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<br />stage may also be caused by a dam, another bridge,
<br />or some other constriction downstream, The water
<br />surface with abnormal stage is not parallel to the
<br />bed (fig, 16).
<br />J.Vvrrnal cro8sings.-A normal crossing- is one with
<br />alignment at approximately 900 to thc general
<br />direction of flow during high water (as shown in
<br />fig, 1),
<br />Eccentric cro8sing.-An eccentric crossing is one
<br />where the main channel and the bridge are not in
<br />the middle of the !lond plain (fig, 8),
<br />Skewed cr088ing,-A skewed crossing is one that
<br />is other than 900 to the general direction of flow
<br />during flood stage (fig, 9).
<br />l)ual cr08:nng,-A dual crossing refers to a pair of
<br />parallel bridges, such as for a divided highway (fig.
<br />14),
<br />Multiple bridge8.-Usually consi8ting of a main
<br />channel bridge and one or more relief bridges,
<br />Width of C<m8triction, b,-No difficulty will be ex-
<br />perienced in interpreting this dimension for abut-
<br />ments with vertical faces 8ince b i8 simply the hori-
<br />zontal distance between abutment faces, In the more
<br />usual case involving spill through abutments, where
<br />the cross section of the constriction is irregular, it i8
<br />suggested that the irregular cross section be con-
<br />verted to a regnlar trapezoid of equivalent area, as
<br />8hown in figure 3C. Then the length of bridge opening
<br />can be interpreted as:
<br />
<br />b = A.,
<br />Y
<br />Width to depth ratio.-Defined lIB width of flood
<br />plain to mean depth in constriction
<br />
<br />B (model) or ~ ' for irregular cross section
<br />Y. Y
<br />
<br />1.9 Conveyance. Conveyance is a measure of
<br />the ability of a channel to transport flow, In streams
<br />of irregular cross section, it is necessary to divide the
<br />water area into smaller but more or less regular sub-
<br />sections, assigning an appropriate roughness coeffi-
<br />cient to each and computing the discharge for each
<br />subsection separately, According to the Manning
<br />formula for open channel flow, the di8charge in a
<br />8ubsection of a channel i8:
<br />
<br />1.49
<br />q = - ar2/3Sol/2
<br />n
<br />
<br />By rearranging:
<br />
<br />q 1.49
<br />- =-ar2/3= k
<br />801/2 n
<br />
<br />where k i8 the conveyance of the subsection, Con-
<br />veyance can, therefore, be expressed either in terms
<br />of flow factors or strictly geometric factors, In
<br />bridge waterway computations, conveyance i8 used
<br />as a means of approximating the distribution of flow
<br />in the natural river channel upstream from a bridge,
<br />The method will be demonstrated in the examples of
<br />chapter XII. Total conveyance K, is the summation
<br />of the individual conveyances comprising section I-
<br />l.IO Bridge opening ratio, The bridge opening
<br />ratio, M, defines the degree of stream constriction
<br />involved, expressed as the ratio of the flow which
<br />can pass unimpeded through the bridge constriction
<br />to the total flow of the river. Referring to figure 1,
<br />
<br />M= Q,
<br />Qo + Q. + Q,
<br />
<br />= Q.
<br />Q
<br />
<br />(1)
<br />
<br />or,
<br />
<br />8,400
<br />M = - = 0,60,
<br />14,000
<br />
<br />The irregular cross section common in natural
<br />streams and the variation in boundary roughness
<br />within any cross section result in a variation in
<br />velocity across a river as indicated by the stream
<br />tubes in figure I- The bridge opening ratio, M, is
<br />m08t easily explained in terms of di8charges, but it
<br />i8 usually determined from conveyance relations.
<br />Since conveyance i8 proportional to discharge, as-
<br />suming all subsections to have the same slope, M
<br />can be expressed also as:
<br />
<br />M= K.
<br />K. + K. + Ko
<br />
<br />K.
<br />K,
<br />
<br />(2)
<br />
<br />I.ll Kinetic energy coefficient. As the veloc-
<br />ity distribution in a river varies from a maximum at
<br />the deeper portion of the channel to essentially zero
<br />along the banks, the average velocity head, computed
<br />as (Q/A,)'/2g for the stream at section 1, does not
<br />give a true measure of the kinetic energy of the flow.
<br />A weighted average value of the kinetic energy i8
<br />obtained by multiplying the average velocity head,
<br />above, by a kinetic energy coefficient, a" defined as:
<br />
<br />T.(qv')
<br />a, = QV,'
<br />
<br />(3a)
<br />
<br />Where
<br />
<br />v = average velocity in a subsection.
<br />q = discharge in same subsection.
<br />Q = total discharge in river.
<br />V 1 = average velocity in river at section 1 or Q/ A"
<br />
<br />10
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