FLOOD06021

• County: Larimer
• Stream Name: Big Thompson
• Basin: South Platte
• Title: Flood History of the Big Thompson River Basin: Flash Floods, Paleofloods, and Dam-Break Floods
• Date: 1/1/1979
• Prepared For: Larimer
• Prepared By: USGS
• Floodplain - Doc Type: Flood Documentation Report

, ~S'../

/' Hydrologic and Hydraulic Research in Mountain Riven

estimated with existing guidelines, typically by a fac-
tor of! to 2.

0.16

f-
Z
!!! 0.14
u
it
~ 0.12
u
l/l
13 0.10
z
:r
g O.OS
o
a:
l/l
to 0.06
:z
Z
:l 0.04
~

Arkansas River (site ,)

Clear Creek Is~e 2)

. Eagle River (site 5)

0.020 2 4 6 S 10 12 14
RELATIVE SMOOTHNESS, R1D50 '

Figure 4. Relation of Manning's Roughness Coefficient
to Relative Smooth..... and Friction Slope.

Because data from higher-gradient rivers indicate
that the flow resistance varies considerably with
depth of flow (and because of the difficulty in visually
estimating n values during onsite inspection), equa-
tions were developed to assist in the assessment of
flow resistance in mountain rivers. Multiple-
regression analyses of Manning's n were related to
measured hydraulic and sediment-size variables. The
analyses indicated that n varies directly with friction
slope and inversely with hydraulic radius. The equa-
tion developed for predicting Manning's n in natural
mountain channels with cobble or boulder bed materi-
al is:

n = 0.32 SO.38~.16

(1)

where S is the energy gradient (Dr friction slope) in
meter per meter, and R is the hydraulic radius in
meters. Alternately,

n = 0.39 SO.38~.16

where S is the energy gradient (or friction slope) in
foot per foot, and R is the hydraulic radius in feet. If
the channel is relatively uniform, water-surface slope
or bed slope (river gradient) can be used in Equations
(1) and (2).

'Z-CR

The average standard error of estimate of
Equations (1) and (2) was 28 percent for the Colorado
data. The equation had the same accuracy when other
data for higher gradient rivers of the world (gradients
as high as 0.052 meter per meter or foot per foot) were
used (Jarrett, 1984). Equations (1) and (2) are appli-
cable for relatively clear-water flow in stable channels
with minimal bank vegetation, regular banks, and
few obstructions. Equations (1) and (2) are defined for
gradients from 0.02 to 0.052 meter per meter (foot per
foot) and for hydraulic radii from 0.15 to 2.2 meters
(0.5 to 7 feet). Paul and Dhillon (1987) and Cheadle
and Thome (1988) verified the accuracy of Equations
(1) and (2) with other data from higher-gradient
mountain rivers, and also determined that Equations
(1) and (2) predict n values with the same accUracy or
better than equations bssed on relative smoothness.
Cheadle and Thorne (1988) also indicated that
Equations (1) and (2) have little bias and that it pre-
dicted n values on rivers with gradients as high as
0.09 meter per meter (foot per foot).
Velocity and discharge for a reach of river generally
are estimated using the Manning equation. Therefore,
regime-flow equations for predicting velocity and dis-
charge in mountain rivers also were developed from
Colorado data (Jarrett, 1984). These equations are:

V = 3.17 RO.83S0.12

(3)

and

Q = 3.17 ARO.83S0.12

(4)

where V is the mean flow velocity in meters per sec-
ond, Q is the discharge in cubic meters per second,
and A is the cross-sectional area of flow in square
meters. Alternatively,

V = 3.81 RO.83S0.12

(5)

and

Q = 3.81 ARO.83S0.12

(6)

(2)

where V is the mean flow velocity in feet per second,
Q is the discharge in cubic feet per second, and A is
the cross-sectional area of flow in square feet. These
equations have the same applicability, limitations,
and accuracy as Equations (1) and (2). Use of
Equations (3) through (6) provides a means of solving
directly for velocity and discharge for mountain rivers
with hydraulic characteristics (R, S, and bed-material
sizes) similar to the Colorado rivers without the need
for a subjective evaluation of channel roughness. A
report is available to assist in the determination of

425

WATER RESOURCES BULLETIN
1/,"1-b) #- 3 I /q'lC)

J"AiZt2eTT