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<br />transition to stabilize the hydr:wlic jump is iIluslrated in <br />USAED, Los Angeles (1961) and USAEWES (1962). A <br />typical example of this type of aransition is given in <br />Plate 25. <br /> <br />(c) USAED. Los Angeles (1958. 1961, 1962) has <br />designed and model tested a number of aransitions arans- <br />forming rapid flow in rectangular channels to aranquil <br />flow in lr:1peZOidal channels without the occurrence of an <br />abrupt hydraulic jump. The high-velocity jet from the <br />rectangular channel is expanded in the aransition by means <br />of lateral and boundary roughness control in such a man- <br />ner that an undular-type jump occurs in the downstre:lm <br />reach of the transition. Plate 26 illustrates a typical <br />design developed through model tests. <br /> <br />d. Transiti<Jn losses. <br /> <br />(1) Tranquil now. Transitions for aranquil flow are <br />designed to effect minimum energy losses consistent with <br />economy of consa-uction. Transition losses are normally <br />computed using the energy equation and are expressed in <br />terms of the change in velocity he:ld Ah., from upsa-eam <br />to downstre:lm of the transition. The head loss hI <br />between cross sections in the step computation may be <br />expressed as <br /> <br />hl = Cc&v <br /> <br />(2-29) <br /> <br />for conlraCtions and as <br /> <br />hl = Ce&v <br /> <br />(2-30) <br /> <br />where <br /> <br />C "contraction coefficient <br />c <br /> <br />C. = expansion coefficient <br /> <br />for expansions. Equations 2-29 and 2-30 have been <br />obtained and published (Chow 1959, Brater and King <br />1976, US Bureau of Reclamation (USBR) 1967). The <br />values in Table 2-3 are generally accepted for design <br />purposes. <br /> <br />EM 1110-2-1601 <br />1 Jul 91 <br /> <br />Tabla 2-3 <br />Tranaition Los. Coefficienta <br /> <br />Transi- <br />tion <br /> <br />Type <br /> <br />C C Source <br />. . <br />0.10 0.20 Chow <br />1959. <br />Brale. <br />and King <br />1976 <br />0.15 0.20 Chow <br />1959 <br />0.30 0.50 USBR <br />1967 <br />0.30 0.50 Chow <br />1959 <br />0.30 0.75 Chow <br />1959 <br /> <br />Warped <br /> <br />Cyfin- <br />dricaI <br />Quedtant <br /> <br />Wedge <br /> <br />Straight <br />Une <br /> <br />Square <br />End <br /> <br />(2) Rapid now. Transition losses may be estimated <br />for rapid-flow conditions from the information supplied in <br />(1) above. However, the effects of standing waves and <br />other factors discussed in c(2) above make exact determi- <br />nations of losses difficulL Model tests should be consid- <br />ered for important mpid-f!ow aransitions. <br /> <br />2.5. Flow In Curved Channels <br /> <br />a. General. <br /> <br />(1) The so-called centrifugal force caused by flow <br />around a curve results in a rise in the water surfxe on the <br />outside wall and a depression of the surface along the <br />inside wall. This phenomenon is called superelevation. <br />In addition, curved channels tend to create secondary <br />flows (helicoidal motion) that may persist for many chan- <br />nel widths downsa-e:un. The shifting of the maximum <br />velocity from the channel center line may cause a disturb- <br />ing innuence downStre:lm. The latter two phenomena <br />could lead to serious local scour and deposition or poor <br />petformance of a downstre:lIn sa-ucture. There may also <br />be a tendency toward separation near the inner wall., espe- <br />cially for very sharp bends. Because of the complicated <br /> <br />2-11 <br />