HYDRAULICS OF H I G H - G R A D I E N T STREAMS
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By Robert D . Jarrett,1 M. ASCE
ABSTRACT: Onsite surveys and 75 measurements of discharge were made on
21 high-gradient streams (slopes greater than 0.002) for the purpose of computing the Manning roughness coefficient, n, and to provide data on the hydraulics of these streams. These data show that: (1) n varies inversely with
depth; (2) n varies directly with slope; and (3) streams thought to be in the
supercritical flow range were actually in the subcritical range. A simple and
objective method was employed to develop an equation for predicting the n of
high-gradient streams by using multiple-regression techniques and measurements of the slope and hydraulic radius. The average standard error of estimate
of this prediction equation was 28% when tested with Colorado data. The equation was verified using other data available for high-gradient streams. Regimeflow equations for velocity and discharge also were developed.
INTRODUCTION
Hydraulic calculations of the flow in channels and overbank areas of
flood plains require an evaluation of roughness characteristics. Most
commonly, the Manning roughness coefficient, n, is used to describe the
flow resistance or relative roughness of a channel or overbank areas.
Term n appears in the general M a n n i n g equation for open-channel flow,
i.e.
V =
1.49R 2/3 S 1/2
(1)
n
in which V = the average cross-section velocity, in ft/sec; R = the hydraulic radius, in ft; S = the energy gradient or friction slope; a n d n =
Manning's roughness coefficient. The M a n n i n g equation is often substituted into the continuity equation, i.e.
Q = AV
(2)
in which Q = the discharge, in cu ft/sec; a n d A = the cross-sectional
area, in sq ft. This substitution yields a variation of the Manning equation
1.49AR 2/3 S 1/2
Q =
(3)
n
and the variables are as defined previously. Eqs. 1 and 3 were developed
for conditions of uniform flow in which the water-surface slope, friction
slope, and energy gradient are parallel to the streambed, a n d the area,
hydraulic radius, and d e p t h remain relatively constant throughout the
stream reach. The Manning equation has been u s e d extensively as an
indirect method for computing discharges or d e p t h s of flow in natural
channels.
'Hydro., U.S. Geological Survey, Lakewood, Colo.
Note.—Discussion open until April 1, 1985. To extend the closing date one
month, a written request must be filed with the ASCE Manager of Technical and
Professional Publications. The manuscript for this paper was submitted for review and possible publication on September 6, 1983. This paper is part of the
Journal of Hydraulic Engineering, Vol. 110, No. 11, November, 1984. ©ASCE,
ISSN 0733-9429/84/0011-1519/$01.00. Paper No. 19272.
1519
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In this application it is assumed that the equation is also valid for the
nonuniform reaches usually found in natural channels and flood plains,
and that the velocity distribution is logarithmic (11). The Manning equation has provided reliable results when used within the range of verified
channel-roughness data. The selection of appropriate n values, however,
requires considerable experience, even though extensive guidelines are
available.
Many studies based on hydraulic theory pertaining to flow resistance
have been made and are summarized by Chow (11), Limerinos (23), and
Carter, et al. (10). A study by Bray (8), who evaluated a number of equations used to predict roughness coefficients of gravel-bed streams, found
that the equations of Limerinos (23) were the most accurate.
The results of the theoretical and laboratory studies relating roughness
to relative smoothness (a depth parameter divided by a particle size) are
not entirely consistent. Verification using field data has not always been
conclusive (23). This is probably due to a combination of several factors:
(1) The theoretical and laboratory-derived relations are based on uniform
flow (a condition rare or absent in natural channels), on particle size and
shape, and on distribution of particle size; (2) few natural-flow streams
exist in which some other factors do not affect channel roughness; and
(3) there is an unknown model-to-prototype error associated with the
theoretical and laboratory-derived relations. In addition, although theoretical solutions provide a sound description of the processes involved
in flow resistance, the solutions have been tested only generally with
flume data or are too complex in terms of data requirements for practical
application.
Barnes (4) presented verified n-value data, color photographs, and descriptive data for 50 stream channels. These verified data are for nearbankfull discharges but do not provide information on the change of
Manning's roughness coefficient with depth of flow. Limerinos (23) presented verified K-value data for 11 streams and a predictive equation for
Manning's n for various depths of flow as a function of relative smoothness. The equation for n developed by Limerinos (23) is:
(0.0926)£1/6
1.16+ 2.0 log —
dm
in which du = the intermediate particle diameter, in ft, that equals or
exceeds that of 84% of the particle diameters determined by methods
described by Wolman (33). The other variables are as described earlier.
Methods such as Limerinos' require particle-size data. These data may
not be available due to the hydraulic conditions of the stream (such as
large depths of flow and high flow velocities), and economic or time
constraints.
Studies have shown that many factors influence flow resistance. Chow
(11), Fasken (15), and Aldridge and Garrett (1), expanded on a practical
technique developed by Cowan (12) to aid in evaluating the total flow
resistance in a channel reach. Total flow-resistance factors include crosssection irregularities, channel shape, obstructions, vegetation, channel
meandering, suspended material, bed load, and channel and flood-plain
1520
J. Hydraul. Eng. 1984.110:1519-1539.
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conditions in agricultural or urban areas. A detailed description of estimating total flow resistance for these conditions can be found in Chow
(11), Hejl (17), and Ree and Palmer (25). In general, all factors that tend
to cause turbulence and retardance of flow, and thus energy loss, increase the roughness coefficient; those that result in smoother flow conditions tend to decrease the roughness coefficient.
Normally, one n value is selected for the entire range of depth of flow.
If the ratio of the depth of flow to the size of the roughness element
(relative smoothness) is low, roughness is not constant. Most relations
between roughness and depth of flow are too technical for general use
and often involve variables that are not usually measured onsite. On
high-gradient streams (for the purpose of this study, slope greater than
0.002), channel roughness can vary markedly with depth of flow.
The available guidelines for selecting roughness coefficients for highgradient streams are based on limited verified roughness data, and, equally
important, are handicapped by a lack of easily applied methods for evaluating the changes of roughness with depth of flow. Streams flowing
on higher gradients generally have shallower depths of flow and larger
bed materials that affect the flow resistance more than the bed materials
in flatter slope streams having larger flow depths. Only a few studies
have been made of the hydraulics of high-gradient channels. Judd and
Peterson (20), Bathurst, et al. (6), and Peterson and Mohanty (24) have
been primarily theoretically-oriented or concerned with methods to evaluate average flow velocity.
