Modified Rational Method Storm Water Runoff Modified Rational Method Norman W. Garrick CE 4410 Spring 2017 Lecture 12

Rational Method Used to estimate PEAK rate of runoff From small drainage areas (< 200 acres) 1 acre = 43,560 sq. feet 1 acre is slightly smaller than a football field

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

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

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

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

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

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

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

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)

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

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

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

Creating Hydrographs Example 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

10-minute Hydrograph Duration = 10 minutes, Time of Concentration = 25 minutes DUR < Tc, therefore, we need Type C Hydrograph

10-minute Hydrograph Type C qmax = CCaiA(DUR/Tc) i is based on duration of storm DUR = 10 min qmax Tc = 25 min DUR = 10 min Time

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

25-minute Hydrograph Duration = 25 minutes, Time of Concentration = 25 minutes DUR = Tc, therefore, we need Type A Hydrograph

25-minute Hydrograph Type A qmax = CCaiA i is based on duration of storm Rate of runoff DUR = 25 qp Tc = 25 Trec = 25 Time

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

50-minute Hydrograph Duration = 50 minutes, Time of Concentration = 25 minutes DUR > Tc, therefore, we need Type B Hydrograph

50-minute Hydrograph Type B qmax = CCaiA i is based on duration of storm DUR = 50 qmax Tc = 25 Trec = 25 Time

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