by Dr. S.O. Russell
There are two basic types of flow:
CLOSED CONDUIT or PIPE FLOW, where the water is
under pressure and, provided the pressure is high enough, the
pipes can run up or down hill; and
OPEN CHANNEL FLOW, where the water can only flow
downhill. Open channel flow can be subdivided into:
uniform or non-uniform flow; and supercritical or
subcritical.
Uniform flow almost never occurs in natural
rivers, but since it is much easier to calculate uniform flow
than non-uniform flow, we generally assume (for calculation
purposes) that the flow is uniform. With uniform flow the most
commonly used formula in North America is the Manning formula.
MANNING FORMULA
v = (R2/3S1/2)/n
where:
v is the average velocity,
R is the "hydraulic radius",
S is the slope and n is the channel roughness (often called
Manning’s n).
R =A/P
where:
A is the cross-section area and
P is the wetted perimeter, which is often approximated as the top
width of the channel.
Q =Av, where Q is the flow in m3/s.
A, P and S can be obtained from field
measurements and n can be obtained from hydraulics textbooks or
guidebooks.
Critical flow is a special
case, where the flow is a maximum for the "energy" in
the water. The energy E = d +v2/2g, where d is the
depth, v the velocity and g the gravity constant. V2/2g
is often referred to as the velocity head.
Subcritical flow (the more
common type of flow) occurs when the velocity is less than
critical (and the channel is fairly flat); and supercritical flow
occurs when the velocity is greater than the critical velocity,
which means that the channel has to be relatively steep. For
example culverts usually have supercritical flow if the slope is
greater than about 1.5%. We can use this to compute flows from
water levels upstream of steep culverts, which have what is known
as "entrance control" and to compute the flow that such
a culvert can carry.
Subcritical flow can only change to supercritical flow by
going through critical flow; and supercritical flow can only
change back to subcritical flow by going through a hydraulic jump.
This has practical importance in that if the flow goes through
critical flow, then the flow can be calculated knowing the
upstream water level and the channel geometry at the critical
section.
In natural streams, supercritical flow can only occur locally,
such as between the pools in tumbling flow in steep creeks.
Otherwise the velocity would built up to the point where it can
move quite large boulders – and in effect steep streams move
their beds around to increase the roughness and prevent
supercritical flow from developing over any significant lengths. We
can use this to estimate flows in steep creeks.
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