A critical need exists to obtain additional data on high-gradient streams
over a range of flow depths and to provide practical guidelines for evaluating channel-flow resistance. The investigation described here was
conducted to provide data and improved methods for estimating the
Manning roughness coefficient as well as other aspects of the hydraulics
of high-gradient streams.
COLLECTION OF DATA
Seventy-five current-meter measurements of discharge using a Price
AA meter and appropriate field surveys were made at 21 high-gradient
natural stream sites in the Rocky Mountains of Colorado for the purpose
of computing channel roughness by the Manning formula, and to evaluate other aspects of the hydraulics of high-gradient streams. A typical
high-gradient stream, Lake Creek (Table 1, site 10) is shown in Fig. 1.
These sites were selected to represent a wide range of channel type, flow
width and depth, channel slope and roughness, and bed-material size.
The reaches were straight and uniform and had a connected water surface and a stable bed and banks with minimal vegetation. The roughness
measured reflects primarily the bed and bank-material roughness. The
discharges at these sites ranged from low to high flows, and recurrence
intervals ranged up to about 25 yr.
The following description of field methods is brief because standard
U.S. Geological Survey procedures were used to measure streamflow
(7,9,13,29). The well-known methods of Wolman (33) were used to measure particle size. At each site, 3-5 cross sections were established and
marked with metal stakes to define the reach of the stream. The cross
1521
J. Hydraul. Eng. 1984.110:1519-1539.
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TABLE 1.—Summary of Basic Data and Results
Site
number
(1)
1.
Velocity,
Discharge,3
in feet
Area, in
in cubic
Friction
square
Width,
per
Froude
feet per
second
number
slope
feet
in feet
second
(5)
(6)
(7)
(2)
(4)
(3)
Arkansas River at Pine Creek School, above Buena Vista
925
1,450
2,120
2,760
4,530
2.
69
73
78
79
80
3.72
4.30
5.27
6.11
8.65
0.35
0.35
0.40
0.45
0.60
0.026
0.023
0.021
0.025
0.026
Clear Creek near Lawson (latitude 39°45'57",
53
214
360
765
3.
249
340
407
454
526
43
71
102
141
42
46
49
52
1.25
3.00
3.58
5.48
0.22
0.42
0.44
0.59
0.015
0.017
0.018
0.019
Cottonwood Creek below Hot Springs, near Buena Vista
31
115
281
465e
4.
21
36
43
67
24
29
30
33
1.48
3.24
6.61
6.98
0.28
0.51
0.97
0.86
0.030
0.034
0.033
0.030
Crystal River above Avalanche Creek, near Redstone
83
272
530
1,220
60
112
161
220
204
224
233
577
2,300
3,710
123
125
135
226
443
528
5.
82
88
95
94
1.40
2.44
3.32
5.58
0.29
0.38
0.45
0.65
0.003
0.004
0.004
0.004
Eagle River below Gypsum (latitude 39°38'58",
6.
101
92
94
112
125
129
1.66
1.89
1.82
2.60
5.19
7.04
0.27
0.29
0.28
0.33
0.48
0.61
0.003
0.004
0.004
0.004
0.004
0.004
Egeria Creek near Toponas (latitude 40°02'12",
14
26
111
14
19
42
26
27
36
7.
0.98
1.36
2.63
0.24
0.28
0.42
0.003
0.003
0.002
Elk River at Clark (latitude 40°43'03",
39
254
1,050
1,410
59
72
81
90
39
105
185
272
1.01
2.42
5.73
5.21
1522
J. Hydraul. Eng. 1984.110:1519-1539.
0.22
0.35
0.66
0.53
0.003
0.004
0.006
0.006
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J. Hydraul. Eng. 1984.110:1519-1539.
lie
s
I
00)
00
^
o o
o o
00)
106
tude
00)
agi
106
Ion
908
:ude
-43
-44
-37
-32
-14
3.61
4.66
5.22
5.75
6.58
3.24
3.99
4.46
4.85
5.51
0.026
0.022
0.020
0.024
0.023
agi
105
Ion
Alpha
(11)
0.081
0.074
0.071
0.074
0.074
0.142
0.132
0.112
0.110
0.086
1.25"
1.34"
1.45"
1.43"
| obs irve
|
val
(equation 9)
rcenl
14)
(1 3)
Manning's
Water |
slope
(8)
atio
TABLE 1.—
(1)
(2)
(3)
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8.
12
94
242
122
224
252
264
(6)
(7)
0.88
2.73
5.06
0.23
0.46
0.73
0.011
0.016
0.014
53
78
82
84
4.05
6.26
6.36
6.94
0.47
0.66
0.65
0.70
0.019
0.014
0.014
0.014
Lake Creek above Twin Lakes Reservoir (latitude 39°03'47",
148
830
1,360
68
147
185
11.
53
64
68
2.21
5.70
7.41
0.35
0.67
0.79
0.019
0.023
0.024
M a d Creek near Steamboat Springs (latitude 40°33'56",
48
92
331
409
32
46
91
127
2,920
3,170
1
12.
54
56
61
63
1.53
2.03
3.72
3.27
0.35
0.39
0.54
0.41
0.026
0.026
0.025
0.021
Piedra River a t Piedra (latitude 37°13'20",
109
110
419
451
13.
6.97
7.03
0.63
0.61
0.004
0.004
Rio G r a n d e at W a g o n w h e e l G a p (latitude 37°46'01",
103
453
680
151
2,060
4,040
116
152
170
1.47
4.56
5.94
0.28
0.46
0.52
0.004
0.004
0.003
Roaring Fork River a t G l e n w o o d Springs (latitude 39°32'37",
571
650
1,170
3,260
245
256
366
559
15.
145
147
158
170
2.34
2.56
3.19
5.83
0.32
0.35
0.37
0.57
0.002
0.002
0.003
0.003
San J u a n River a t Pagosa Springs (latitude 37°15'58",
2,700
3,175
16.
(5)
Hermosa Creek near H e r m o s a (latitude 37°25'19",
493
1,380
1,580
1,800
14.
29
32
32
14
35
48
9.
10.
(4)
Halfmoon Creek near Malta (latitude 39°10'20",
396
434
119
126
6.84
7.34
0.66
0.70
0.008
0.007
South Fork Rio Grande at South Fork (latitude 37°39'25",
70
800
l,450 e .
17.
