FLOOD08489

• County: Statewide
• Community: State of Colorado
• Basin: Statewide
• Title: Determination of Urban Watershed Response Time
• Date: 12/1/1974
• Prepared By: E.F. Shulz and O.G. Lopez
• Floodplain - Doc Type: Flood Mitigation/Flood Warning/Watershed Restoration

Chapter 2
RESUME OF PREVIOUS WORK

RATIONAL FORMULA

One of the early developments in urban flood hy-
drology occurred after the enactment of the Arterial
Drainage Act of Ireland in 1842 (dealing with urban
drainage). The first Commissioner fOT Drainage was
Thomas James Mulvaney. According to Biswas (1970),
Mulvaney was responsible for the planning, design and
construction of various urban drainage, navigation and
harbor projects. According to Dooge(1957), it was
William Mulvaney (the younger brother of Drainage Com-
missioner ~~lvaney) who first proposed the use of the
Rational Formula in 1851:

Q = CIA

According to Biswas, Mulvaney correctly realized the
importance of the time of concentration in applying
the Rational Formula.

In 1889, Kuichling discussed the use of the ra-
tional formula in connection with the design of storm
drainage in Rochester, New York. Ramser (1927) de-
fined the time of concentration for small simple agri-
cultural watersheds as the time interval between the
low flow stage and the maximum flow stage. Later
Kirpich (1940) empirically related Ramser's Time of
Concentration, Tc, to the wateTshed variables. chan-
nel length, L. and slope, s, for some small Pennsyl-
vania watersheds:

Tc

L
,Is

,77

0.0013

The importance of the watershed response time (the
time of concentration) and the channel length - slope
parameter were recognized early in the development
of hydrology.

GEOMORPHOLOGY

The research work of Horton (1945) was a natural
outgrowth of the earlier work on the formation of the
flood hydrograph from the watershed runoff. These
watershed properties were commonly used:

a) The watershed area;
b) The length of the longes~ channel;
c) The slope of the channel.

Horton developed many concepts which formed the basis
of modern geomorphology. The basis for Horton's con-
cept was the ordering of stream channels beginning
with the most elementary channels in the headwater re-
gion. The most elementary channel branch is given
order number one. When two first order channels join,
a second order channel is formed. Horton found that
simple geometric relationships developed between the
number of channels of the different order numbers, the
length of channel of a particular order number and the
watershed size were all related to the stream order
number. It can be inferred from Horton's work that
the drainage density of the watershed has an important
bearing on the characteristics of the watershed which
have a bearing on the flood hydrograph Horton found
that the ratio of the number of channels of a parti-

cular order
nels in the
Bifurcation

number was
next lower
Ratio:

related to the number of chan-
order. This he defined as the

Rb

N
u
N+T
u

(1)

where Rb is the Bifurcation Ratio,
N is the number of channels of order of u
u
N u+1 is the number of channels of order u+1
(the next higher order) .

Since the bifurcation ratio tends to
served as the more complex drainage patterns
the number of channels of a given order. Nu'

computed using Horton's Law of Stream Numbers:

be pre-
evolve.
can be

Nu = Rb k-u

(2)

Where k is the order number of the trunk segment at
the outlet of the watershed. This law has been veri-
fied by a number of researchers. The application is
rather impractical for any natural watershed of appre-
ciable size because of the laborious procedure re-
quired to obtain the data. Furthermore, the task is
influenced by the quality and consistency with which
the cartographer prepared the map. The urban region
superimposes a new channel pattern upon the original
consequent stream pattern. It is possible that some
of the resultant urban flood hydrograph character-
istics can be explained using principles of geomor-
phology.

Hack (1957) studied streams in Pennsylvania and
Virginia and later extended his findings to a wide
variety of rivers around the world, He found a con-
sistent relationship between the longest channel and
the drainage area:

L

kAn

(3)

where L is the length of the longest collector in
miles,
A is the watershed area in square miles,
k is a coefficient varying from 1 to 2.5 with
an average of 1.4,
n is an exponent which varies from 0.6 to 0.7
with an average value of 0.6.

These results were based on observations on
natural watersheds in which the channel systems were
free to evolve. In the case of an urban watershed,
parts or sometimes all of the channel systems are
fixed and therefore they may not be free to evolve
into other networks. The superposition of the street
network over the watershed has a great deal to do with
the final shape and extent of the watershed as well as
channel network and length of the channels.

2