1. Modified Rational Method
Storm Water Runoff
Modified Rational Method
Norman W. Garrick
CE 4410 Spring Lecture 13

2. Peak Rate of Runoff
Peak rate of runoff is used to design features that are
CARRYING water
Such as culverts, channels, swales, pipes

3. Total Runoff Volume
Total runoff volume is used to design features that are
Storing or Retaining water
Such as rain gardens, retention or detention ponds

4. Hydrographs A 20 minute hydrograph Is for a storm 20 minutes long
Each hydrograph is
associated with
a certain storm duration
A 20 minute hydrograph
Is for a storm 20 minutes long
Rate of runoff
Maximum for Hydrograph A
Maximum for Hydrograph B
Time

5. Hydrographs Rate of runoff Time Maximum for Hydrograph A
Area under hydrograph = total runoff volume

6. Modified Rational Method
The Rational Method is used to estimate PEAK rate of runoff
The Modified Rational Method estimates a bit more information
It is used to produce a simplified HYDROGRAPH for a storm
A hydrograph is a graph of rate of runoff versus time

7. Modified Rational Method
q = CCaiA
q = peak runoff rate (cu. feet per second)
C = runoff coefficient (between 0 and 1)
Ca = antecedent precipitation factor
i = rainfall intensity (inches per hour) for the design storm frequency
and the duration of the storm
A = area of drainage area (acres)
The antecedent precipitation factor is added to account for the fact that during a long storm event the ground will be saturated and will not be able to absorb more water
Note: CCa is never greater than 1.0

8. Recommended Antecedent Precipitation Factor
Storm Frequency Ca
2 to 10
1.0 25
1.1 50
1.2
100
1.25

9. Modified Rational Method Hydrographs
The Modified Rational Method is based on three types of hydrographs
Type A, Type B and Type C hydrographs
Type A Hydrograph: Storm Duration = Time of Concentration
Type B Hydrograph: Storm Duration > Time of Concentration
Type C Hydrograph: Storm Duration < Time of Concentration
MMR is recommended for very small drainage areas (< 20 acres)

10. Type A Hydrograph Storm Duration = Time of Concentration
Rate of runoff
qp = CCaiA
i is based on duration of storm
DUR qp Tc
Trec
Time

11. Type B Hydrograph Storm Duration > Time of Concentration
qmax = CCaiA
i is based on duration of storm
Rate of runoff
DUR
qmax Tc
Trec
Time

12. Type C Hydrograph Storm Duration < Time of Concentration
qmax = CCaiA(DUR/Tc)
i is based on duration of storm
DUR
qmax Tc
DUR
Time

13. Total Runoff Volume Run-off volume is the area under the curve
Runoff volume is used to design features that are
Storing or Retaining water
Run-off volume is the area under the curve

14. Create Hydrographs and Calculate Run-off Volume Example
Develop 10-, 25-, and 50-minute hydrographs for a 15 acre drainage area,
with C-value of 0.3 and a time of concentration of 25 minutes.
A 100-year frequency is desired
Calculate run-off volume.

15. 10-minute Hydrograph Type C
qmax = CCaiA(DUR/Tc)
i is based on duration of storm
C = 0.3
Ca = 1.25
i: Return period = 100 year
Duration = 10 minutes
Figure 12.2
i = 7.9 iph
A = 15 acres
qmax = 0.3*1.25*7.9*15*(10/25) = 17.8 cfs
Time
10 min
qmax
25 min
35 min
Volume of run off = Area under graph
= (17.8*10*60)/ *15*60 + (17.8*10*60)/2
= cubic feet

16. 25-minute Hydrograph Type A
qp = CCaiA
i is based on duration of storm
C = 0.3
Ca = 1.25
i: Return period = 100 year
Duration = 25 minutes
Figure 12.2
i = 5.1 iph
A = 15 acres
qp = 0.3*1.25*5.1*15 = 28.7 cfs
Time 25 qp 50
Volume of run off = Area under graph
= (28.7*25*60)/2 + (28.7*25*60)/2
= cubic feet