48
157
271
49
64
75
1.51
5.12
5.36
0.27
0.58
0.50
0.009
0.007
0.007
Trout Creek near O a k Creek (latitude 40°18'44",
13
29
57
164
190e
22
23
25
26
33
11
14
19
31
54
1.23
2.11
2.97
5.36
3.54
1524
J. Hydraul. Eng. 1984.110:1519-1539.
0.31
0.48
0.59
0.87
0.49
0.016
0.017
0.016
0.013
0.013
Continued
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(8)
(12)
(9)
(10)
(11)
longitude 106°23'19") (Gaging station 07083000)
(13)
(14)
0.079
0.080
0.072
-28
28
73
0.087
0.052
0.054
0.049
0.076
0.065
0.065
0.063
-13
26
20
28
longitude 107°50'40") (Gaging station 07084500)
2.00d
0.019
1.20
1.28
0.098
0.023
2.30
1.11"
0.062
2.12,
1.08b
0.024
2.72
0.056
2.53
0.084
0.083
0.082
-15
33
47
0.106
0.100
0.091
0.081
-10
-7
11
-22
0.039
0.040
15
9
0.049
0.039
0.036
-15
-3
1
0.037
0.036
0.037
0.037
-16
-11
-13
14
0.050
0.049
20
32
0.087
0.043
0.052
0.064
0.050
0.048
-26
17
-7
0.089
0.065
0.053
0.033
0.064
0.091
0.091
0.084
0.074
0.070
2
41
60
123
10
0.011
0.016
0.015
0.50
1.05
1.42
0.48
1.09
1.50
C
1.40"
1.68b
0.109
0.062
0.042
longitude 107°50'40") (Gaging station 09361000)
0.019
0.014
0.014
0.014
2.23
2.85
3.03
3.36
2.30
2.87
3.07
3.14
1.64b
1.27b
1.21"
1.27b
longitude 106°53'19") (Miscellaneous site)
0.026
0.026
0.027
0.023
0.60
0.80
1.40
1.92
0.59
0.82
1.49
2.02
1.56d
1.40d
1.36b
1.90"
0.117
0.108
0.082
0.105
longitude 107°20'32") (Gaging station 09349500)
3.80
0.034
1.20"
0.004
3.84
0.037
4.03
1.16"
0.005
4.10
longitude 106°49'51") (Gaging station 08217500)
0.004
0.004
0.004
0.89
2.97
3.98
0.89
2.98
4.00
c
1.30d
1.15d
0.058
0.041
0.035
longitude 10719'44") (Gaging station 09085000)
0.003
0.003
0.003
0.004
1.73
1.80
2.32
3.29
1.69
1.74
2.32
3.29
1.14d
1.25d
1.15d
1.10d
0.044
0.041
0.043
0.032
longitude 107°00'37") (Gaging station 09342500)
0.008
0.007
3.34
3.43
3.33
3.44
1.23b
1.39"
0.042
0.038
longitude 106b38'55") (Gaging station 08219000)
0.009
0.006
0.007
0.98
2.44
3.52
0.98
2.45
3.61
<
1.78d
1.18d
longitude 107°00,34") (Miscellaneous site)
0.016
0.018
0.016
0.015
0.014
0.50
0.60
0.80
1.13
1.57
0.5
0.61
0.76
1.19
1.64
1.00d
1.46d
1.42d
1.11"
1.16"
1525
J. Hydraul. Eng. 1984.110:1519-1539.
TABLE 1.—
(1)
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18.
(2)
(3)
(5)
(6)
(7)
46
51
73
110
3.27
5.46
0.45
0.66
0.027
0.031
White River above Coal Creek, near Meeker (latitude 4 0 W 1 8 " ,
358
1,350
1,740
20.
61
88
95
154
276
314
2.40
4.91
5.54
1
0.32
0.49
0.54
0.002
0.003
0.004
Yampa River at Steamboat Springs (latitude 40°29'01",
86
335
1,170
1,870
68
86
103
105
63
117
250
282
1.37
2.89
4.68
6.64
0.25
0.44
0.53
0.71
0.006
0.006
0.005
0.005
Yampa River near O a k Creek (latitude 40°16'47",
21.
Range:
Minimum
Maximum
1
Walton Creek near Steamboat Springs (latitude 40°34'39",
234
590
19.
(4)
51
119
135
29
44
50
38
42
42
1.85
2.74
2.72
0.38
0.48
0.44
0.004
0.004
0.004
12
4,530
11
680
22
170
0.88
8.65
0.22
0.97
0.002
0.034
"Discharge does not exactly equal the product of area and velocity as they are
b
A natural channel with bridge piers, abutments, or manmade obstructions
c
Not available.
d
A natural trapezoidal-shaped channel without overbank flow and no bridge
e
Not used to develop prediction equation due to extreme bank vegetation.
FIG. 1.—Typical High-Gradient Stream. Upstream View on Lake Creek above Twin
Lakes Reservoir, Colo.
1526
J. Hydraul. Eng. 1984.110:1519-1539.
Continued
(8)
(9)
(10)
(12)
(11)
(13)
(14)
0.091
0.095
-11
28
0.032
0.034
0.038
-18
0
8
0.074
0.047
0.041
0.032
0.056
0.052
0.046
0.045
-24
11
11
44
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longitude 106°47'11") (Gaging station 09238500)
0.103
1.59
1.40"
0.074
2.16
1.34"
longitude 107°49'29") (Gaging station 09304200)
0.027
0.034
1.63
1.87
0.002
0.003
0.004
1.80
3.10
3.25
2.52
3.14
3.31
c
.
1.17"
1.11"
0.039
0.034
0.035
longitude 106°49,54") (Gaging station 09239500)
0.006
0.006
0.005
0.006
0.90
1.30
2.40
2.66
0.93
1.36
2.43
2.66
1.38"
1.38"
1.37"
1.54"
longitude 106°50'50" (Miscellan sous site
0.004
0.005
0.005
0.76
1.10
1.20
0.76
1.05
1.19
1.19"
1.35"
1.03 d
0.041
0.034
0.038
0.049
0.047
0.048
20
38
25
0.002
0.039
0.50
5.51
0.48
6.58
1.00
2.00
0.028
0.159
0.032
0.106
-44
123
averages for the reach; similarly, other values are averages for the reach,
which may affect the flow pattern.
piers or other manmade obstructions.
sections were spaced approximately one channel width apart. W h e n a
current-meter m e a s u r e m e n t of discharge w a s m a d e , concurrent watersurface elevations were measured from about one channel w i d t h u p stream to one channel w i d t h d o w n s t r e a m of the site on each bank, including the e n d s of each cross section to define t h e water-surface profile.
