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<br />three types of flow which may be encountered in
<br />hridge waterway design, These are labeled type8 I
<br />through III on figure 4, The long dllllh line8 shown
<br />on each profile represent normal water surface, or
<br />the stage the design flow would SBSume prior to
<br />placing a constriction in the channel. The solid
<br />lines represent the configuration of the water sur-
<br />face, on centerline of channel in each Clllle, after the
<br />bridge is in place, The short dllllh lines represent
<br />critical depth, or critical stage in the main channel
<br />(Y 10 and Y.,) and critical depth within the constric-
<br />tion, Y.., for the design discharge in each Clllle, Since
<br />normal depth is shown essentially the same in the
<br />four profiles, the discharge, boundary roughness and
<br />slope of channel must all inerelllle in pSBSing from
<br />type I to type IIA, to type lIB, to type III flow,
<br />
<br />Type I Flow
<br />
<br />Referring to figure 4A, it can be observed that
<br />normal water surface is everywhere above critical
<br />depth, This hllB been labeled type I or subcritical
<br />flow, the type usually encountered in practice, With
<br />the exception of chapter X, and example 11, all
<br />design information in this publication is limited to
<br />type I (subcritical flow). The backwater expression
<br />for type I flow is obtained by applying the con-
<br />servation of energy principle between sections I
<br />and 4, The method of analY8is is presented in 8ection
<br />A,I, appendix A.
<br />
<br />Type II A Flow
<br />
<br />There are at least two variations of type II flow
<br />which will be described here under types IIA and
<br />lIB. For type IIA flow, figure 4B, normal water
<br />surface in the unconstricted channel again remains
<br />above critical depth throughout but the water
<br />surface pSBSes through critical depth in the con-
<br />striction, Once critical depth is penetrated, the
<br />water surface upstream from the constriction, and
<br />thu8 the backwater, becomes independent of con-
<br />ditions downstream (even though the water surface
<br />returns to normal stage at sec'ion 4), Thus the
<br />backwater expression for type I flow is not valid for
<br />type II flow.
<br />
<br />Type lIB Flow
<br />
<br />The water surface for type lIB flow, figure 4C,
<br />8tarts out above both normal water surface and
<br />critical depth upstream, pssses through critical
<br />depth in the constriction, next dips below critical
<br />depth downstream from the constriction and then
<br />
<br />l
<br />
<br />2511-9250-78-2 5,
<br />
<br />returns to normal. The return to. normal depth can
<br />be rather abrupt as in figure 4C, taking place in the
<br />form of a poor hydraulic jump, since normal water
<br />surface in the stream is above critical depth, A back-
<br />water expression applicable to both types IIA and
<br />lIB flow has been developed by equatiug the total
<br />energy between section 1 and the point at which the
<br />water surface pllllses through critical stage in the
<br />constriction, (See section A,2, appendix A,)
<br />
<br />Type I II Flow
<br />
<br />In type III flow, figure 4D, the normal water
<br />surface is everywhere below critical depth and the
<br />flow throughout is supercritical. This is an unusual
<br />case requiring a steep gradient but such conditions
<br />do exist, particularly in mountainous regions,
<br />Theoretically backwater should not occur for this
<br />type, since the flow throughout is supercritical, It is
<br />more than likely that an undulation of the water
<br />surface will occur in the vicinity of the constriction,
<br />however, lIIl indicated on figure 4D,
<br />1.6 Field verification. The first edition of this
<br />bulletin was prepared principally from the results
<br />of model studies verified by several backwater
<br />measurements taken by the U.S, Geological Survey
<br />during floods on medium size bridges. The field
<br />structures measured up to 220 feet in length with
<br />flood plains lIIl wide as 0.5 mile, A summary of this
<br />information is contained in the comprehensive
<br />model study report (18), It was presumed that the
<br />design information could be used in the range pre-
<br />scribed with confidence, The applicability of the
<br />information to structures with larger width to
<br />depth ratios remained to be proven,
<br />Since publication of the first edition, the U,S,
<br />Geological Survey hllll made additional field meas-
<br />urements during floods at an SBSortment of bridges,
<br />These mellllurements were sponsored by the Missis-
<br />sippi Highway Department and the Bureau of
<br />Public Roads and were l!1ade at bridges up to 2,100
<br />feet in length in the State of Mississippi. Flood
<br />plains were generally heavily vegetated and ex-
<br />tremely wide which boosted the width to depth
<br />ratios, formerly limited to 112, to over 700, A sum-
<br />mary of the field data to date is included in tables
<br />B-1, B-2, and C-l.
<br />ThL recently acquired field data have indicated
<br />that the model studies are only partially valid for
<br />type I flow, This WllB principally due to the width
<br />to depth limitation, For bridge opening ratios (see,
<br />1.10) less than M = 0,55, the flow in the model
<br />could change from type I to type II, but regardless
<br />
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