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<br />right side, facing downstream) (figs. 2B
<br />and 3B and sec. 1.9),
<br />K. = Total conveyance at section 1 (sec, 1.9),
<br />4-4 = Distance from point of maximum back
<br />water to reestablishment of normal water
<br />surface downstream, measured along cen-
<br />terline of stream (figs, 2A and 3A) (ft,).
<br />L.-, = Distance from point of maximum back-
<br />water to water surface on downstream
<br />side of roadway embankment (figs, 2A
<br />and 3A) (ft,),
<br />L,_, = Distance from point of maximum back-
<br />water to upstream face of bridge deck
<br />(figs, 2A and 3A) (ft,),
<br />L* = Distance from point of maximum back-
<br />water to water surface on upstream side
<br />of roadway embankment, measured paral-
<br />lel to centerline of stream (fig, 13) (ft,) ,
<br />L. = Distance between upstream face of first
<br />bridge and downstream face of second
<br />bridge (dual bridges) (ft,) ,
<br />I = Overall width of roadway or bridge (ft,).
<br />M = Bridge opening ratio (sec, 1.10).
<br />n = Manning roughness coefficient (table 1).
<br />P = Wetted perimeter of a subsection of a
<br />channel (It.),
<br />Q. = Flow in portion of channel within pro-
<br />jected length of bridge at section 1 (fig, 1)
<br />(d,s,),
<br />Q., Q. = Flow over that portion of the natural
<br />flood plain obstructed by the roadway
<br />embankments (fig, 1) (d,s,).
<br />Q = Q.+Q.+Q. = Total discharge (ds.),
<br />r = alp = Hydraulic radius of a subsection of
<br />flood plain or main channel (ft.),
<br />S. = Slope of channel bottom or normal water
<br />surface,
<br />V. = QI A. = Average velocity at section 1
<br />(ft,/sec.).
<br />V. = QI A. = Average velocity at section 4
<br />(ft./sec,),
<br />V", = QI A., = Average velocity in constriction
<br />for flow at normal stage (ft./sec,),
<br />V" = Critical velocity in constriction (ft./sec,),
<br />Wp = Width of pier normal to direction of flow
<br />(fig, 7) (ft,),
<br />W = Surface width of stream including flood
<br />plains (fig, 1) (ft.),
<br />Yl = Depth of flow at section 1 (ft,),
<br />Y. = Depth of flow at section 4 (ft.),
<br />Y. = Normal depth of flow in model (ft.).
<br />ii = A..lb = Mean depth of flow under bridge,
<br />referenced to normal stage, (fig,3C) (ft.),
<br />
<br />Y.. = Critical depth at section 1 (ft,) ,
<br />Y" = Critical depth in constriction (ft,).
<br />y., = Critical depth at section 4 (ft,),
<br />a, = Velocity head coefficient at section 1 (sec.
<br />1.11) (Greek letter alpha),
<br />a, = Velocity head coefficient for constriction
<br />(Greek letter alpha,),
<br />~ = h.*lh.* = Backwater multiplication factor
<br />for dual bridges (Greek letter eta).
<br />(T = Multiplication factor for influence of M on
<br />incremental backwater coefficient for piers
<br />(fig,7B) (Greek letter sigma,),
<br />",h = h.*+h,* = for single bridge (Greek letter
<br />psi,),
<br />"'haB = hd*+h'B* = Term used in computing
<br />difference in water surface elevation across
<br />two embankmentB (dual crossings) (fig.
<br />14).
<br />~ = "'h'BNh = Differential level multiplica-
<br />tion factor for dual bridges (sec, 5.3)
<br />(Greek letter xi.) ,
<br />'" = Correction factor for eccentricity (fig, 13)
<br />(Greek letter omega.).
<br /><I> = Angle of skew-degrees (fig, 9) (Greek
<br />letter phi,).
<br />
<br />SPUR DIKES
<br />
<br />L, = Length of spur dike (ft,) (fig, 30),
<br />Qf = Lateral or flood plain flow (c.f ,s,) .
<br />QlOO = Discharge confined to 100 feet of stream
<br />width adjacent to bridge abutment
<br />(c,f.s.) ,
<br />ii.oo = Average depth of flow in 100 feet of
<br />stream adjacent to bridge abutment.
<br />QrlQ,OO = Spur dike discharge ratio.
<br />
<br />1.8 Definition of terms, Specific explanation
<br />is given below with respect to the concept of several
<br />of the terms and expressions frequently used through-
<br />out the discussion:
<br />
<br />Normal stage,-Normal stage is the normal water
<br />surface elevation of a stream at a bridge site, for a
<br />particular discharge, prior to constricting the stream
<br />(8ee figs, 2A and 3A), The profile of the water sur-
<br />face is essentially parallel to the bed of the stream,
<br />Abnormal stage,-Where a bridge site is located
<br />upstream from, but relatively close to, the confluence
<br />of two streams, high water in one stream can pro-
<br />duce a backwater effect extending for some distance
<br />up the other stream, This can cause the stage at a
<br />bridge site to be abnormal, meaning higher than
<br />would exist for the tributary alone. An abnormal
<br />
<br />9
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