The average maximum wave w a s h u p d u e to extreme turbulence w a s
taken to represent the high-water elevation, as d o n e by Barnes (4) a n d
Limerinos (23). W h e n streamflow w a s low, a transit-stadia survey w a s
made of each reach to obtain cross sections.
The size distribution of the b e d materials w a s determined by measuring the intermediate diameters of sampled particles during low flows.
For each particle, a determination also w a s m a d e to which axis—short,
intermediate, or long—was closest to being vertical (here called axis orientation). Finally, r o u n d n e s s of the particle w a s determined using
guidelines provided by Krumbein (22) a n d Wolman (33). Channel evidence indicated that the streambed material did n o t move during high
flows measured in this study.
DATA ANALYSIS AND INTERPRETATION
Streamflow Data.—The simple forms of the M a n n i n g equation s h o w n
1527
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in Eqs. 1 and 3 (13) are used only for uniform flow—that is, flow in a
channel whose cross-sectional area does not vary within the reach. The
energy equation for a reach of nonuniform channel between two sections (1 and 2) is
(h + Mi = (h + Kh + (fy)i.2 + KUivhz
(5)
in which h = elevation above a common datum of the water surface at
the respective section; hv = velocity head at the respective section = aV2/
2 ? ; a =• velocity-head coefficient which is considered to be 1.0 for a uniformly shaped cross section; g = acceleration due to gravity = 32.2 ft/
sec2 (9.81 m/s 2 ); hf = energy loss due to boundary friction in the reach;
Ahv = upstream velocity head minus the downstream velocity head; k{Ahv)
- energy loss due to acceleration of velocity or deceleration of velocity
in a contracting or expanding reach, respectively; and k = a coefficient
equal to 0 for contracting reaches and 0.5 for expanding reaches (4).
The friction slope, S, to be used in the Manning equation is thus defined as:
hf_Ah
S =^ =
L
+ Ahv - k(Ahv)
(6)
in which Ah = the difference in water-surface elevation at the two sections; and L = the length of the reach (13).
The quantity (1.49/n)AR2/3 in the Manning equation is called the conveyance, K, and is computed for each cross section. The mean conveyance in the reach between any two sections is computed as the geometric mean of the conveyance of the two sections. The discharge equation
in terms of conveyance is:
Q = K&S
(7)
0.15
1 COTTONWOOD
1 (SITE 3)
0.14
ARKANSAS RIVER
(SITE 1)
-
CREEK
"
0,1 1 0-10 0.13
0.13
0,09
~ }
\\
0.08
0.07
0.06
\
- 1
\l\ t
\
\
0.05
RIO GRANDE
(SITE 13)
HYDRAULIC
0.04
RADIUS, IN FEET
\f\S
\,
.
\l/\
\
<
>
/TROUT CREEK
V ( S I T E 17)
HYDRAULIC
FIG. 2.—Relation of Manning's Roughness Coefficient to Hydraulic Radius
SOUTH FORK
RIO
GRANDE
SITE 16
.
-
RADIUS, IN FEET
FIG. 3.—Relation of Manning's Roughness Coefficient to Hydraulic Radius,
Showing Effects of Streambank Vegetation
1528
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in which S = the friction slope as previously defined.
In this investigation the average value of the Manning n was computed for each reach from the k n o w n discharge, the water-surface profile, and the hydraulic properties of the reach as defined by the cross
sections. The equation applicable to a multisection reach of M cross sections which are designated 1, 2, 3, . . . M - 1, M is:
1.486
(h + hv), -(h + hv)M - [(fcAfo)L2 + (fcAfo)2.3 + ... + (kAhv\M-lyM]
^1.2
ZjZ 2
1
^2.3
\- ^ ^ ^ -|MM-1)-M
Z2Z3
Z( M _DZ M
in which Z = AR2/3 and other quantities are as previously defined (4).
Although Manning's n w a s c o m p u t e d for each subreach or combination
of cross sections within the reach, an average value of n for each reach
was adopted to represent the average conditions at the site. The average
TABLE 2.—Summary of Bed-Material Data for Colorado Streams
Statistical Size Distribution of Intermediate Diameter of
Bed Material, in Feet," Shown in Following Percentiles
Site number in
Table 1
(1)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
16
25
50
^16
^25
^50
(2)
0.5
0.1
0.2
0.2
0.1
(3)
1.0
0.2
0.2
0.3
0.2
(4)
1.4
0.6
0.5
0.4
0.4
0.05d
0.7
0.3
0.8
1.0
0.4
0.4
0.3
0.5
0.4
0.5
0.2
0.7
0.2
0.4
0.1 d
c
C
0.3
0.1
0.3
0.4
0.1
0.05
0.2
0.3
0.1
0.2
0.1
0.1
0.1
0.1
0.4
0.2
0.4
0.6
0.2
0.05
0.2
0.4
0.1
0.3
0.1
0.3
0.1
0.1
C
C
Range
Minimum 0.05
Maximum 0.4
0.05
1.0
0.2
1.4
Average
Krumbein
roundness"
(9)
0.5
0.6
0.4
0.4
0.5
75
84
90
95
dre
(5)
2.0
1.3
1.2
0.6
0.7
du
(6)
2.6
1.8
1.4
0.6
0.8
d9o
(7)
3.2
2.3
2.1
0.7
1.0
dgs
c
c
c
(8)
4.0
2.8
2.4
0.8
1.2
c
C
1.0
1.1
1.2
1.5
0.9
0.8
0.4
0.7
0.8
0.9
0.4
1.3
0.2
0.7
1.3
1.3
1.5
2.0
1.2
0.9
0.5
0.8
1.1
0.9
0.5
1.6
0.3
0.9
1.5
1.4
1.6
2.2
1.4
1.2
0.6
1.0
1.2
1.0
0.5
2.0
0.3
1.1
1.7
1.7
1.9
2.4
1.6
1.6
0.6
1.1
1.3
1.3
0.6
2.5
0.4
1.4
0.5
0.6
0.3
0.4
0.5
0.4
0.6
0.6
0.7
0.5
0.6
0.5
0.5
0.4
c
c
0.2
2.0
0.3
2.6
c
c
0.3
3.2
0.4
4.0
"Determined by using methods of Wolman (33).
