27-5-2014

Challenge the future

DelftUniversity ofTechnology

CIE4491Lecture. Quantifying stormwater flow –Rational method

Marie-claire ten Veldhuis, Watermanagement Department

2CIE4491 Lecture Rational Method

Storm event dynamic modelling

Rainfall series dynamic modelling

Robust method stationary modelling

Design storms Standard rainfall seriesIDF curves

Branched networks (few loops)

Rational method

Detailed branched and looped networks

Hydrodynamic model calculations

Hydrodynamic model calculations

Simplified branched and looped networks

Stationary hydraulic calculations

Dynamic hydraulic calculations

Dynamic hydraulic calculations

Water levels in nodesQ-t diagram per node

per storm event

Q-t diagram per node for series of storm events

Rainfall runoff modelling Rainfall runoff modelling Rainfall runoff modelling

3CIE4491 Lecture Rational Method

Rational method for stormwater

drainage system design

Rational method: 𝑄 𝑡 = 𝐶. 𝐼. 𝐴

Q = inflow into manhole (m3/s)

C = Runoff coefficient, representing runoff losses (-)

I = rainfall intensity (mm/h or l/s/ha)

A = catchment area connected to urban drainage system (m2)

4CIE4491 Lecture Rational Method

Rational method for stormwater

drainage system design

Rational method: 𝑄 𝑡 = 𝐶. 𝐼. 𝐴

1. Determine size and characteristics of subcatchment areas

2. Determine runoff coefficient C for subcatchment areas

3. Calculate concentration time at critical inflow points in drainage

system

4. Determine critical rainfall intensity based on concentration time and

IDF curve

5. Calculate Q at all critical inflow points

5CIE4491 Lecture Rational Method

Runoff coefficient C: dependent on

catchment type

Flat roofsInclined roofsImpervious areaPervious area

6CIE4491 Lecture Rational Method

Inflow points

7CIE4491 Lecture Rational Method

Contributing area per inflow point (manhole)

8CIE4491 Lecture Rational Method

Catchment areas connected to sewer system

Example: Bomenwijk Delft

9CIE4491 Lecture Rational Method

Time of concentration

Time required for surface runoff to flow from remotest part of catchment to inflow point under consideration

Two components time of entry (te) time of flow (tf)

Return period (y)

Time of entry (min)

1 4-8

2 4-7

3 3-6

c e ft t t

10CIE4491 Lecture Rational Method

Time of entry & time of flow

In reality, time of entry varies with• surface roughness

• slope & length of flow path

• rainfall intensity

Time of flow depends on• Hydraulic properties of pipe – flow velocity

• Length of flow path

11CIE4491 Lecture Rational Method

Rational method for urban drainage

design

Steady state stormwater flow:

Qn = flow at location with n upstream sections (l/s)

i = critical rainfall intensity (l/s/ha (or mm/h)) for return period T and concentration time t

Cm = runoff coefficient of catchment discharging tosection m

Am = catchment area discharging to section m (ha)

Q i C An m m

m

n

1

12CIE4491 Lecture Rational Method

Assumptions:

Rainfall is uniform over the whole catchment area Catchment imperviousness remains constant throughout

storm Flow in the system is at constant velocity throughout tc Steady state flow reached when tstorm tc

Critical rainfall intensity for at points in systemat time t = tc

Rational method

13CIE4491 Lecture Rational Method

Rational method: stationary

conditions

Hydrograph response to continuous rainfall (graph b)

14CIE4491 Lecture Rational Method

Critical rainfall intensity

50

10 403020 8070600 10090500

100

150

duration (min)t=tc

i

inte

nsity (

l/s.h

a)

Intensity duration curve

15CIE4491 Lecture Rational Method

Summary rational method for

stormwater system design

• Choose return period of rainfall (T )

• Estimate contributing areas for each pipe and run-off coefficient

• Assume flow velocity of 1 m/s

• Estimate maximum time of concentration (tc) for connected

catchment areas

• Read critical rainfall intensity from IDF curve

• Calculate flow rate in each pipe according to:

• Adjust diameters of pipes if necessary

• Check flow velocity and concentration time

Q i C An m m

m

n

1

16CIE4491 Lecture Rational Method

Example: calculate design flow for

each node

BC

D

E

A

200 m

+ 4,00 m

+ 3,00 m

400 m300 m500 m

+ 5,95 m

+ 4,95 m

+ 4,10 m+ 4,50 m

E BCD A

Surface water

50 m

50 m

50 m

17CIE4491 Lecture Rational Method

Determine contributing area

200 m400 m500 m300 m

50 m

50 m

Surface

water

E BCD A

50 m

Area A B C D E

Area per node (ha) 0.5 2 4 5 3

Impervious area (%) 50 60 40 30 30

Impervious area per node (ha)

Cum. Area per node (ha)

18CIE4491 Lecture Rational Method

Determine contributing area

200 m400 m500 m300 m

50 m

50 m

Surface

water

E BCD A

50 m

Area A B C D E

Area per node (ha) 0.5 2 4 5 3

Impervious area (%) 50 60 40 30 30

Impervious area per node (ha) 0.25 1.2 1.6 1.5 0.9

Cum. Area per node (ha) 5.45 5.2 4.5 2.4 0.9

19CIE4491 Lecture Rational Method

Time of concentration

Assume flow velocity 1 m/s

200 m400 m500 m300 m

50 m

50 m

Surface

water

E BCD A

50 m

Area A B C D E

Time of concentration (min)

20CIE4491 Lecture Rational Method

Time of concentration

Assume flow velocity 1 m/s

200 m400 m500 m300 m

50 m

50 m

Surface

water

E BCD A

50 m

Area A B C D E

Time of concentration (min) 29 28 25 18.3 10

21CIE4491 Lecture Rational Method

Critical rainfall intensities from IDF curve

50

10 403020 8070600 10090500

100

150

duration (min)

60

inte

nsity (

l/s.h

a)

Area A B C D E

Time of concentration (min) 29 28 25 18.3 10

Rainfall intensity (l/s/ha) 40 40 45 50 70

22CIE4491 Lecture Rational Method

Design flow for each node Area A B C D E

Time of concentration (min) 29 28 25 18.3 10

Rainfall intensity (l/s/ha) 40 40 45 50 70

Cumulative area (ha) 5.45 5.2 4.5 2.4 0.9

Design flow (l/s) 218 208 202 120 63

200 m400 m500 m300 m

50 m

50 m

Surface

water

E BCD A

23CIE4491 Lecture Rational Method

Rainwater flow, remember:

• Highly variable (0 – extreme):

no system can cope with all

possible rainfall intensities

• High rainfall intensity is critical

• Stormwater flow is large

compared to wastewater flow

• Translation into design values :

statistics and assumptions

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