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Last modified
1/25/2010 7:08:19 PM
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10/5/2006 2:07:13 AM
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Title
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 />(b) It may be noted in Plate 6 that in the proximity <br />of critical depth. a relatively large change of depth may <br />occur with a very small variation of specific energy. <br />Flow in this region is unstable and excessive wave action <br />or undulations of the water surface may occur. <br />Experiments by the US Army Engineer District (USAED). <br />Los Angeles (1949). on a rectangular channel established <br />criteria to avoid such instability, as follows: <br /> <br />Tranquil flow: d > l.ldc or F < 0.86 <br /> <br />Rapid flow: d < 0.9dc or F > 1.13 <br /> <br />where F is the flow Froude number. The Los Angeles <br />District model indicated prototype waves of appreciable <br />height occur in the unstable range. However. there may <br />be special cases where it would be more economical to <br />provide sufficient wall height to confme the waves rather <br />than modify the bottom slope. <br /> <br />(c) Flow conditions resulting with Froude numbers <br />near 1.0 have been studied by Boussinesq and Fawer. <br />The results of their studies pertaining to wave height with <br />unstable flow have been summarized by Jaeger (1957. <br />pp 127-131). including an expression for approximating <br />the wave height. The subject is treated in more detail in <br />paragraph 4-3d below. Determination of the critical depth <br />instability region involves the proper selection of high and <br />low resistance coefficients. This is demonstrated by the <br />example shown in Plate 6 in which the depths are taken <br />as normal depths and the hydraulic radii are equal to <br />depths. Using the suggested equivalent roughness design <br />values of k = 0.007 ft and k = 0.002 ft , bottom slope <br />values of So = 0.00179 and So = 0.00143 , respectively, <br />are required at critical depth. For the criteria to avoid the <br />region of instability (0.9dc < d < l.ldJ, use of the <br />smaller k value for tranquil flow with the bottom slope <br />adjusted so that d? l.ldc will obviate increased wall <br />heights for wave action. For rapid flow. use of the larger <br />k value with the bottom slope adjusted so that d S. 0.9dc <br />will obviate increased wall heights should the actual <br />surface be smoother. Thus, the importance of equivalent <br />roughness and slope relative to stable flow is emphasized, <br />These stability criteria should be observed in both uniform <br />and nonuniform flow design. <br /> <br />(2) Pulsating rapid flow. Another type of flow <br />instability occurs at Froude numbers substantially greater <br />than I. This type of flow is characterized by the <br />formation of slugs particularly noticeable on steep slopes <br />with shallow flow depth. A Manning's n for pulsating <br />rapid flow can be computed from <br /> <br />2-4 <br /> <br />116 ( J!3 <br />0.0463R ~ 4 04 _ I F <br />. oglO - <br />n Fs <br /> <br />e <br /> <br />(2-10) <br /> <br />The limiting Froude number Fs for use in this equation <br />was derived by Escoffier and Boyd (1962) and is given <br />by <br /> <br />Fs <br /> <br />~ <br />Ii ~3f2 (1 + Z~) <br /> <br />(2-11) <br /> <br />where ~. the flow function, is given by <br /> <br />~ ~ <br /> <br />Q <br />b5f2 <br /> <br />where Q is the total discharge and ~, the depth-width <br />ratio, is given by <br /> <br />. d <br />~ ~- <br />b <br /> <br />e <br /> <br />where b is the bottom width. <br /> <br />Plate 7 shows the curves for a rectangular channel and <br />trapezoidal channels with side slopes Z of I, 2, and 3. <br /> <br />(3) Varied flow profIles. The flow profIles discussed <br />herein relate to prismatic channels or uniform cross sec- <br />tion of boundary. A complete classification includes <br />bottom slopes that arc horizontal, less than critical, equal <br />to critical, greater than critical, and adverse. However. <br />the problems commonly encountered in design are mild <br />slopes that are less than critical slope and steep slopes <br />that are greater than critical slope. The three types of <br />profiles in each of these two classes are illustrated in <br />HOC 010-1. Chow (1959) gives a well-documented <br />discussion of all classes of varied flow profiles. It should <br />be noted that tranquil-flow profiles are computed proceed- <br />ing upstream and rapid-flow profiles downstream. Flow <br />profiles computed in the wrong direction result in diver. <br />gences from the correct profile. Varied-flow computa- <br />tions used for general design should not pass through <br />critical depth. Design procedures fall into two basic cate- <br />gorics: uniform and nonuniform or varied flow. Many <br /> <br />e <br />
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