Determined by using methods of Krumbein (22).
c
Data not available.
d
Estimated.
b
1529
J. Hydraul. Eng. 1984.110:1519-1539.
c
0.3
0.7
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TABLE 3.—Correlation Coefficients for Selected Hydraulic Characteristics for
Colorado Streams8
(1)
n
S
Manning's
Water
Bed
coeffiFriction slope, material
cient, n
slope, S
size, dm
Sm
(2)
(5)
(3)
(4)
1.00
bw
dM
R
D
Q
a
—
—
—
—
—
—
—
0.71
1.00
—
—
—
—
—
—
0.68
0.99
1.00
—
—
—
—
—
Hydraulic
radius, R
(6)
Hydraulic
depth, D
(7)
-0.09
0.02
-0.02
0.33
1.00
-0.04
0.07
0.04
0.39
0.99
1.00
0.64
0.66
0.62
1.00
—
—
—
—
—
—
—
—
—
Discharge, Alpha,"
a
Q
(8)
(9)
-0.23
-0.12
-0.14
0.12
0.91
0.88
1.Q0
—
0.52
0.52
0.51
0.79
-0.24
-0.24
-0.34
1.00
a
For untransformed data.
b
For a natural trapezoidal-shaped channel without overbank flow and no bridge
piers or other manmade obstructions.
hydraulic properties for the reach and computed values of the Manning
coefficient, n, are given in Table 1. Occasional inconsistencies in the data
are due to difficulties in data collection as a result of the extremely turbulent flow conditions. The minimum and maximum values of each variable are given at the end of Table 1.
The data in Table 1 indicate the marked variation of Manning's roughness, n, with depth in terms of hydraulic radius. The relation of Manning's roughness coefficient to the hydraulic radius of the four streams
shown in Fig. 2 is typical of the relations of all of the streams listed.
Roughness decreases markedly as depth of flow increases. This change
indicates the need for developing relations between roughness and depth
of flow. On three streams—Cottonwood Creek, South Fork Rio Grande,
and Trout Creek—flow was affected by bank vegetation at the highest
discharge. Dense willows created additional turbulence and increased
channel roughness markedly. The relation of Manning's roughness coefficient to the hydraulic radius of these three streams is shown in Fig. 3.
This indicates that dense vegetation can have a marked effect on total
flow resistance and should be accounted for.
Particle-Size Data.—The intermediate-axis particle-size data on the bed
material and the average Krumbein roundness are summarized in Table
2. Correlation coefficients showing the relation between selected hydraulic data and bed-material data are shown in Table 3. Data on axis
orientation indicates that the particle offers the least resistance to flow;
that is, when the short axis is vertical.
PREDICTION EQUATION FOR MANNING'S ROUGHNESS COEFFICIENT
Most equations used to predict channel roughness require streambed
particle-size information (5,10,11,23,30). Studies by Golubtsov (16), Riggs
(27), and Ayvazyan (3) indicate that channel roughness is directly related
to channel gradient in natural stable channels. Ayvazyan (3) evaluated
a number of formulas used worldwide to evaluate channel roughness in
1530
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earthen canals and found that the equations yield basically equivalent
results, but do not truly reflect the nature of hydraulic resistance. Ayvazyan (3) showed the reason for disagreement was the failure to allow
for the effect of slope. This relation of resistance and slope is due, in
part, to the interrelation between channel slope and particle size of the
bed material. As slope increases, finer material is removed and larger
particles remain in the channel. The effect of increased turbulence and
resistance results in increased friction slope. The correlation coefficients
for selected hydraulic characteristics of the data in Table 1 are shown in
Table 3. The coefficient for Manning's n is higher for friction slope (0.71)
than for dm particles size (0.64). This supports the idea that slope has a
strong influence on roughness. For similar bed-material size, channels
with low gradients have much lower n values than channels with high
gradients. Values of n as small as 0.032 have been obtained for channels
having very low gradients, shallow depths, and large boulders (4).
This implies that the channel roughness associated with streambedmaterial size can be evaluated in terms of the more easily obtained friction slope. The relation of Manning's roughness coefficient to friction
slope, which indicates that roughness increases with slope, is shown in
Fig. 4. The scatter is due to the at-a-site decrease of roughness with
increasing depth of flow. There also is much greater scatter, or change
-
. ..
1
:
• •• • •. .
!
t
I
o : •
! S.•
-
'
OBSERVATIONS
. ONE
A TWO
a FOUR
. 1
0.001
0.002
0.005
0.01
0.02
FRICTION SLOPE, S
FIG. 4.—Relation of Manning's Roughness Coefficient to Friction Slope
FRICTION SLOPE,
FIG. 5.—Relation of Manning's Roughness Coefficient to Friction Slope and Hydraulic Radius
1531
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in the roughness coefficient, on higher gradient streams. The method
for predicting channel roughness uses multiple-regression analysis, which
related Manning's roughness coefficient to the easily measured hydraulic characteristics shown in Tables 1 and 2. Multiple-regression analyses were performed using several different types of equations (arithmetic, polynomial, semilogarithmic, and logarithmic or power) to
determine the best type of equation to estimate channel roughness.
The three highest measurements for Cottonwood Creek, South Fork
Rio Grande, and Trout Creek were not used to develop the equation
because of the extreme effect of bank vegetation.
The resulting equation from the multiple-regression analyses developed for predicting Manning's n in steep natural channels is
n = 0.39 s03BR-°-16
(9)
and is graphically depicted in Fig. 5. In Eq. 9, S = the friction slope.
However, the data in Table 1 indicate that the water-slope values are
about the same and could be used interchangeably for fairly uniform
channels. Similarly, Table 1 indicates that the values of hydraulic radius
and hydraulic depth were approximately the same and could be used
interchangeably.
The average standard error of estimate of Eq. 9 is 28% and ranges from
-24-32% for the data in Table 1. Eq. 9 was used to predict n for the
sites, and the percent deviation of computed from observed values is
also shown in Table 1. The algebraic mean of percentage differences was
5.8 and ranged from -44-123%, indicating that Eq. 9 tends to slightly
overestimate n. The standard deviation of the percentage differences was
31%. The w-values having the greatest error are typically low-flow measurements when the ratio of R-dso is less than 7 for the data in Table 1.
The concept of flow resistance at low flows may be subject to question
due to nonconnection of the water surface. Another explanation is that
ongoing research indicates that the vertical-velocity profile is S-shaped
rather than logarithmic with much lower bottom velocities and higher
surface velocities in shallow, steep, cobble-and-boulder bed streams.