17. 50-minute Hydrograph Type B
qmax = CCaiA
i is based on duration of storm
C = 0.3
Ca = 1.25
i: Return period = 100 year
Duration = 50 minutes
Figure 12.2
i = 3.4 iph
A = 15 acres
qp = 0.3*1.25*3.4*15 = 19.1 cfs
Time 25
qmax 50 75
Volume of run off = Area under graph
= (19.1*25*60)/ *25*60 + (19.1*25*60)/2
= cubic feet

18. Create Hydrographs and Calculate Run-off Volume Summary
Develop 10-, 25-, and 50-minute hydrographs for a 15 acres drainage area,
with C-value of 0.3 and a time of concentration of 25 minutes.
A 100-year frequency is desired
Calculate run-off volume.
Duration of Storm (minutes)
Maximum Run-off
(cfs)
Total Run-off (cu.ft.) 10
17.8
26,700 25
28.7
43,050 50
19.1
57,300
The storm with the maximum rate of run-off does not always have
the highest run-off volume

19. Which Arrangement has the highest Peak Run-off Rate?X Y
Pavement
Lawn
Lawn
Pavement X X
Discharge Point
Discharge Point

20. Rational Method - X i = 2.8 inches per hour A total = 3 + 3 = 6 acres
Peak Runoff
10 year return
q = CiA
C area weighted average
= 0.8*(3/6) + 0.3*(3/6) = 0.55
i = 2.8 inches per hour
A total = = 6 acres
q = 0.55 * 2.8 * 6 = 9.24 cfs
Peak runoff = 9.24 cfs
Pavement – 3 acres
C = 0.8
Tc = 6 min
Lawn – 3 acres
C = 0.3
Tc = 30 min X
Discharge Point

21. Rational Method - Y i = 6.6 inches per hour A total = 3 acres
Peak Runoff
10 year return
Lawn is ignored since flow is negligible
q = CiA
C = 0.8
i = 6.6 inches per hour
A total = 3 acres
q = 0.8 * 6.6 * 3 = cfs
Peak runoff = 15.8 cfs
Lawn – 3 acres
C = 0.3
Tc = 36 min
Pavement – 3 acres
C = 0.8
Tc = 6 min X
Discharge Point

22. Modified Rational Method - Y
Lawn – 3 acres
C = 0.3
Tc = 36 min
We can get separate hydrograph for each area
10 year return storm
Pavement – 3 acres
C = 0.8
Tc = 6 min X
Discharge Point

23. Modified Rational Method - Y
Hydrograph for Pavement
For DUR = time of concentration
Type A hydrograph
qp = CCaiA
C = 0.8
Ca = 1.0
i = 6.6 inches per hour
A total = 3 acres
q = 0.8 *1.0* 6.6 * 3 = cfs
Peak runoff = 15.8 cfs
Lawn – 3 acres
C = 0.3
Tc = 36 min
Pavement – 3 acres
C = 0.8
Tc = 6 min X
Discharge Point

24. Modified Rational Method - Y
Hydrograph for Pavement
For DUR = time of concentration
Type A hydrograph
Peak runoff = 15.8 cfs
Lawn – 3 acres
C = 0.3
Tc = 36 min
Pavement – 3 acres
C = 0.8
Tc = 6 min
Time (min) 6
15.8 12 X
Discharge Point

25. Modified Rational Method - Y
Hydrograph for Lawn
DUR = 6 min, ToC = 42 minutes
For DUR < time of concentration
Type C hydrograph
qmax = CCaiA(DUR/Tc)
C = 0.3
Ca = 1.0
i = 6.6 inches per hour
A total = 3 acres
q = 0.3*1.0 * 6.6 * 3*(6/42) = 0.85 cfs
Max runoff = 0.85 cfs
Lawn – 3 acres
C = 0.3
Tc = 36 min
Pavement – 3 acres
C = 0.8
Tc = 6 min X
Discharge Point

26. Modified Rational Method - Y
Hydrograph for Lawn
DUR = 6 min, ToC = 42 minutes
For DUR < time of concentration
Type C hydrograph
Max runoff = 0.85 cfs
Lawn – 3 acres
C = 0.3
Tc = 36 min
Pavement – 3 acres
C = 0.8
Tc = 6 min
Time
6 min
0.85
42 min
48 min X
Discharge Point