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

volumes as a function of discharge constitutes the
slorage/outflow relation. Such a relation ignores the
effects of unsteadiness on the flood wave profile and
hence on slorage. The method can be successful if the
local accelerations are negligible; i.e., if the reach is so
geometrically nonuniform that advective accelerations
from that source are large, and, at the same time, the rate
of rise of the flood is so small that local and advective
accelerations resulting from the unsteadiness are neg-
ligible in comparison.

(5) A potential source of major error with the Modi-
fied PuIs method is that, in some flow circumstances,
there is no physical relation between reach storage and
outflow. The method does not account for the time
changes in water flow that are transmitted as waves and
not instantaneously from one end of the reach to the
other. For example, a sharp increase in discharge at the
upstream end of a reach produces a wave of increased
depth that travels downstream at some velocity, generally
somewhat greater than the water velocity. Thus, the
storage in the channel starts to increase immediately, but
the outflow is not affected at all until the wave fmally
arrives at the downstream end of the reach.

(6) The slorage/outflow relation derived from a
sequence of steady flows is unique; it plots as a single
curve without hysteresis. But even a stage/outflow rela-
tion at a gaging station exhibits hysteresis in unsteady
flow, with one branch of the hysteresis loop describing
the function for the rising limb of the hydrograph and the
other for the falling limb. This is due 10 the influence of
local acceleration and its effect on water surface slope
and advective acceleration. While a small amount of
hysteresis is not of great concern, the hysteresis loop for
a storage/outflow relation can be markedly more pro-
nounced because of the traveling flood wave volume
passing through the reach.

(7) In order to devise a more correct theoretical
relation between storage and outflow than is possible
using the entire reach as a unit (typically, the shape of
the water surface within the reach is unknown)" the reach
may be broken inlo a number of subreaches. In each of
these, the water surface is assumed level, or parallel to
the bottom, and the outflow of a subreach is related 10
the depth through some uniform flow formula such as the
Manning equation. As the number of subreaches is

5-32

increased indefinitely, the scheme approaches that of the
kinematic wave theory.

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(8) Except for level-pool routing, the Modified PuIs
method should be used with caution, particularly for
conditions outside the range of events used for
calibration.

e. Muskingum technique. The assumption is made
that the slorage in a reach at some instant is related to
both the inflow and outflow of the reach at that instant,
which is more realistic than relating storage to outflow
alone, as in the Mndified Puis method. In the
Muskingum technique storage is assumed to be in part
directly proportional to inflow and in part directly pr0-
portional to outflow. The constants of proportionality
can be determined either empirically from a study of
known events or theoretically as in the Muskingum-
Cunge technique. The major cause for concern in empir-
ical derivations is that the subject simulation event may
not produce the same wave prof1les as the calibration
event(s).

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f. Muskingum-Cunge technique. In addition to the
diffusion wave assumptions, the assumption is made that
during the passage of the flood wave down the reach,
departures from normal depth in the reach are not great.
Then the proportionality constants in the Muskingum
method can be determined theoretically. The diffusion
equations are linearized about normal depth for some
average condition in the reach and the results manipu-
lated 10 yield the proportionality coefficients. The the0-
retical nature of the determination of the coefficients
suggests that this is a hydraulic rather than hydrologic
technique, especially, if the reach is broken up into a
large number of subreaches 10 account for the unknown
shape of the flood wave and to better schematize the
boundary geometry. It is also discussed in section 5-16.

e

g. Working Rand D method. This method is the
same as the Muskingum method in that storage is
assumed to be related to both inflow and outflow, but not
necessarily proportional. Tabulated or graphed relations
are envisioned. The method has more potential than
Modified Puis (which can be considered a subset of the
working R and D method) because it allows for the pos-
sibility that reach storage depends on inflow as well as
outflow.

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