Geology Reference
In-Depth Information
Box 3.4
REYNOLDS AND FROUDE NUMBERS
Reynolds number
is a dimensionless number that
includes the effects of the flow characteristics, veloc-
ity, and depth, and the fluid density and viscosity. It
may be calculated by multiplying the mean flow veloc-
ity,
v
, and hydraulic radius,
R
, and dividing by the
kinematic viscosity,
where
v
is the flow velocity,
g
is the
ac
celeration of
gravity,
d
is the depth of flow, and
gd
is the veloc-
ity of the gravity waves. When
F
<
1 (but more than
zero) the wave velocity is greater than the mean flow
velocity and the flow is known as
subcritical
or
tran-
quil
or
streaming
. Under these conditions, ripples
propagated by a pebble dropped into a stream create
an egg-shaped wave that moves out in all directions
from the point of impact. When
F
(nu), which represents the ratio
between molecular viscosity,
ν
µ
(mu), and the fluid
σ
density,
(rho):
=
1 flow is crit-
ical, and when
F
1itis
supercritical
or
rapid
or
shooting
. These different types of flow occur because
changes in discharge can be accompanied by changes
in depth and velocity of flow. In other words, a given
discharge can be transmitted along a stream channel
either as a deep, slow-moving, subcritical flow or else
as a shallow, rapid, supercritical flow. In natural chan-
nels, mean Froude numbers are not usually higher
than 0.5 and supercritical flows are only temporary,
since the large energy losses that occur with this type
of flow promote bulk erosion and channel enlarge-
ment. This erosion results in a lowering of flow velocity
and a consequential reduction in the Froude num-
ber of the flow through negative feedback. For a fixed
velocity, streaming flow may occur in deeper sections
of
>
ρν
R
µ
R
e
=
For stream channels at moderate temperatures, the
maximum Reynolds number at which laminar flow is
sustained is about 500. Above values of about 2,000,
flow is turbulent, and between 500 and 2,000 laminar
and turbulent flow are both present.
The
Froude number
is defined by the square root of
the ratio of the inertia force to the gravity force, or the
ratio of the flow velocity to the velocity of a small gravity
wave (a wave propagated by, say, a tossed pebble) in still
water. The Froude number is usually computed as:
v
gd
the
channel
and
shooting
flow
in
shallower
=
F
sections.
named after English scientist and engineer Osborne
Reynolds, may be used to predict the type of flow
(laminar or turbulent) in a stream (Box 3.4).
In natural channels, irregularities on the channel bed
induce variations in the depth of flow, so propagating
ripples or waves that exert a weight or gravity force. The
Froude number
,
F
, of the flow, named after the English
engineer and naval architect William Froude, can be used
to distinguish different states of flow -
subcritical flow
and
critical flow
(Box 3.4).
Plunging flow
is a third
kind of turbulent flow. It occurs at a waterfall, when
water plunges in free fall over very steep, often verti-
cal or overhanging rocks. The water falls as a coherent
mass or as individual water strands or, if the falls are very
high and the discharge low, as a mist resulting from the
water dissolving into droplets.
Flow velocity controls the switch between subcrit-
ical and supercritical flow. A
hydraulic jump
is a
sudden change from supercritical to subcritical flow.
It produces a stationary wave and an increase in water
