FLOOD05043

• County: Statewide
• Basin: Statewide
• Title: Dimensionless Graphs of Floods from Ruptured Dams
• Date: 1/1/1974
• Prepared For: US
• Prepared By: COE
• Floodplain - Doc Type: Educational/Technical/Reference Information

III. DIMENSIONLESS FLOOD GRAPHS

1. Dam-break Flood Variables

,;

For practical purposes it is desirable and adequate that the time of
arrival of the wave front as well as the maximum flood level and the
time of its occurrence after dam rupture, be known for any given location
downstream of the dam. In some cases and for preliminary investigations
a rough estimate of the above factors is sufficient. Under these condi-
tions approximate results can be drawn quickly from properly prepared
graphs representing solutions to a series of simple cases.

..

A simplification of the river valley geometry leads to a prismatic
channel of general parabolic cross-section as defined by Eq. 5. In this
case Eqs. 4 contain three parameters, namely Dro, M and C, besides the
dependent variables y and V and the independent variables x and t. Thus
the variables y and V are functions of five variables, that is

y = q (x, t, Fo, M, Cl
V = r (x, t, fo, M, C

(9)
(10)

For given values of x, 10, M and C, EQs. 9 and 10 represent the stage and
velocity hydrographs, respectively.

From the stage hydrograph and for practical purposes, one is mainly
interested in the maximum value of depth, YM' occurring at time t~1 such
that in Eq. 9

~I - 0
ar-- t=tM -

(11)

Then

YM = q (x, tM' Fo' 1"1, C)
Solving Eq. 11

(12)

t =
M
Introduction of Eq. 13 into

for tw one obtains
s (x, Fo' M, C)

(13)

Eq. 12 yields

YM = u (x, Fo' M, C)

(14)

:;.

The speed of propagation of the wave front, W, is equal to the flow velocity
at the wave front. If Xw and tw designate the wave-front location in the
x-t plane, then

W = ~~ = r (xw, tw, Fa, M, C) (15)

5