Stormwater Calculations - Mathematics and Statistics for the Environment - page 796

TABLE 25.9
Hydrologic Summary, Rational Method

Condition Area Developed Runoff Coefficient ( c ) t c Q 2 Q 10

Pre-developed 25 ac 0.38 0.87 hr (52 min) 17 cfs 24 cfs

Post-developed 25 ac 0.59 0.35 hr (21 min) 49 cfs 65 cfs

The rainfall intensity averaging periods are chosen arbitrarily; however, the designer should
select periods for which the corresponding intensity-duration-frequency (IDF) curves are avail-
able (e.g., 10 min, 20 min, 30 min). The shortest period selected should be the time of concentration
( t c ). A straight line starting at Q = 0 and t = 0 and intercepting the inflow hydrograph on the reced-
ing limb at the allowable release rate ( Q o ) represents the outflow rating curve. The time averaging
period hydrograph that represents the greatest storage volume required is the one with the largest
area between the inflow hydrograph and outflow-rating curve. This determination is made by a
graphical analysis of the hydrographs.
The next procedure presents a graphical analysis very similar to the one described earlier. Note
that the rational and modified rational methods should normally be used in homogeneous drainage
areas of less than 20 acres, with a t c of less than 20 minutes. Although the watershed in our example
has a drainage area of 25 acres and a t c of greater than 20 minutes, it will be used here for illustra-
tive purposes. Note that the pre- and post-developed peak discharges are much greater than those
calculated using the SCS method applied to the same watershed. This difference may be the result
of the large acreage and t c values. A summary of the hydrology is found in Table 25.9. Note that the
t c calculations were performed using the more rigorous SCS TR-55 method.

25.7.6.1 Information Needed
The modified rational method-critical storm duration approach is very similar to SCS methods
because it requires pre- and post-developed hydrology in the form of a pre-developed peak rate
of runoff (allowable release rate) and a post-developed runoff hydrograph (inflow hydrograph), as
developed using the rational method.

25.7.6.2 Procedure
Refer to Figures 25.14 and 25.15.

1. Plot the 2-year developed condition inflow hydrograph (triangular) based on the developed
condition ( t c ).

2. Plot a family of hydrographs, with the time averaging period ( T d ) of each hydrograph
increasing incrementally from 21 minutes (developed condition t c ) to 60 minutes, as shown
in Figure 25.14. Note that the first hydrograph is a Type 1 modified rational method trian-
gular hydrograph, where the storm duration ( d ) or ( T d ) is equal to the time of concentra-
tion ( t c ). The remaining hydrographs are trapezoidal, or Type 2 hydrographs. The peak
discharge for each hydrograph is calculated using the rational equation, Q = CIA , where
intensity I from the IDF curve is determined using the rainfall intensity averaging period
as the storm duration.

3. Superimpose the outflow-rating curve on each inflow hydrograph. The area between the
two curves then represents the storage volume required, as shown in Figure 25.14. Similar
cautions, as described in the SCS methods, regarding the straight-line approximation of the
outlet discharge curve apply here as well. The actual shape of the outflow curve depends on
the type of outlet device.