Geoscience Reference
In-Depth Information
Volume curve slope = 0
Slope of storage volume curve
= first derivative of
storage volume equation
T d
Time
FIGURE 25.17
Storage volume vs. time curve.
shown in Figure 25.17. Equation 25.9 represents the first derivative of the storage volume equation
with respect to time and can be solved for the critical storm duration ( T d ):
(
)
2
CAab t
Q
4
c
T
=
b
(25.9)
d
o
where
T d = Critical storm duration (min).
C = Runoff coefficient.
A = Drainage area (ac).
a , b = Rainfall constants developed for storms of various recurrence intervals and various
geographic locations (Table 25.10).
t c = Time concentration (min).
Q o = Allowable peak outflow (cfs).
Equation 25.9 is solved for T d . Then, T d is substituted into Equation 25.7 to solve for Q i , and when
Q i is known, the outlet structure and the stormwater facility can be sized. This method provides a
direct solution to the graphical analysis of the family of hydrographs and is quicker to use. The fol-
lowing procedure illustrates this method.
25.7.7.4 Information Needed
The modified rational method-direct solution is similar to the previous methods because it requires
determination of the pre- and post-developed hydrology, resulting in a pre-developed peak rate
of runoff ( allowable release rate ) and a post-developed runoff hydrograph . Table 25.9 provides a
summary of the hydrology. The rainfall constants a and b for the watershed are determined from
Table 25.10.
2 5 . 7. 7. 5
P r o c e d u r e
1. Determine the 2-year critical storm duration by solving Equation 25.9:
(
)
2
4
CAab t
Q
c
T
=
b
d
2
o
2
 
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