FLOOD06873

• County: Statewide
• Basin: Statewide
• Title: Hydraulic Engineering volume 1
• Date: 1/1/1994
• Prepared By: American Society of Civil Engineers
• Floodplain - Doc Type: Educational/Technical/Reference Information

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6.4

HYDRAULIC ENGINEERING '()4

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at-a.sitc v;uialion in resistance from the fam.iliar ~m.il~)~a.rithmic relatio~~h,ip.
Use ot' this rc~alionship bas no theoretical jusllflcaUolI at low re atlv~
submer ences although empirically it has had some success. However, II
mi hi ;e spe~uJated that at large relative submcr.gcllce.s (d~D~ > I~) ~he
rel~tionship for mountain rivers would adopt a senuloganlhmlC trend. .." hlle
with the relationship for gravel#bed rivers. A fre(IUently used r~slslance
equation for gravel-bed rivers (Hey. 1979) is therefore also shown:

(8)"2 ( a R )
f = H5 log 3.5 D"

(I)

where R = hydraulic radius (here approximaled by mean d~pth); and u varies
belween 11.1 and 13.46 as a function of channel cross-sectional shape.

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a:

Data Source Slope 1"/0)
I , Bathurst 119851 0.4-0.6
A Jarrell (19841 0,2-05
n . Bathurst (19781 0.8
o Jarrell 119841 0.6-0,9
m . Bathurst 11985) 1.1-1.S
c Jarrell 119841 1.S-2.0
I1l V Jarrell 119841 1.4-1.8
, Thorne & 1.4 -1,6
Zevenbergen (19851

0,5

1
Relative Submergence

log ID84/0501
0.309
0.301
0.219
0.255
0.490
0.477
0.398
0.385

~

S
d/D84

I,'igurc 1. At-a-Sile Variation of Flow Resistan('e Function ,(81/)'"' with !tel~.i:~
Submergence dlDII4' for Four Combinati~ns of Channel Slope and Sian a
()~vi.ation of Bed Material Size Distribution

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10

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FLOW RESISTANCE YARlATlON

6115

Few reliable sets of data on at-a-sile variation in flow resistance in
mountain rivers are available in the literature. Here the data of Jarrett
(1984), Balhursl (1978,1985) and Thorne and Zevenbergen (1985) are used.
The quantity of data is not sufficient to enable the different effects of channel
slope and bed ,material size distribution to be distinguished. Consequently
plots are shown for different combinations of slope and standard deviation of
size distribution (log DIU I DjO). Each combination was carefully chosen so
that it could be represented by data from two of the sources, thereby
providing some verification of consistency between datasets. However, this
meant that only four combinations showing sufficient at-a-site variation to be
meaningful could be gleaned from Ihe available dala.

At-a-Site Variation in Flow Resistance

Figure 1 shows that at relative submergences less than about 1.5, the
rate of change of flow resistance with relative submergence may be described
approximately by the semilogarithmic law, albeit without theoretical
justification. In this region most of the flow occurs between the larger
boulders and flow resistance is high as a result of boulder drag, wake vortices
and jelling of flow between boulders. In particular, wave drag arising from
thc distortion of the water surface by protruding boulders is high. At larger
relative submergences, Ihough. there are sharp decreases in flow resistance
marked by significant divergences from the semilogarithmic relationship. An
important cause of the derrease is likely to be the steep fall in wave drag
which has hocn shown by Flammer el at (1970) 10 occur in Ihis region. The
divergence from the semilogarithmic relationship (which is based on the
assumplion of a seOlilogarilhmic velocily profile) is also likely 10 be
accentuated by the development of "skimming" flow and the appearance of the
S-shaped velocity profile. The importance for now resistance of the factors
controlling the velocily profile is demonstraled by Ihe way in which Ihe plots
for each combination of channel slope and bed material size distribution lie
separately. Also, in each case, Ihe data from the two sources making up each
combination plot together. confirming the consistency of the datasets.

In general, the steeper the slope the lower is the relative submergence
111 which the divergence from the semilogarithmic relationship begins.
lIowever. the precise links between r~'<.:i!, 'we. slope. bed material size
distribution and relative submergence <1;-. -", u'lllplex to disentangle wilh the
available data. Part of the reason may be that wave drag is a highly nOllline.lf
functjuncof Froude number and relative submergence (rlammer et al., 1970)
and ils vtuiatioll has yet to be represented by a quantitative relationship.
Likewise, the developmcnt of the S-shapcd velocity profile has yet to be linked
Ilu8ntilillivcly with its conholling fa{Olors.

It is undear whcther Ihe rate of {'hange of now resistance reverts at
high rel<llive suhmergcll('cs to that of the scmilogarithmic law. "Jlle conditions

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