Overall, the measured velocity is too small; thus, the n-value would be
somewhat overpredicted. Roughness-prediction equations such as Eq. 4
were developed in terms of relative smoothness. However, the standard
error of estimate for Eq. 4 and for a similarly developed relative smoothness type equation was considerably higher, biased, and did not fit the
data as well as Eq. 9.
Data from Barnes (4) and Limerinos (23) were used to determine whether
Eq. 9 produced reasonable results and to determine the equation's range
of applicability. These data are based on 59 observations of n in which
slopes are greater than 0.002, and the hydraulic radii are less than 7 ft
(2.1 m). The algebraic mean of the percentage differences in the results
was —7.8. The standard deviation of the percentage differences was 23%
and ranged from —44-50%.
RESULTS
Although Eq. 9 provides a good means of estimating channel roughness, there are several explanations for the error associated with the
1532
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equation. Eq. 9 predicts the average roughness of the reach of a stream
rather than of an individual subreach. The flow conditions in high-gradient streams are extremely turbulent and add an unknown component
to the measurement error, which is not present in more tranquil streams.
Although the channel reaches selected were primarily uniform to slightly
contracting, there were some cases where expansion did occur and could
not be avoided. Expanding reaches also affected the stream data collected by Barnes (4) and Limerinos (23) and probably most other natural
channel data. Although a detailed investigation was not made, it was
noted that in some cases the energy loss in terms of the variation of
observed Manning's n was as much as 61% higher in expanding reaches
than in contracting reaches. There were no measurable differences in
bed material throughout each reach, indicating that the energy losses
were due to channel expansion. These losses could pose serious problems in hydraulic studies of streams because these studies encompass
many expanding reaches.
REGIME EQUATIONS FOR VELOCITY AND DISCHARGE
One of the reasons for developing an equation to predict Manning's
roughness coefficient (Eq. 9) using friction slope and hydraulic radius as
power variables was that the Manning equations (Eqs. 1 and 3) are in
the form of power equations. Therefore, for the simple case of uniform
flow and no other factors affecting bank roughness, Eq. 9 could be directly substituted into the Manning equations (Eqs. 1 and 3). Substituting Eq. 9 into Eqs. 1 and 3 results in regime equations for velocity:
V = 3.81 R°-83S0-12
(10)
and for discharge
Q = 3.81 ARomS012
(11)
in which the variables are the same as defined previously. Eq. 10 was
also derived by multiple-regression techniques using velocity as the dependent variable, and Eq. 11 was derived by substituting Eq. 10 into the
continuity equation, Eq. 2. These equations provide a means of solving
directly for velocity and discharge in uniform natural channels without
the need for subjectively evaluating channel roughness.
LIMITATIONS OF PREDICTION AND REGIME EQUATIONS
The following restrictions need to be observed when using the previously developed equations to predict the Manning's n (Eq. 9), the velocity (Eq. 10), and the discharge (Eq. 11) of high-gradient streams:
1. The equations are applicable to natural main channels having stable
bed and bank materials (gravels, cobbles, and boulders) without backwater.
2. The equations can be used for slopes from 0.002-0.04 and for hydraulic radii from 0.5-7 ft (0.15-2.1 m). The upper limit on slope is due
to a lack of verification data available for the slopes of high-gradient
streams. Results of the regression analyses indicated that for hydraulic
1533
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radius greater than 7 ft (2.1 m), n did not vary significantly with depth;
thus extrapolation to larger flows should not be too much in error as
long as the bed and bank material remain fairly stable.
3. The energy-loss coefficients were assigned the values 0 and 0.5.
4. Hydraulic radius does not include the wetted perimeter of bed particles.
5. These equations are applicable to streams having relatively small
amounts of suspended sediment.
FLOW REGIME IN STEEP CHANNELS
Standard hydraulic theory and analysis indicate that when slope exceeds critical slope—that is, when the Froude number exceeds unity—
higher velocities and supercritical flow result. Peterson and Mohanty
(24) observed extended reaches of supercritical flow; however, these were
observed in high-gradient flumes. The field data collected for this study
(Table 1) included slopes as steep as 0.052 and indicate that the Froude
numbers for flow in high-gradient streams are less than unity
(4,5,8,20,21,23). The combined effects of channel and cross-section variations create extreme turbulence and energy losses that result in increased flow resistance. The characteristic turbulence of a high-gradient
stream is shown in a photograph (Fig. 6) taken at the Arkansas River
site (Table 1, site 1). Studies of the flow resistance of boulder-filled streams
indicated that there is a spill-resistance component with increasing flow
(18,26). Spill resistance is a result of increased turbulence or roughness
resulting from the velocity of water striking the large area of protruding
bedroughness elements and eddy currents set up behind the larger boulders. Aldridge and Garrett (1) believe the effect of the disturbance of
water surrounding boulders and obstructions increases with velocity and
may overlap with nearby obstruction disturbances and further increase
FIG. 6.—Characteristic Turbulence. Upstream View at Arkansas River at Pine Creek
School, above Buena Vista, Colo. (Discharge is 4,530 cu ft/sec = 128 m3/s)
1534
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1.0
1
'
0.9
-
0.8
-
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1
1
9
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0
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s
9
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tr
dQ ° -
1
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0.3
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9
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OBSERVATIONS
.
*
• ONE
A TWO
1
0.005
0.010
0.015
FRICTION
0.020
0.025
0.030
0.035
SLOPE, S
FIG. 7.—Observations of Froude Number and Various Friction Slopes
turbulence and thus, roughness. Bathurst (5) noted supercritical flow
over boulders in natural channels and hydraulic jumps occurring just
downstream, but these were very limited in areal extent. Very localized
areas of supercritical flow were observed during the collection of data
for this study where flow went over boulders. Observations of Froude
number and various friction slopes for the data in Table 1 are shown in
Fig. 7.
The Froude number is computed as:
V
(12)
where F = the Froude number and the other variables are as previously
defined. Froude numbers less than 1, indicating subcritical flow, were
characteristic of all sites. There also does not appear to be any tendency
for Froude numbers to increase with friction slope.
