FLOOD01888

• County: Statewide
• Title: River Hydraulics
• Date: 10/15/1993
• Prepared By: US Army Corps of Engineers
• Floodplain - Doc Type: Educational/Technical/Reference Information

EM 1110-2-1416
15 Oct 93

'"'

v

,

~

, '

tAMlNAR OPEN C~NEL
fLOW VELOCITY PROFlLE

/ "

'/

,

,~ ,,'

-..:" ,,,<

LAIoI1NAR PIPE fLOW
VELOCITY PROFILE

Figure 2-2. laminar and turbulent velocity profilas

should refer to texts by Chow (1959), Henderson (1966),
and Rouse (1959).

c. Effects of gravity (subcritical and supercritical
flow). The ratio of inertial to gravitational forces is an
important measure of the state of open channel flow and
is represented by the Fronde number:

F~~
IiL

(2-2)

where

F = Froude number (dimensionless)
V = mean flow velocity in the channel (ft/sec)
g = acceleration of gravity (ftlsec2)
L = characteristic length term (ft)

In open charmels and rivers the characteristic length (L)
is often taken as the hydraulic depth; i.e., the
cross-sectional area normal to the flow divided by the top
width at the free surface. Depending on the magnitude
of the Fronde number, the state of flow is either "sub-
critical', "criticar', or "supercriticaI."

2.6

v

, ,,<

,

TURBULENT OPEN CHANNEL
fLOW VELOCITY PROFILE

, '/

, .

-..:" ,Y

TURBULENT PIPE FLOW
VELOCITY PROFlLE

(I) When the Fronde number is less than 1, the
effects of gravitational forces are greater than inertial
forces, and the state of the flow is referred 10 as subcriti-
cal, or tranquil flow. Note that the denominalor in the
Froude number (Equation 2-2) is the expression for celer-
ity of a shallow water wave. Therefore, in subcritical
flow, the wave celerity is greater than mean channel
velocity, and a shallow water wave can move upstream.
As a simple field test, toss a slone into the river; if you
observe the ripples from the stone hitting the water mov-
ing upstream, the flow for that location, depth, and dis-
charge is subcritical (F < I).

(2) When inertial and gravitational forces are equal,
the Froude number is equal 10 unity, and the flow is said
to be at the critical state (i.e., critical flow). For these
conditions, a shallow water wave remains approximately
stationary in the flow relative to the banks. At critical
flow, the depth is referred 10 as "critical depth."

(3) When inertial forces exceed gravitational forces
(F > I) the state of flow is referred to as supercritical, or
rapid flow. For this state, the flow is characterized by
high velocity, and shallow water waves are immediately

e

.
,

..
.

e

1

.

e