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

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Figure 3

The factor K, as defined above, has the dimension of time. It can be shown that the time interval
represented by K is equivalent to the time required for an elemental discharge wave to traverse the
routing reach. This indicates that a relationship should exist between K and At, the selected length of
routing period. For example, if At is less than K, an elemental discharge wave will not have traversed
the reach during a routing period and the computed hYdrograph for the downstream end of the reach,
which is bssed in part on changes in the discharge at the upstream end of the reach during the routing
period, c.nnot represent the actual hydrograph. From such reasoninl; it appears that At should equal K.
In applications a moderate departure from this equality is permissible because, as has been mentioned,
. the routed hydrograph is relatively insensitive to the value of At. However, At should not be less than
2KX in order to a'l'oid negative values of C,.
The relation between K and celerity of the elementary wave signifies also that K is very nearly
the time interyal between the centers of mass of the inflow and outflow hydrographs.

b. Methods of Derhing K. From the above discussion it is evident It can be determined by
8e"i'eral procedures as follows:
(1) K for a reach between two stations at which flood hydrographs are available may be taken as
the time of travel of the center of mass of the flood wave, of a selected discharge on the recession
curve of the hydro graphs, of the mid ordinate discharge of the rising leg of the hydrographs,
or of some other characteristic point on the hydrographs.
(2) The celerity of the elementary discharge wave, V.., can be approximated from the discharge
rating curve of s station whose cross section is representative of the reach by use of Seddon's
principle,' which is expressed by the following equatiou:

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V .=~ ~~___:_ __ _ ___ - _.- - - __m_ __ _. _ _m_ _- _ _ _(19)
where ~i, is the slope of the rating curve. As shown by Gilcrest,' by evaluating ~i by the Man-

ning formula, the ratios between V.. and mean velocity V for various types of channels are as follows:

Chon...1 Ratio V.IV
Wide ~t.&Dgul8J'. __ _ __ __ _' __ __ __ _ __ _ __ __ u 1. 67
Wide panbolicn.__u______________-'__.___ I. 44
Triangular..__. ___ _ __ ____ _ __ ___ u__ u___ __ 1.33

The value of the mean velocity V may be obtained from the discharge and cross-sectional area of
the representative section. The value of K is then the ratio of reach length to wave celerity V...
Seddon'. formula becomes less applicable as the .":;ave height increases and therefore as the selected
At value increases. The ratios in the table were'derived for a condition of constant slope and there-
fore do not apply to the reach of a river entering a reservoir where slopes piyo,t on the pool level.
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