Environmental Engineering Reference
In-Depth Information
The relationship between
C
of de Chézy and Manning's
n
can be found
by taking the same average velocity
v
.
R
1
/
6
n
C
=
(2.36)
2.7 NON-UNIFORM STEADY FLOW
A gradually varied flow is a steady flow, whose depth varies gradually
along the channel:
•
Hydraulic flow characteristics remain constant in time,
•
Streamlines are practically parallel; hydrostatic pressure prevails,
•
Bed friction is assumed to be equal to the friction in uniform flow
(e.g. as used in the equations of Manning and de Chézy).
Figure 2.11 gives the energy considerations for unsteady flow in open
channels, which also can be used for gradually varied flow (steady flow
with d
v
/d
t
=
0).
dx
horizontal
h
a
= S
a
*
dx
h
f
= S
f
*
dx
y
y + dy
S
0
dx
z
z + dz
Figure 2.11. Energy
considerations in a channel
with unsteady flow.
datum
The assumptions made in deriving the gradual varied flow equations
are (Cunge et al., 1980):
- the flow is one dimensional;
- the flow velocity is uniform over the cross section;
- the water level across the section is horizontal;
- the streamline curvature is small and the vertical accelerations are
negligible, hence the pressure is hydrostatic;
- the effect of boundary friction and turbulence can be accounted for
through resistance laws analogous to those used for steady state flow;
- the average bed slope is small, so that the cosine of the angle it makes
with the horizontal may be replaced by unity.
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