Stormwater Calculations - Mathematics and Statistics for the Environment - page 797

t c = 21 min. 1.5 t c = 31.5 min.

50

40

30

20

2-yr allowable
release rate = 17 cfs

10

0

t c

0 15 30 45

Time (minutes)

60 75 90

Conversion of in. 2 to ft 3 = 10 cfs/in × 0.25 hr/in. × 3600 sec/hr = 9000 ft 3 /in. 2
Rainfall Avg.
Period ( T )
21 min
30 min
35 min
40 min
50 min
60 min

Intensity
I (in./hr)

Q Peak
(cfs)

Area
(in 2 )

Storage Volume
(ft 3 )

3.3
2.6
2.4
2.1
1.8
1.6

49
38
35
31
27
24

5.62
5.51
5.53
5.29
5.25
5.24

50,580*
49,590
49,770
47,610
47,250
47,160

FIGURE 25.14

Modified rational method runoff hydrograph, 2-year post-developed condition.

4. Compute and tabulate the required storage volume for each of the selected durations or
time-averaging periods (T d ). The storm duration that requires the maximum storage is the
critical storm and is used for the sizing of the basin. (Storm duration equal to the t c pro-
duces the largest storage volume required for the 2-year storm presented here.)

5. Repeat Steps 1 through 4 above for the analysis of the 10-year storage area requirements.
(Figure 25.15 shows this procedure repeated for the 10-year design storm.)

Note: Conveyance systems should still be designed using the rational method, as opposed to the
modified rational method, to ensure their design for the peak rate of runoff.

25.7.7 m odiFied r ational m ethod , C ritiCal s torm d uration —d ireCt s olution
A direct solution to the modified rational method, critical storm duration has been developed to
eliminate the time intensive, iterative process of generating multiple hydrographs. This direct
solution takes into account the storm duration and allows the engineer to solve for the time at
which the storage volume curve has a slope equal to zero, which corresponds to maximum stor-
age. The basic derivation of this method is provided below, followed by the procedure as applied
to our examples.