FLOOD09697

• County: Statewide
• Community: Nationwide
• Basin: Statewide
• Title: Mathematical Modeling of a Sociological and Hydrologic Decision System
• Date: 6/1/1978
• Prepared By: Institute for Social Science Research on Natural Resources, Utah State Univ.
• Floodplain - Doc Type: Educational/Technical/Reference Information

Ihrough a channel of lenglh, L. In order to simplify
the analysis, a rectangular channel cross-section was
assumed. Appropriate pararnelers of width and depth
of flow can be substiluted to represenl a particular
storm drainage system. If b is assumed to represent
channel width and y the deplh of flow, Ihe cross..ec-
tional area of flow, A, is given by:

A=by . .

. (3.15)

and the wetted perimeter, p, is

p=b+2y=b. . . . . (3.16)

Manning's open channel flow equation is

Q=VA=1.49 AR2/3 SI/2 . (3.17)
n

in which
Q
S
n
R
R2/3

= discharge in cfs
= channel slope in ftlft
= Manning's rouglmess coefficienl.
= hydraulic radius = AlP
= (A2/3)1(J>2/3) = y2/3

Therefore,

Q= 1.49 (by)y2/3 Sl/2 -1.49 bSl/2 (y5/3)
n n

. . (3.18)

Solving for y as function of Q,

3/5
Y = f(Q) = ( n ) Q3/5.. (3.19)
1.49 bSl/2

= KQ3/5

in which

K=( n )315
1.49 bSI/2

. (3.20) ,

T L can Ihen be estimated as a function of instanane.
ous discharge by Ihe computer program as:

dislance ~ ~
TL = velocity = LQ Q . (3.21)

Substituting Equation 3.19 into Equation 3.21 yields

T L = L bKQo.6 - L bKQ .0.4
Q

. (3.22)

T L is Ihus given in lerms of readily oblained channel
or storm drain design dimensions. Dividing Equation
3.22 by 60 gives T L in minules.

By assuming a linear distribution of inflow into
the channel or the storm drain syslem along its length,
the added Q wi thin a subzone is

Q(+Qo
Q 2

. (3.23)

Narayana et a!. (1969) did not use a lag time
concept in Iheir study because a single watershed area
was assumed and routing was not required. The Eve-
lyn el aI. (1970) study utilized a subzone approach
and a lag time parameter which was reduced 10 a con-
stant based on subzone characteristics and peak dis-
charge rales from individual storm even Is. The dis-
charge for each subzone was assumed proportional to
the area drained. The lag time parameter for each
sub watershed therefore was expressed in lerms of the
peak discharge at the outflow point of the most down-
slream subzone. The melhod (Evelyn el aI., 1970)
gave satisfactory results. This lag lime parameter, in
essence, had an attenuation effect on the outflow
hydrographs and increased the recession time. The
time of the peak discharge was not shifled, however.

In this study, discharge rates are determined
for each subzone and used to calculate Ihe lag time
parameter. The lag time parameter is applied to cal-
culate the time shift due to channel routing effects
by dividing the lag time parameter into the time scale
and then rounding to the nearest integer. In routing
Ihe upstream hydrograph is delayed by the calculated
number of lime units. This process is continued for
each subzone until the outflow hydrograph is com.
puted for Ihe enlire watershed area.

Model Verification

Compuler Synlhesis

The computer model was produced by program-
ming the mathematical relationships and logic func-
tions described above. The model is analogous to the
prolotype to the degree that the mathematical rela-
tionships represent real world conditions. A mathe-
matical function which describes a basic process,
such as evapolranspiration, is applicable to many diff-
erent hydrologic models. A simulation modei incor-
porates general equations of the various basic processes
which occur within the system. The result, therefore,
is free of the geometric restrictions characteristic of
network analyzers and physical models. The model is
applied 10 a parlicular prololype system by estab.
lishing, through a calibration procedure appropriate
values for the "constants" of the equations used.

Model Verificalion

Hydrologic models require verificalion. Verifi-
cation is performed in two steps, namely calibration,
or system identification, and testing (described in a

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