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Last modified
1/25/2010 6:27:01 PM
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10/4/2006 11:40:45 PM
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Title
Engineering and Design Hydraulic Design of Flood Control Channels
Date
7/1/1991
Prepared By
US Army Corps of Engineers
Floodplain - Doc Type
Educational/Technical/Reference Information
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<br />EM 1110-2-1601 <br />1 Jul 91 <br /> <br />I _ ~ <br /> <br />b, <br />.:::: can Pl <br /> <br />(2-26) <br /> <br />and <br /> <br />. s <br />....2 <br /> <br />bJ <br />.:::: t.an lP2 - t;I) <br /> <br />(2-27) <br /> <br />The correct lransition design for a given change in chan- <br />nel width and Fronde number involves selection of a <br />value of 9 so that L = Ll + L:t. A computation ilIus- <br />lI:lling the design procedure is given in Plate 23, <br /> <br />(b) Rectangular expansions. In channel expansions <br />the changes in flow direction take place gradually in <br />contrast to the steep wave front associated with conlrac- <br />tions. In 1951, Rouse, Bhoora. and Hsu (1951) published <br />the results of a swdy of expanding jets on a horizonlal <br />floor. A graphical method of characteristics, described in <br />Ippen (1951), was used for the theoretical development <br />of flow depth contours. These results were verified <br />experimenlally. The following equation based on theoreti- <br />cal and experimental studies was found to give the most <br />satisfactory boundary shapes for the expansion of a <br />high-velocity jet on a horizonlal floor. <br /> <br />;: = j (o~ J 12 + j <br /> <br />(2-28) <br /> <br />where <br /> <br />Z = transverse distance from channel <br />center line <br /> <br />b] = approach channel width <br /> <br />x = longitudinal distance from <br />beginning of expansion <br /> <br />F 1 " approach flow Froude number <br /> <br />Equation 2-28 is for an infmitely wide expansion. Opti- <br />mum design of expansions for rapid flow necessitates <br />control of wall curvature so that the negative waves gen- <br />erated by the UpStre:lm convex wall are compensated for <br />by positive waves formed by the downslream concave <br />wall. In this manner. the flow is restored to uniformity <br />where it enters the downstream channel. A typical design <br /> <br />2.10 <br /> <br />of a channel expansion is shown in Plate 24b. Plate 24a <br />reproduces generalized design curves presented in Rouse. <br />Bhoola. and Hsu (1951). It is to be noted that the convex <br />wall curve equation is appreciably less severe than that <br />indicated by Equation 2-28. Equations for laying out the <br />lransition and a definition sketch are given in Plate 24b. <br />The data given in Plate 24 should be adequate for prelimi- <br />nary design. In cases where the wave effects are critical, <br />the design should be model tested. Laboratory experi- <br />ments based on the generalized curves have indicated that <br />the downstre:lm channel depths may be appreciably in <br />excess of those indicated by the simple wave theory. The <br />simple wave theory can be applied to the design of <br />straight-line lransitions. An illustration of the computa- <br />tion procedure is given on pages 9-10 through 9-12 of <br />Brater and King (1976). It is to be noted that this compu" <br />tation does not include any wave effects reflected from <br />one sidewall to the other. Also, an abrupt positive wave <br />exists where the expanding wall intersects the downstre:lm <br />channel wall. Application of this method of characteris- <br />tics is illuslrated on pages 9-12 through 9-16 of Brater <br />and King (1976). <br /> <br />(c) Nonrectangular aransitions. The necessary tech- <br />niques for applying the wave theoty to channel aransitions <br />involving both rectangular and lrapezoidal sections have <br />not been developed. and generalized design curves are not <br />available. Limited tests on straight-line and warped-wall <br />channel lransitions for lrapezoidal to rectangular sections <br />and for rectangular to lrapezoidal sections have been <br />m:lde at Pennsylvania Slate University (Blue and Shulits <br />1964). Tests were limited to three different transition <br />shapes for Froude numbers of 1.2 to 3.2. Each shape was <br />tested for five different lransition lengths. The lrapezoidal <br />channel invert was 0.75 ft wide. The rectangular channel <br />was 1.071 ft wide. Generalized design curves were not <br />developed. However. the studv results should be useful <br />as design guides. <br /> <br />(3) Rapid to lranquil flow. <br /> <br />(a) The design of rapid-flow channels may require <br />the use of lransitions effecting flow IransfonnaUon from <br />rapid to lranquil flow. Such lransitions normally involve <br />channel expansions in which the channel shape changes <br />from rectangular to lrapezoidal. <br /> <br />(b) Channel expansions in which the flow changes <br />from rapid to lranquil are normally of the wedge type. <br />The flow lransformation can be accomplished by means <br />of the abrupt hydraulic jump or by a gradual flow change <br />involving an undular-type jump. In either case. it is <br />necessary that the flow lransformation be contained in the <br />transition section. The use of a stilling.basin type of <br />
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