FLOOD09784

• County: Statewide
• Basin: Statewide
• Title: Engineering and Design Routing of Floods Through River Channels
• Date: 3/1/1960
• Prepared For: US
• Prepared By: US Army Corps of Engineers
• Floodplain - Doc Type: Educational/Technical/Reference Information

EM 1110-2-1{08
t' 1 Mareh 1MO
(
\. routing of holdouts is advantageous in determining stage rcductions and benefits at damage points
downstream from the reservoirs. This method, like any other method in which the outflow can be
expressed as the summation of products of routing constants and inflows, will reproduce a flood recession
of the exponential form, retaining thc same recession coefficient as the inflow hydrograph.

2-02. BASIC ASSUMPTIONS. The method stems from sn assumption relating storage within a
routing reach to discharges st each end of the rea.ch as follows:

S=K[XI+(I-X)O)=KO+KX(I-O) __________n_____.______ (5)

in which 0 and I represent simultaneous values of outflow and inflow, respectively, for the reach; S
repreR"nts the storage in the reach; and K llnd X are constants. The term KO has been considered as
representing prism storage under the profile for steady flow 0 (fig. 1) and the term KX (I~) as represent-
ing the wedge storage produced by variations from a steady-flow profile due to differences between
inflow and outflow occurring during rising and falling stages.

o

WedQe storoQe: KX (I -0)
Prism storoQe: KO

I ---...

.

-0

Figi,re 1

f
I
,

2-03. ROUTING EQUATIONS. For application to the problems of flood rC)uting, equation (5) is
expressed in increments and combined with the continuity equation,

t.8=0,5 t.t [(I,+I,)-(O,+O,))

(6)

to yield

O,-O,=C,(I,-O,) +C,(I,-I,) _ __ __ __ __ __ _ __ _ __n _ _ nu _ _ (7)

where the subscripts of the instantsneous discharges refer to the beginning and ending of time period t
and coefficient C, and C, have values of

and

C,= 2t1t _h________u___U_n_h_____nn (8)
2K(I-X)+tlt
C, t.t-2KX _____.... ___ .___.... ____.n__ ..___ (9)
2K(I-X)+tlt

This is the form of routing equation developed in the Ohio River Division and described by Gilcrest and
Marsh,' Its use is illustrated in paragraph 8-07 snd plate No. 1. An alternate form of the routing
equation was used in the first appIiCf,tions of the method and is as follows:" 17

O,=C[I,+C;I, +C;O, ___n. _ n _ __ _ ___ __ _n_n n _ _On (10)

where the coefficients have values of

t,_.,

c; t.t-2KX
2K(I-X)+t.t
C; t.t+2KX
2K(1 X)+t.t,
C; 2K(I-X)-t.t
2K(I-X)+t.t
3

...----------.------------------

(11)

--------------------------------

(12)

(13)