FLOOD01888

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

e

.
,

~

e

~

e

and the subscripts on V and A designate different river
section locations. Equatinn 2-4 is not valid where the
discharge changes along the river. That type of flow is
referred 10 as spatially varied flow and occurs when
water runs into or out of the river from tributaries, storm
drains, drainage canals, and side-channel spillways.

(2) The continuity equation for unsteady, one-
dimensional flow requires consideration of storage as
shown below:

B!!:!..+aQ=O
at ax

(2-5)

where

B = channel top width (ft)
x = longitudinal distance along the centerline of the
channel (ft)
d = depth of flow (ft)
t = time (seconds)

The two terms represent the effects of temporal change
in slorage and spatial change in discharge, respectively.
Further detail regarding the derivation and alternative
forms of the continuity equation are presented by Chow
(1959), Henderson (1966), and French (1985). See also
Chapters 4 and 5.

b. Conservation of energy. The second basic com-
ponent that must be accounted for in one-dimensional
steady flow situations is the conservation of energy. The
mathematical statement of energy conservation for steady
open channel flow is the modified Bernoulli energy equa-
tinn; it states that the sum of the kinetic energy (due to
motion) plus the potential energy (due to height) at a
particular locatinn is equal to the sum of the kinetic and
potential energies at any other location plus or minus
energy losses or gains between those locations.
Equation 2-6 and Figure 2-6 illustrate the conservation of
energy principle for steady open channel flow.

2
lX;zV2
WS2 + - = WSj
2g

2
ajV1
+ - + he
2g

(2-6)

where

WS = water surface elevation (ft)
he = energy loss (ft) between adjacent sections

EM 1110-2-1416
15 Oct 93

and the other terms were previously defined. This equa-
tion applies to uniform or gradually varied flow in chan-
nels with bed slopes (e) less than approximately
to degrees. Units of measurement are cited in Table 2-l.
In steeper channels, the flow depth 'd' must be replaced
with (d*cosll) 10 properly account for the potential
energy. For unsteady flows refer to Chapters 4 and 5.

Tobie 2-1
Cony.--ion F.-.., Non-Sl to 51 (Metric)
Unl" of .......rem..'
Non-Sl urn.. of _urement u_ In this report can be
con_ to 51 (metric) unl.. .. followe:

Multiply By To Obtain
cubic feet 0.02831685 cubic meters
cubic yards 0.7645549 cubic meters
dogrees Fahrenheit 519' dogrees Celsius or
Kelvin
feet 0.3048 meters
inches 2.54 centimeters
miles (US statute) 1.609347 kilome_
tons (2.000 pounds.
mass) 907.1847 kilograms

'To obtain Celsius (C) temperature readings from Fahrenheit (F)
readings, use tha following formula: C = (5J9)(F - 32). To obtain
Kelvin (I<) readings. use: K = (5J9)(F - 32) + 273.15.

c. Application to open channels. Even though the
same laws of conservation of mass and energy apply 10
pipe and open channel flow, open channel flows are
considerably more difficult to evaluate. This is because
the location of the water surface is free to move tempo-
rally and spatially and because depth, discharge, and the
slopes of the channel bottom and free surface are inter-
dependent (refer to Figure 2-1 and to Chow (1959) for
further explanation of Ihese differences). In an open
channel, if an obstruction is placed in the flow and it
generates an energy loss (h" in Figure 2-6), there is some
distance upstream where this energy loss is no longer
reflected in the position of the energy grade line, and
thus the flow depth at that distance is unaffected. The
flow conditions will adjust 10 the local increase in energy
loss by an increase in water level upstream from the dis-
turbance thereby decreasing frictional energy losses.
This allows the flow 10 gain the energy required to

2-11