Environmental Engineering Reference
In-Depth Information
threshold, there are
two alternate water depths
. For the threshold value,
the specific energy is the minimal energy needed to convey that discharge
Q
through that cross section. In the case of the minimum energy the two
alternate depths coincide for the given discharge
Q
and the water depth
becomes the 'critical depth' (
y
c
). The Froude number for that discharge
and water depth becomes 1 (Fr
2
1). In other words, for this critical depth
the specific energy has a minimum value for the given discharge
Q
and
cross section A.
When the flow depth is greater than the critical depth, the flow is
subcritical; if it is less the flow is supercritical (see Table 2.2). For any
discharge
Q
there are two possible flow regimes, but in reality only one
will occur. These two flow regimes are either a slow and deep subcritical
flow or a fast and shallow supercritical flow.
=
Table 2.2.
Flow type as a function of the actual water depth.
Actual depth
y
in
relation to
y
c
Froude number
Flow type
Fr
2
<
1
y > y
c
Subcritical
Fr
2
y
=
y
c
=
1
Critical
Fr
2
>
1
y < y
c
Supercritical
For critical flow conditions:
•
and for a given discharge
Q
the specific energy
E
s
has a minimum
value;
•
and for a given specific energy
E
s
the discharge
Q
has a maximum
value;
•
the velocity head is half the hydraulic depth
D
;
the Froude number Fr
2
•
is one (unity).
2.5 VELOCITY DISTRIBUTION
In the next chapters it will be shown that the average velocity
v
Q/A
,
and the deviation from this average velocity, are very important aspects
in hydraulics and sediment transport. Water flowing in a cross section
with a rigid or movable boundary (bottom and wall) will show a specific
velocity distribution across that section. The velocity will be zero at the
fixed boundary and next the velocity increases rapidly towards the middle
and upper part of the channel. The velocity in a specific point is a function
of the
x
,
y
and
z
coordinates (Figure 2.7).
=
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