The question remains as to whether flow becomes supercritical (Froude
number exceeds 1) at higher flood discharges. At higher flows, channelbank roughness (vegetation or bank irregularities) can markedly increase
total channel roughness as shown in Fig. 3. During larger floods, channel erosion is common. Usually when large floods occur in small steep
basins, large amounts of channel erosion occur and sediment is subsequently transported. About 60,600 tons (55,000 metric tons) of sediment
were eroded from the valley floor of Loveland Heights tributary to the
Big Thompson River, Colo., during the 1976 flood (2). Additional energy
is consumed in transporting the bed material. Flume studies by Bathurst
et al. (6) indicate there is a sharp increase in resistance when bed material moves. Rubey (28) showed that energy is required to move sediment, and transport of fine-grained sediment tends to reduce turbulence
and, thus, flow resistance. However, this decrease in resistance is normally offset by a much greater increase in flow resistance caused by the
formation of dunes (32). The movement of the bed material probably
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makes the channel react like an alluvial channel in which bed forms produce standing waves and additional energy losses as a result of an increase in friction. Critical and supercritical flow can occur locally in these
channels, in smooth bedrock channels, and in fine-grained alluvial channels. Dobbie and Wolf (14), Thompson and Campbell (31), and the writer
believe that during large floods, n values are much higher than those
normally selected and that flows in high-gradient natural channels containing cobbles and boulders generally approach, but do not exceed, critical flow. For these conditions of high-gradient streams and extreme flows,
a limiting assumption of critical depth in subsequent hydraulic analyses
appears reasonable. Chow (11) provides information on the critical-depth
method for computing discharge.
VELOCITY HEAD COEFFICIENT
Eqs. 5, 6, and 8 require the computation of the velocity head V2/2g.
Streambed roughness, cross-section irregularities, channel variations,
obstructions, vegetation, channel meandering, and other factors cause
velocity in a channel to vary from point to point. Because of this variation in velocity, velocity head is greater than the value computed from
V2/2g. True velocity head is expressed as aVz/2g, where alpha is velocity head coefficient. Velocity head coefficient, or kinetic energy coefficient (11) is computed as:
in which v = the measured velocity in an elementary area A A and the
other variables are as previously defined. Alpha was computed from the
discharge measurements made using Eq. 13 and the values are shown
in Table 1. These values are based on the average velocity in the vertical
subarea rather than on the vertical-velocity distribution (from multiplepoint velocity measurements) in each subarea because these data were
not available. Hulsing and others (19) showed that the values of alpha
computed from multiple-point velocity measurements were similar to the
one-point (0.6 depth) and two-point (0.2 and 0.8 depth) velocity measurements. The two-point method of determining velocity was used for
the majority of the measurements in this study.
The values of alpha shown in Table 1, which ranged from 1.0-2.0,
had the correlation coefficients shown in Table 3 indicate a slight tendency for alpha to decrease with discharge and depth. There also is a
slight tendency for alpha to increase with channel roughness, slope, and
particle size. Because the alpha values consist of two subsets, one including natural channels and another including channels having roanmade obstructions, subsequent analyses were made on each subset. Attempts made to develop relations between alpha and other hydraulic or
bed-material properties were unsuccessful because of the complexity of
the changes in alpha and these variables. The mean of all the alpha values and the means of the two subsets ranged from 1.33-1.34.
Inspection of the values of alpha in Table 1 indicates the values are
much greater than the value of 1 assumed in Eqs. 5, 6, and 9. However,
1536
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the solution of Eq. 8 for a multisection reach involves an evaluation of
the difference between the alpha coefficients of upstream and downstream sections. Therefore, although the value of alpha may be greater
than 1.0, what is important and consequently what would affect the accuracy of the computed n value is the relative difference between alpha
upstream and downstream. It would be nearly impossible to measure
the alpha of all cross sections at high flows. The majority of the reaches
used are basically uniform throughout, although slightly contracting, as
indicated by the basic hydraulic properties. Therefore, the higher values
of alpha should not introduce much error in the computed n values.
However, those studies that evaluate the velocity head to determine mean
channel velocity at one cross section, such as techniques using superelevation around bends, slope-conveyance, or dynamic uprise (velocity head
buildup), could be in considerable error in assuming alpha equals 1 in
a simple trapezoidal-shaped channel cross section.
SUMMARY AND CONCLUSIONS
Hydraulic calculations of the flow in channels and overbank areas of
flood plains require an evaluation of roughness characteristics. Most
commonly, Manning's roughness coefficient is used to describe the flow
resistance or relative roughness of a channel or overbank area. Available
guidelines for selecting the roughness coefficients of high-gradient streams
have not been verified.
Field surveys and 75 current-meter measurements of discharge were
made at 21 high-gradient natural stream sites in the Rocky Mountains of
Colorado for the purpose of computing channel roughness by the Manning formula and to evaluate other hydraulic characteristics of high-gradient streams. These data indicate that Manning's roughness coefficient
decreases markedly with depth and increases with friction slope. Multiple-regression techniques were used to develop a method for predicting Manning's roughness coefficient from the easily measured friction
(or water) slope and hydraulic radius (or hydraulic depth). The average
standard error of the prediction equation is 28% and ranges from —2432%. The equation was verified using other available data on high-gradient streams. Regime equations were developed to estimate velocity
and discharge without requiring a subjective estimate of channel roughness.
The data collected for this and other studies indicate that Froude numbers for flow in high-gradient, natural mountain streams are generally
less than unity. There is no tendency for Froude numbers to increase
with slope. Subcritical flow is due to the combined effects of channel
and cross-section variations, bank roughness, spill resistance, and to an
increase in the effect of these factors with increasing discharge, which
creates extreme turbulence and energy losses that result in increased
flow resistance. During floods, energy is required to transport eroded
material; thus, flow conditions may approach, but probably do not exceed, critical flow, except in very localized areas in the channel.
Alpha, the velocity-head coefficient, was computed from discharge
measurements and was found to range from 1.0-2.0 in these high-gradient streams. Alpha showed a slight tendency to increase with an in1537
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crease in M a n n i n g ' s r o u g h n e s s coefficient, b u t this w a s n o t always the
case.
Streambed particle-size data were obtained a n d presented but not used
directly in the analysis of flow resistance. The bed-material size (rf84)
ranged from 0.3-2.6 ft (0.1 to 0.8 m).
ACKNOWLEDGMENTS
This study was authorized by a cooperative agreement between the
U.S. Geological Survey a n d the State of Colorado, D e p a r t m e n t of Natural Resources, Colorado Water Conservation Board. I would like to thank
my colleagues at the Colorado District for their help with field work a n d
preparation of the data.
