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<br />73~
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<br />HYDRAULIC ENGINEERING '94
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<br />Jarrett, 1987). These include debris, obstructions,
<br />effects of unsteady flow, turbulence, sediment and
<br />bedload, flood plain-main channel interface, bedforms,
<br />hydraulic jumps, etc.
<br />It is not uncommon in channels having steep
<br />gradients and/or large flows, for n-values to be as
<br />much as .08, .09, and exceeding 0.10. Such n-values
<br />have been verified for channels having steep gradients
<br />(Jarrett, 1984), steep gradients with large' flOWS
<br />(Jarrett and Costa, 1986; Trieste, 1992), and heavy
<br />vegetation (Arcement and Scheider, 1984; Wilson, 1973).
<br />
<br />Sunsrcritical Flow
<br />
<br />When performing hydraulic computations on, or
<br />modeling flows through steep channel reaches, the
<br />majority of analysts assume occurrence of supercritical
<br />flow. Such occurrence of supercritical flow can be
<br />justified computing Froude number (F) if Manning'S
<br />n-values are small.
<br />When computing Froude number, velocity is normally
<br />computed via Manningls equation. And, when usinq
<br />"typical textbook" n-va1ues, velocities will be high
<br />'for steep channel qradients resulting in F to be
<br />greater than one, thus, supercritical flow.
<br />The "typical textbook" n-values mentioned in the
<br />previous paragraph are usually from commonly used and
<br />accepted sources (Chow, 1959, Barnes, 1967, U.S.
<br />Department of Agriculture, 1955). such n-values
<br />account for the effects of boundary friction of the
<br />channel only, which may be sufficient for flOWS to be
<br />computed in the subcritical range until discharge
<br />and/or channel gradient significantly increase. Then,
<br />for the same n-values flows will be computed to be in
<br />the supercritical range.
<br />Thus, when typical n-values are used in open-
<br />channel hydraulic calculations, flows may be
<br />subcritical for lower discharges and/or channel
<br />gradients, and supercritical for higher discharges
<br />and/or gradients.
<br />It appears that this approach has been taught in
<br />schools, passed down through the years, widely
<br />accepted, and rarely questioned. It is interesting-
<br />that there is little documentation to support it's
<br />occurrence. However, a recent report (Wahl, 1994)
<br />presents data on four streams where Froude number
<br />exceeds 1.
<br />
<br />Discussion
<br />
<br />It appears that for with-in bank flOWS in channelS
<br />not having high gradients (say, less than 0.002), most
<br />analysts agree as to occurrence of sUbcritical flOW.
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<br />SUPERCRITICAL V, SUBCRITlCAL FWWS
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<br />But, when large floods occur, and/or channel gradient
<br />increases, there is controversy as to flow regime.
<br />Many of the n-values published in the industry are
<br />sUbjective and not based on research, nor have been
<br />verified. Exceptions are that of Barnes (1967) and
<br />Jarrett (1984). However, even with the use of
<br />references having verified n-values, n will vary with
<br />discharge, depth, and slope. This is especiallY true
<br />for large flOods. Barnes (1967) cites channels having
<br />gradients as-Much-as 0.034 with associated n-values
<br />of 0.075. Froude number computes as less than one in
<br />such channels; thus, flows are subcritical. However,
<br />if discharge increases, and/or gradient increases, an
<br />n-value of 0.075 for a similar channel COUld reSUlt in
<br />computation of supercritical flow which may not be
<br />valid.
<br />Little is known about the occurrence of super-
<br />critical flow in natural channel reaches of the length
<br />typicallY used in open channel flow modelS such as
<br />DAMBRK (Fread, 1988), HEC2 (U.S. Army Corp of
<br />Engineers, 1983). A channel reach may be specified by
<br />users as a few hundredths of a mile, to more than
<br />10 miles (16.1 km). However, modeling supercritical
<br />flow in a long reach (say, greater than 0.1 mile
<br />! 0 .16 km)) may be invalid for most situations except
<br />possiblY high-gradient, smooth, uniform, solid bedrock
<br />channels (and, even this may be questionable).
<br />
<br />Additional Research
<br />
<br />Model parameters other than n-values should be
<br />investigated and developed for use in accounting for
<br />flow resistance. These include energy losses due to
<br />turbulence, eddies and currents, sediment and debris
<br />transport, hydraulic jumps, and other factors that use
<br />tremendous amounts of energy during large floods,
<br />and/or high-gradient channels.
<br />During large floods, and/or when channel gradient
<br />increases, flow resistance also increases. In these
<br />situations, the assumption of steady-state, uniform,
<br />gradually-varied flow is no longer valid. Typical
<br />n-values are no longer large enough to account for all
<br />energy losses. Systemically increasing n-va1ues,
<br />and/or developing parameters that account for other
<br />torms of flow resistance, should be considered.
<br />More studies of flows in high-gradient channelS,
<br />and/or large flows, would help improve the under-
<br />standing of the hydraulic characteristics actually
<br />occurring in natural channels including flow regime
<br />(supercritical or sUbcritical). From the information
<br />accumulated in these studies, guidelines and criteria
<br />can be developed to assess steep gradient and large
<br />flow hydraulics and for determining the flow regime.
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