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

the Saint-Venant equations take the dimensionless form

.

A ~ + V2L + 2L = 0
Ti ax ax at
~ + V~ + 1 2L = 1 [1 _ \ltRo)4/3]
at ax "r? ax 17
~her~ Ro is the dimensionless hydraulic radius corresponding to depth
y = Yo or to a dimensionless depth of unity.

(4a)

(4b)

.

For simplicity Yo is taken equal ~o the maximum value of water depth
behind the dam. Then, for a given channel_geowetry, bottom slope and
roughness, Eqs. 3 yield the values of Yo, Lo, To and Fo.

Equations 4 are applicable to channels with non-zero bottom slope.

3. Channel Geometry

In this work a prismatic channel is assumed with breadth B related
to depth y by a formula of the type

B = C t (5)

where C and M are constants. Non-dimensionalization of Eq. 5 yields
B = C yM (6)

where

C=CyM-l
o

(7)

If 80 denotes the breadth corresponding to depth Y = Yo' it is easily
seen that C = no/Yo' the relative top width of the channel cross-section
at the dam site.

4. Solution of the Equations

For details in solving Eqs" 4 and for the initial conditions, upstream
and downstream boundary conditions used in the solution, reference should
be made to (3, 4, 5).

:;.

In brief Eqs. 4 are transformed intc characteristic form and solved
numerically over the irregular grid formed by the characteristic lines
in the x-t plane using a predictor-corrector scheme.

The water behind the dam is assumed to be at rest prior to dam
failure and the downstream channel is dry. A generalized Ritter solution
(3, 4) is taken to represent initial conditions along a forward charac-
teristic shrunk to the point x = 0, t = 0 in the x-t plane.

3