FLOOD06873

• County: Statewide
• Basin: Statewide
• Title: Hydraulic Engineering volume 1
• Date: 1/1/1994
• Prepared By: American Society of Civil Engineers
• Floodplain - Doc Type: Educational/Technical/Reference Information

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HYDRAUI.IC ENGINEERING '94

h
A :: A + J T dh
o h
o
wIth the initial condition T=To' A=Ao and P=Po for h=q.
1 (18) has the only one solution descrlblng the
In fact equal on one of constant side slopes above the initial
original channel.111-e1, g a small deviation from the depth-dlschar'ge
level. However a ow n
curve, l.r. replacing equation {14l by
G (h) - '(h).G (h) . G (h)
2 1 I t an
h a:<h) Is the relative error assumed to be small, one ge 5
:p:~~ximate alternative shape whic1h1 can dl[{:~ ~~~~l~~ab~e~r::l~:~
1 i alone In order to show equa
o~m:r~callY by the Runge-Kulla fourth order method for varl~US de~th
n () The exam les of the approximate alternatl ve 5 apes or
step ~h. =0 25 a~d the initial rectangular channel of 2 m wide
side s ope Z-. e shown at Fig.2a and the corr!?'spondlng relative
and 1 m de:" e:~etrlc factor at Figure 2b. As can be expected the
~:~:~l~; :~rorg 6(hl increases both with the length of the dept~ st~r
tI d lth the distance from the initial leve.
o~a~lom:eut:Ot:dn f~~m ;tgure 2b that the alternative ~>hap'Js show lO~~
~IOW capacity than the original one, which Is in contl.adlclion W h
_ 1 In fact the contradiction can be shown in a muc
~~:p~:~O~y a~.:~.bY a comparison of the depth-discharge curves above
an inItial level tor various side slopes z.

( 19d)

( 140)

h-ho{rn)
3.'

h-ho(m)
3.r.

.0

000) T'I- 0-
l".:
~ ::::: - .0.\ .
)!'! -
;...- ~
,/...- 01 In)

3

AI (Ill)

3

2.'

.005

2.5

2

2

0' l

. 10 O:o-..-o.~']'-I-HI'
(b) OG (ll)

...

0.'
o
o ,
(0)

2345678
(T-T ,l/2 (m)

figure 2. (a) Example of approxieate alternative shapes
d (b) The corresponding relative error of G.
CONCLUSI0NS~n Jt Is a warning of application of the Chezy-Manning
formula regardless of channel shape.

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A New Formula for Mean Velocity In Torrents

Hanspeler Hodel', Isidor SIocchenegger2

Abstract
In this paper we present a new equation for mean velocity in lomnls based on
Iraveltime measurements and geomorphological relations. Here, the emphasis is nol
on understanding the physical phenomena of nuid now in torrents, but on the
combination of travel time with morphological characterisrics in stream networks.
The formula presented can be used for stream velocity as a meaD value or a function
of watershed characteristics over long reaches. In further research most progress can
be assumed by the skilled combination of fractal concepts with relations based on
velocity measUrpuenls in differenl river basins.

I. Background - Basics
Many problems concerning the determination of parameters for river basins
may be solved with fonnulas, which calculate the velocity with basin characteristics.
and discharge. These problems can occur in the following applications:
i) time of concentration
ii) time lag in pollution control and risk management
Hi) nood routing by kinematic waves
Such formulas are based on relations like:
i) v = f(Q(x).C(x)) velocity
ii) A = QIv cross-section area of now
iii) IiN/iQ = g(Q(x), C(x)) derivation to gel the time of coocentration (integration)

In general, the streamnow velocity is expressed by the CMzy equation. The
application of this fonnula requires quantitative infonnation concerning channel
shape, size, roughness, and slope. Using this equation the biggest problem for the
practical men is the integration over long, reaches. The amount of data to be
collected, processed and analyzed for the correct use of this equalion is enormous. In
order to reduce cost. practitioners prefer simple solutions. Different approuches
perfonn the requirements under simplified assumptions
i) neglect of discharge. roughness, channel shape and size, regard only average
.Iope (Kirpich's fonn"la for the time of concentration (Kirpich, 1940}),
Ii), reduction of river basin to triangular or paraoolic channel (Aron el al., /99/).
iii) reduction of stream network according to geomorphical fractal concepts
(Slorchenegger 1984, Aron ., ai, 1990)

ISwis.lI National Hydrological and Geological Survey, CH-300J Berne. Switzerland
2Undcnslnissc 23, CH-8307 Errmi1mR. Switzerland

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