Geoscience Reference
In-Depth Information
within meandering channels (see below), with a spiral
or
helical flow
pattern and accompanying transverse
currents.
Vital parameters of velocity and discharge are bound
up in river flow and its geomorphic activity. In addition
to varying with distance from the river bed and banks,
velocity changes at-a-point with turbulence and discharge
but is fairly constant downstream. This reflects down-
stream increases in hydraulic efficiency which compensate
(a)
(b)
Flow
Flow
v
max
v
max
Zone of
maximum shear
Laminar flow
Turbulent flow
(c)
v
max
0.4
0.8
0.6
0.2
1.0
7
7
7
Figure 14.13
Vertical long sections (a) and (b) and cross-
section (c) through a stream, showing styles of water
movement and isovels linking points of equal velocity (1.0
marks the v
max
).
7
7
= Turbulence
Channel hydraulics
KEY PROCESSES
Channel geometry is defined by width, depth, length and slope, best seen in a short
channel segment
which
emphasizes the role of water level in two further, derived channel parameters. The
wetted perimeter
(wp) equals
2d + w in a rectangular channel and
hydraulic radius
R is the cross-sectional area A=(d w) divided by wetted
perimeter (2d+w) (
Figure 14.14
).
This allows us to measure discharge as:
Q = v
mean
. R
where v
mean
is the mean velocity. Natural channels have irregular wetted perimeters, and the magnitude of energy
loss at the bed emphasizes the role of bed roughness. This is assessed through the
Manning equation
, which defines
the v
mean
in terms of hydraulic radius, channel slope (S) and a roughness coefficient (n):
v
mean
= (R
2/3
S
1/2
) n
-1
n ranges from 0·02 for smooth, straight channels to 0·1 for rocky channels.
A number of other channel and flow conditions now fall into place. As well as measuring the effect of roughness in
retarding flow, the Manning equation makes the role of slope and hydraulic radius clear. The latter is particularly
important to hydraulic efficiency, as shown by the hypothetical geometry and discharge of three streams in
Figure
14.14b
)
. The shallowest channel has the smallest hydraulic radius and lowest efficiency. The combined flow of A
and B in C demonstrates the normal advantages of trunk over tributary rivers and the response to variations in stage
and discharge. Hydraulic radius and velocity are linked with distinctions between laminar and turbulent flow via the
Reynolds number (Re):
Re = (v
mean
R) v
-1
where v is kinematic viscosity (the ratio of dynamic viscosity to density). Laminar flow and turbulent flow are found
separately, or both types together, where Reis less than 500, over 2,000 and 500-2,000 respectively. Velocity, linked
this time with stage (d), is also used to distinguish between two types of
flow regime
defined by their
Froude
number
(F):
F = v
mean
/
gd
where g is the gravitational acceleration. The flow is said to be critical when F = 1, separating tranquil or subcritical
flow regime (F = 1) from rapid or supercritical flow regime (F 1).