APPENDIX.—REFERENCES
1. Aldridge, B. N., and Garrett, J. M., "Roughness Coefficients for Streams in
Arizona," U.S. Geological Survey Open-File Report, Feb., 1973.
2. Andrews, E. D., and Costa, J. E., "Stream Channel Charges and Estimated
Frequency of a Catastrophic Flood, Front Range of Colorado," Geological Society of America Abstracts with Programs, Vol. 11, No. 7, 1979, p. 379.
3. Ayvazyan, O. M., "Comparative Evaluation of Modern Formulas for Computing the Chezy Coefficient," Soviet Hydrology, Vol. 18, No. 3, 1979, pp.
244-248.
4. Barnes, H. H., Jr., "Roughness Characteristics of Natural Channels," USGeological Survey Water-Supply Paper 1849, 1967.
5. Bathurst, J. C , "Flow Resistance of Large-Scale Roughness," Journal of the
Hydraulics Division, ASCE, No. HY12, Dec, 1978, pp. 1587-1603.
6. Bathurst, J. C , Li, R-M, and Simons, D. B., "Hydraulics of Mountain Rivers," Report No. CER78-79JCB-RML-DBS55, Civil Engineering Department,
Colorado State University, Fort Collins, Colo., 1979.
7. Benson, M. A., and Dalrymple, T., "General Field and Office Procedures for
Indirect Discharge Measurements," U.S. Geological Survey Techniques of WaterResources Investigations, Book 3, Chpt. A-l, 1967.
8. Bray, D. I., "Estimating Average Velocity in Gravel-Bed Rivers," Journal of
the Hydraulics Division, ASCE, No. HY9, Sept., 1979, pp. 1103-1122.
9. Buchanan, T. J., and Somers, W. P., "Discharge Measurements at Gaging
Stations," 17.5. Geological Survey Techniques of Water-Resources Investigations,
Book 3, Chpt. A-8, 1969.
10. Carter, R. W., et al., "Friction Factors in Open Channels," Journal of the Hydraulics Division, ASCE, No. HY2, Mar., 1963, pp. 97-143.
11. Chow, V. T., Open Channel Hydraulics, New York, McGraw-Hill, 1959.
12. Cowan, W. L., "Estimating Hydraulic Roughness Coefficients," Agricultural
Engineering, Vol. 37, No. 7, July, 1956, pp. 473-475.
13. Dalrymple, T., and Benson, M. A., "Measurement of Peak Discharge by the
Slope-Area Method," U.S. Geological Survey Techniques of Water-Resources Investigations, Book 3, Chpt. A-2, 1967.
14. Dobbie, G. H., and Wolf, P. O., "The Lynmouth Flood of August 1952,"
Proceedings of the Institute of Civil Engineers, Part 2, 1953, pp. 522-588.
15. Fasken, G. B., "Guide for Selecting Roughness Coefficient 'n' Values for
Channels," Soil Conservation Service, U.S. Department of Agriculture, D e c ,
1963.
16. Golubtsov, V. V., "Hydraulic Resistance and Formula for Computing the
Average Flow Velocity of Mountain Rivers," Soviet Hydrology, No. 5, 1969,
pp. 500-510.
17. Hejl, H. R., "A Method for Adjusting Values of Manning's Roughness Coef1538
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18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
ficients for Flooded Urban Areas," U.S. Geological Survey, Journal of Research, Vol. 5, No. 5, Sept.-Oct., 1977, pp. 541-545.
Herbich, J. B., and Shulits, S., "Large-Scale Roughness in Open-Channel
Flow," Journal of the Hydraulics Division, ASCE, No. HY6, Nov., 1964, pp.
203-230.
Hulsing, H., Smith, W., and Cobb, E. D., "Velocity-Head Coefficients in
Open Channels," U.S. Geological Survey Water-Supply Paper 1869-C, 1966.
Judd, H. E., and Peterson, D. F., "Hydraulics of Large Bed Element Channels," Report No. PRWG17-6, Utah Water Research Laboratory, Utah State
University, Logan, Utah, Aug., 1969.
Kellerhals, R., "Stable Channels with Gravel-Paved Beds," Journal of the
Waterways and Harbors Division, ASCE, No. WW1, Feb., 1967, pp. 63-84.
Krumbein, W. C , "Measurement and Geological Significance of Shape and
Roundness of Sedimentary Particles," Journal of Sedimentary Petrology, Vol.
11, No. 2, Aug., 1941, pp. 64-72.
Limerinos, J. T., "Determination of the Manning Coefficient From Measured
Bed Roughness in Natural Channels," U.S. Geological Survey Water-Supply Paper 1898-B, 1970.
Peterson, D. F., and Mohanty, P. K., "Flume Studies of Flow in Steep, Rough
Channels," Journal of the Hydraulics Division, ASCE, No. HY9, Nov., 1960,
pp. 55-76.
Ree, W. O., and Palmer, V. J., "Flow of Water in Channels Protected by
Vegetative Linings," U.S. Soil Conservation Service, Department of Agriculture, Technical Bulletin 967, 1949.
Richards, K. S., "Hydraulic Geometry and Channel Roughness-—A Non-Linear System," American Journal of Science, Vol. 273, 1973, pp. 877-896.
Riggs, H. C , "A Simplified Slope-Area Method for Estimating Flood Discharges in Natural Channels," Journal of Research, U.S. Geological Survey,
Vol. 4, No. 3, May-June, 1976, pp. 285-291.
Rubey, W. W., "Equilibrium Conditions in Debris-Laden Streams," Transactions, American Geophysical Union, June, 1933, pp. 497-505.
Savini, J., and Bodhaine, G. L., "Analysis of Current-Meter Data at Columbia
River Gaging Stations, Washington and Oregon," U.S. Geological Survey WaterSupply Paper 1869-F, 1971.
Simons, D. B., and Senturk, F., "Sediment Transport Technology," Water
Resources Publications, 1977.
Thompson, S. M., and Campbell, P. L., "Hydraulics of a Large Channel Paved
with Boulders," Journal of Hydraulic Research, Vol. 17, No. 4, 1979, pp. 341354.
Vanoni, V. A., and Nomicos, G. N., "Resistance Properties of SedimentLaden Streams," Transactions, ASCE, Vol. 125, 1960, pp. 1140-1175.
Wolman, M. G., "A Method of Sampling Coarse River-Bed Material," Transactions, American Geophysical Union, Vol. 35, No. 6, 1954, pp. 951-956.
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