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<br />EM 1110-2-1601 <br />1 Jul 91 <br /> <br />water surface H3 in terms of critical depth is presented <br />as a function of the downstre:lm depth d3 and critical <br />depth in the unObslrUCted channel. Separate curves are <br />given for channel contraction ratios of between 0.02 and <br />0.30. In rectangular channels. 1I is the horizonla! con- <br />t!:lction ratio. The basic graph is for round nose piers. <br />The insert graph provides correction factors (y) for other <br />pier shapes. Use of the chart is illuslrated in Plate 15. <br />Plate 16 (HDC 010- 6{3) presents the USAED. Los <br />Angeles. (1939), solution for class B flow using the mo- <br />mentum method. Plate 17 (HDC 010-6/4) presents the <br />USAED, Chic:lgo, solution for class B flow by the energy <br />method. The use of these charts for rectangular channel <br />sections is shown in Plate 15. <br /> <br />c. Bridge pier exrensWn. Upslre:llTl pier extensions <br />are frequently used to reduce now disturbance C3used by <br />bridge piers and to minimize collection of debris on pier <br />noses. In addition. it is often necessary and economical <br />to make use of existing bridge SlrUCtures in designing <br />flood channels. In some instances there is insufftcient <br />vertical clearance under these structures to accom modate <br />the design now. With class B flow, the maximum now <br />deplb occurs at the upsa-eam end of the pier and the criti- <br />cal depth occurs within the constriction. Field observa- <br />tions and model studies by USAED. Los Angeles (1939), <br />indicate that the minimum deplb within the constricted <br />area usually occurs 15 to 25 ft downsa-eam from the <br />upslre:lm end of the pier. Pier extensions are used to <br />effect an UpStre:lm movement of the conlrOl section, <br />which results in a depth reduction in the flow as it enters <br />the constricted pier section. The use of bridge pier exten- <br />sions to accomplish this is illustrated in USAED. Los <br />Angeles (1943). and USAEWES (1957). The general <br />statements relative to bridge pier extensions for class B <br />flow also apply to class C now. However, in the latter <br />=, the degree and extent of the disturbances are much <br />more severe than with class B flow. Excellent iIIuS!ra- <br />lions of the use of bridge pier extensions in high.velocity <br />channels are given in USAED, Los Angeles (1943), and <br />USAED. Walla willa (1960). The bridge pier extension <br />geomelry shown in Plate 18 was developed by USAED. <br />Los Angeles, and pier extensions of this design have been <br />found to perform satisfactorily. <br /> <br />d. Model studies. Where flow conditions at bridge <br />piers are affected by severe changes in channel geomelry <br />and alignment. bridge abutments. or multiple bridge <br />crossings. consideration should be given to obtaining the <br />design flow proftle from a hydraulic model study. <br /> <br />2.8 <br /> <br />2-4. Transitions <br /> <br />a. General. Transitions should be designed to ac- <br />complish the necessary change in cross section with as <br />little flow disturbance as is consistent with economy. In <br />aranquil now. the he:Jd loss produced by the aransition is <br />most important as it is reflected as increased upslre:lm <br />Slages. In rapid flow, standing waves produced by <br />changes of direction are of great concern in and down- <br />Stre:lm from lbe aransition. S a-eamlined lransitions reduce <br />he:Jd losses and standin g waves. As lransition <br />construction costs exceed those of uniform channel cross <br />section and tend to incre:ISC wilb the degree of streamlin- <br />ing, alternative aransition designs, their costs, and the <br />inaemenla! channel costs due to head losses and/or stand- <br />ing waves should be assessed. <br /> <br />b. Types. The three most common types of aransi- <br />tions connecting trapezoidal and rectangular channels are <br />cylindrical quadrant. warped. and wedge, as shown in <br />Plate 19. For comparable design, the wedge.type aransi- <br />lion, although easier to construct. should be longer than <br />the warped because of the miter bends between channel <br />and aransition faces. WaIped and wedge types can be <br />used generally for expansions or conlraCtions. <br /> <br />(I) Tranquil flow. Each of these three lransition <br />types may be used for lranquil flow in either direction. <br />The cylindrical quadrant is used for expansions from <br />rectangular to trapezoidal section and for conlractions <br />from lrapezoidal to rectangular section. An abrupt or <br />straight-line aransition as well as the quadrant aransition <br />can be used in rectangular channels. <br /> <br />(2) R:lpid flow. The cylindrical quadrant is ased for <br />lransitions from aranquil now in a tr:lpeZOidal section to <br />ropid flow in a rectangular section. The straight.line <br />aransition is used for rectangular sections with rapid flow. <br />Specially designed curved expansions (c(2)(h) below) are <br />required for rapid flow in rectangular channels. <br /> <br />c. Design. <br /> <br />(I) Tranquil flow. Plate 20 gives dimensions of <br />plane surface (wedge type) transitions from rectangular to <br />tr:lpeZOidal cross section having side slopes of I on 2: 1 <br />on 2.5, and I on 3. In accordance with the recommenda- <br />lions of Winkel (1951) the maximum change in flow line <br />has been limited to 6.0 degrees (deg). Water-surface <br />profIles should be determined by step computations with <br />