <br />the limit for breaking waves when Equation 4-4 gives a <br />value of Y2/Y 1 " 2. Further configuration information <br />on undular jumps may be obtained from Figures 44, 45, <br />and 46 of USBR (1948). <br /> <br />e. Stilling basins. Stilling basin design for high <br />Froude numbers is covered in EM 1110-2.1603. The <br />design of stilling basins in the range of Froude numbers <br />from 1.0 to about 1.3 is complicated by undular waves <br />that are dissipated only by boundary friction with increas- <br />ing distance downstream. This range of Fronde numbers <br />should be avoided whenever possible because of flow <br />instability. The hydraulic jump with Fronde numbers of <br />1.3 to 1.7 is characterized by breaking undulations with <br />very little energy dissipation (see Plate 5 I). Wall heights <br />in this range of Fronde numbers should be designed to <br />contain waves up to the value given by the Keulegan and <br />Patterson (1940) limit <br /> <br />4-4. Open Channel JunctIons <br /> <br />a. General. The design of channel junctions is com- <br />plicated by many variables such as the angle of intersec- <br />tion. shape and width of the channels, flow rates, and type <br />of flow. Appendix E presents a theoretical analysis. <br />based on the momentum principle. that can be ased for <br />several types of open channel junctions. The design of <br />large complex junctions should be verified by model tests. <br /> <br />b. Wave effects. <br /> <br />(I) Standing waves (Ippen 1951) in rapid flow at <br />open channel junctions complicate flow conditions. These <br />waves are similar to those created in channel curves de. <br />scribed in paragraph 2-4. and may necessitate incre:lSCd <br />wall heights in the vicinity of the junction. The studies <br />by Bowers (1950) indicate that a hydraulic jump may <br />form in one or both of the inlet channels. depending on <br />the flow conditions. <br /> <br />EM 1'10-2-1601 <br />1 Jut 91 <br /> <br />(2) Wave conditions that may be produced by rapid <br />flow in and downstre:lm of a typical junction are shown <br />in Plate 53. One area of maximum wave height can <br />occur on the side channel wall opposite the junction point <br />and another on the main channel right wall downstre:lm <br />from the junction. Behlke and Pritchett (1966) ltave <br />conducted a series of laboratory tests indicating that wave <br />pileup against the channel walls can be up to 7 times the <br />initial depth with a flow Froude number of 4. The design <br />of walls to contain these wave heights over long channel <br />distances is usually not economical. The practical remedy <br />is to reduce or minimize standing waves. <br /> <br />(3) Peak flows from the side channel may not occur <br />simultaneously with peak nows in the main channel. <br />Laboratory tests by Behlke and Pritchett (1966) indicate <br />that occurrence of the design flow in one of the channels <br />with zero flow in the other can result in very high wave <br />pileup on the junction walls. Plates S4a and b show <br />maximum wave height as a function of upStre:lm Froude <br />number for conditions of zero flow in the side channel <br />and main channel, respectively. This plate demonslrates <br />the need for keeping the angle of the junction intersection <br />relatively small. The data are also useful in designing <br />wall heights; for example, the maximum wave pileup on <br />the main channel wall would be greater than twice the <br />side channel flow depth for F2" 3.0 , a junction angle of <br />IS deg, and no flow in the main channel. <br /> <br />c. Wave height criteria. Behlke and Priu:helt's <br />(1966) recommended criteria for the design of channel <br />junctions in rapid flow to minimize wave effects are listed <br />below: <br /> <br />(1) Enlarge the main channel below the junction <br />apex to maintain approximately constant flow depths <br />throughout the junction. <br /> <br />(2) Provide equal water.surface elevations in the side <br />and main channels in the vicinity of the junction. <br /> <br />(3) Ensure that the side channel wave originating at <br />the junction apex impinges on the opposite side channel <br />wall at its intersection with the enlarged main channel <br />wall. <br /> <br />(4) Provide tapered lfaining waI1s between the main <br />channel and the side channel flows. <br /> <br />(5) Ensure that maximum wave heights occur with <br />maximum flows. Plate 55 illuslrates typical design <br />examples for rectangular and lrapezoidaJ channels using <br /> <br />4-5 <br />