Environmental Engineering Reference
In-Depth Information
Figure 1
(a) Geometry and (b) hydraulic efficiency in stream
channels. Principal parameters are identified in the text; h
1
-h
2
and
W
1
-W
2
represent the height decline in bed and water surface
respectively along segment length L. (b) shows the combined flow of
two tributary streams, A and B, downstream in C, assuming a
uniform velocity of 1 m sec
-1
. C has a greater channel efficiency,
reflected by the increase in R; R is still greater than 2·0 even if the
stage (depth) falls towards 4 m.
A number of other channel and flow conditions now fall into place. As well as
measuring the effect of roughness in flow retardation, the Manning equation also 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 1(b). 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
):
where
v
is
kinematic viscosity
(the ratio of dynamic viscosity to density). Laminar
flow and turbulent flow are found separately, or both ty pes together, where Re is less
than 500, over 2000 and 500-2000 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
):
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).
