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<br />
<br />EXPLANATION
<br />
<br />A.
<br />o
<br />a
<br />
<br />WATERSHED BOUNDARY
<br />SUB. BASIN BOUNDARY
<br />BEDROCt( CHANNEL
<br />SAND CHANNEL
<br />SLOPE-AREA MEASUREMENT sITe
<br />
<br />CONVEYANCE-SLOPE SITE
<br />PALEOFLOOD sITe (Hou.. and Pearthree 1994)
<br />
<br />~_J
<br />
<br />.
<br />I
<br />.
<br />
<br />2'-1LES
<br />I
<br />
<br />I
<br />2 KILOMETERS
<br />
<br />FIG. 1. Bronco Creek Wetel'8hed Showing Subbeeln Bounderle.. Location 01 Slope-Area Meaaurement SIte, Locations 01 Convey-
<br />ance-Slope end Paleoflood SItea, and Bedrock and Send-Channel Reachee
<br />
<br />8T/p vl
<br />
<br />where T = average boundary shear equals pgRS; p = mass
<br />density of the lIuid; B = width of channel; D, = depth of 1I0w
<br />measured normal to the channel lloor; BID, = channel aspect
<br />ratio; V, = average velocity; g = acceleration of gravity; R =
<br />hydraulic radius or depth of 1I0w for wide, shallow rectangular
<br />channels; and S = slope of the energy gradient, The Froude
<br />number is
<br />
<br />F = V,I(gD, cos e)'I> (3)
<br />
<br />where e = channel slope in degrees,
<br />In general, for wide, lIat, and steep channels, unstable 1I0w
<br />conditions exist for F greater than about 1.6 (Koloseus and
<br />Davidian 1966), Equations (I), (2), and (3) were applied to
<br />cross sections 3 and 4 of the slope area measurement. Base
<br />discharges (lIow preceding or beneath the waves, Q,) that
<br />ranged from 142 m'ls (arbitrarily selected) to 1,076 m'ls were
<br />used for free-surface instability computations to determine the
<br />possible duration of unstable 1I0w and roll wave development
<br />[Note: Manning's roughness coefficient (n) values selected for
<br />the original slope area were questioned at the time of the office
<br />review; therefore, n values of 0,030 and 0,040 are used for the
<br />analyses in this report], Values of V, and D, were determined
<br />from base discharge computations in the slope area reach using
<br />the original survey data and the standard step method (Shear-
<br />man 1990), Computed F. for all discharges and n values
<br />ranged from about 1.60 to 1.65. All average values of F/F.
<br />for n = 0.040 are less than I, and 1I0w is considered stahle,
<br />Conversely, all average values of F/F. for n = 0,030 are
<br />greater than I, and 1I0w is considered unstable, The data in,
<br />dicate that roll waves are possible at this site for flow rates as
<br />small as 142 m'ls, Fancher's report of waves for about 2 h is
<br />supported by the computed unstable 1I0w conditions for a wide
<br />range of discharge using n = 0,030,
<br />
<br />Wave Celerity
<br />
<br />The often used and rather elementary equation developed
<br />by Brater and King (1954) for wave velocity and celerity was
<br />
<br />572/ JOURNAL OF HYDRAULIC ENGINEERING / JUNE 1997
<br />
<br />(2)
<br />
<br />considered appropriate for the reported llood and channel con,
<br />ditions, The equation, which was developed for large abrupt
<br />waves in rectangular channels, was derived using momentum
<br />considerations where celerity was a function of force differ-
<br />ences associated with the weight of water at the vertical wave
<br />front, The Brater and King fonnula for a frictionless positive
<br />surge wave is
<br />
<br />Vw = c + V, or (46)
<br />
<br />Vw = [(gD,!2D,)(D, + DI))'I> + V, (4b)
<br />
<br />where Vw = velocity of the wave, in mls; c = celerity, in mls;
<br />VI = velocity of water preceding the wave, in mls; g = accel-
<br />eration of gravity, in mls'; D, " depth of water preceding the
<br />wave, in m; and D, = depth of water following the wave front,
<br />in ID.
<br />The static effect of the water weight difference at the wave
<br />front is considered; however, the effects of channel slope and
<br />roughness, atmospheric resistance and increased fluid viscosity
<br />and mass density from the transported suspended sediment are
<br />neglected, Other possible effects of transported sediment, such
<br />as lowering of the F. (Trowbridge 1987) also are neglected,
<br />
<br />Discharge Computations
<br />
<br />The method of determining the discharge of pulsating 1I0w
<br />requires (I) Computation of the discharge in the overriding
<br />waves; and (2) computation of 1I0w in the shallow depth, or
<br />overrun, part of 1I0w (Rantz et ai, 1982), The sum of the two
<br />discharges is the to1al discharge, Thompson (1968) assumed
<br />steady uniform-lIow conditions for the water preceding the
<br />waves (base discharge), and Manning's equation was used to
<br />compute V" For analysis of the peak discharge for the Bronco
<br />Creek 1l00d, a base discharge (Q'mu) of 799 m'ls (Carmody
<br />1980; House and Pearthree 1994) was used with an n of 0,030
<br />and 0,040 for computations of assumed steady uniform 1I0w
<br />preceding the wave, The computations to obtain values of D,
<br />and VI for Qlmax were made using Manning's equation in the
<br />standard step method (Shearman 1990) with channel, and sec-
<br />
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