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Time of Time of ConcentrationConcentration

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ObjectivesObjectives

Know how to calculate time of Know how to calculate time of concentrationconcentration

Know why it’s important to be Know why it’s important to be able to determine the time of able to determine the time of concentrationconcentration

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DefinitionDefinition

Time required for runoff to travel Time required for runoff to travel from the hydraulically most from the hydraulically most distant point on a watershed to distant point on a watershed to another point of interest within another point of interest within the watershedthe watershed

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Factors Factors

Surface roughnessSurface roughness Channel shape and flow patternsChannel shape and flow patterns SlopeSlope

Urbanization generally increases the Urbanization generally increases the runoff velocities and therefore runoff velocities and therefore decreases the time of concentrationdecreases the time of concentration

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ImportanceImportance

Rational methodRational method– Calculate time of concentration, tCalculate time of concentration, tcc

– Set duration = tSet duration = tc c

– Use IDF curve to find rainfall intensityUse IDF curve to find rainfall intensity

TR-55 MethodTR-55 Method– Calculate time of concentration, tCalculate time of concentration, tcc

– Look up unit peak discharge on the appropriate Exhibit Look up unit peak discharge on the appropriate Exhibit 4-#4-#

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Typical Values for TcTypical Values for Tc < 50 Acres < 50 Acres

5 minutes to 30 minutes5 minutes to 30 minutes

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Water can move Water can move through a watershed through a watershed as:as: Sheet flow (max of 300 ft; ---usually Sheet flow (max of 300 ft; ---usually

100 ft)100 ft) Shallow concentrated flowShallow concentrated flow Open channel flow Open channel flow

– GutterGutter– DitchDitch– SwaleSwale– CreekCreek

Some combination of aboveSome combination of above

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ExamplesExamples

UrbanUrban– Sheet flow from back end of a residential lotSheet flow from back end of a residential lot– Open channel flow once water drops over the Open channel flow once water drops over the

curb and into a guttercurb and into a gutter RuralRural

– Sheet flow in upper part of watershedSheet flow in upper part of watershed– Shallow concentrated flow as water forms Shallow concentrated flow as water forms

rivuletsrivulets– Open channel flow (ditch/creek)Open channel flow (ditch/creek)

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Calculating TcCalculating Tc

Calculate Tc for each type of flow and Calculate Tc for each type of flow and add togetheradd together

See the following TR-55 worksheet to See the following TR-55 worksheet to be used for all Tc calculations in this be used for all Tc calculations in this class!!class!!

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Sheet FlowSheet Flow

1.1. Manning’s Kinematic SolutionManning’s Kinematic Solution– See TR-55, pg 3-3 & equation 3-3See TR-55, pg 3-3 & equation 3-3

2.2. Kinematic Wave EquationKinematic Wave Equation

3.3. FAA MethodFAA Method

4.4. NomographNomograph– See appendix C-2 of your bookSee appendix C-2 of your book

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Manning’s Kinematic Manning’s Kinematic SolutionSolution TTtt=[0.007(nL)=[0.007(nL).8.8]/[P]/[P22

.5 .5 SS.4.4]] TTtt is travel time (hrs) is travel time (hrs) n-Manning’s coefficient n-Manning’s coefficient for sheet flowfor sheet flow

(dimensionless - (dimensionless - must use Table 3-1 in TR-must use Table 3-1 in TR-5555))

L is flow length (ft)L is flow length (ft) PP2 2 is 2-yr, 24-hr rainfall (in)is 2-yr, 24-hr rainfall (in)

– TR-55 Appendix B, Figure B-3 orTR-55 Appendix B, Figure B-3 or– Local IDF curve (change intensity to inches)Local IDF curve (change intensity to inches)

S is slope (decimal format)S is slope (decimal format)

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Kinematic Wave Kinematic Wave EquationEquation ttcoco=[56(L=[56(Loo)).6 .6 (n)(n).6.6]/[S]/[Soo

.3 .3 ii.4.4]] ttcoco is travel time (sec) is travel time (sec) n-Manning’s coefficient (dimensionless)n-Manning’s coefficient (dimensionless) LLoo is overland flow length (ft) is overland flow length (ft) ii is rainfall intensity for a desired frequency is rainfall intensity for a desired frequency

(in/hr)(in/hr)– TR-55 Appendix B (change inches to intensity) orTR-55 Appendix B (change inches to intensity) or– Local IDF curve Local IDF curve

SSoo is overland slope (decimal format) is overland slope (decimal format)

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Kinematic Wave Kinematic Wave EquationEquation

Includes the rainfall intensity for a Includes the rainfall intensity for a desired frequencydesired frequency

Must use iterative approachMust use iterative approach1.1. Assume a rainfall intensityAssume a rainfall intensity

2.2. Calculate travel time Calculate travel time

3.3. Set storm duration = travel timeSet storm duration = travel time

4.4. Look up intensity from IDF curve and Look up intensity from IDF curve and compare to assumed valuecompare to assumed value

5.5. If intensity differs go back to step 1If intensity differs go back to step 1

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FAA EquationFAA Equation

t=[1.8(1.1-C)(Lt=[1.8(1.1-C)(Loo)).5 .5 ]/[S]/[S.333.333]] t is travel time (min)t is travel time (min) C-rational coefficient (dimensionless)C-rational coefficient (dimensionless)

– See Appendix C-1 of your bookSee Appendix C-1 of your book LLoo is overland flow length (ft) is overland flow length (ft)

SSoo is overland slope (decimal format) is overland slope (decimal format)

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NomographNomograph

Your book – C-2Your book – C-2– LengthLength– Ground character Ground character

PavedPaved Bare soilBare soil Poor, average or dense grassPoor, average or dense grass

– Percent slopePercent slope

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ExampleExample

Dense Grass (n=0.24, C=0.2)Dense Grass (n=0.24, C=0.2) Flow Length (200 ft)Flow Length (200 ft) Location (SUNYIT; 2-yr 24-hr Location (SUNYIT; 2-yr 24-hr

duration)duration) Slope (3%)Slope (3%)

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Example: Manning’s Example: Manning’s Kinematic SolutionKinematic Solution TTtt=[0.007(nL)=[0.007(nL).8.8]/[P]/[P22

.5 .5 SS.4.4]]

TTtt=[0.007(.24*200)=[0.007(.24*200).8.8]/[2.5]/[2.5.5.5*.03*.03 .4 .4]] n=.24n=.24 L=200 ftL=200 ft PP2 2 = 2.5 in (TR-55; Figure B-3) = 2.5 in (TR-55; Figure B-3) S = .03S = .03 TTtt=0.398 hours = =0.398 hours = 24 minutes24 minutes

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IDF Curve

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

0 10 20 30 40 50 60 70

Storm Duration (minutes)

Rai

nfa

ll In

ten

sity

(in

/ho

ur)

2-year frequency

5-year frequency

10-year frequency

25-year frequency

50-year frequency

100-year frequency

Kinematic Wave- IDF Curve is Kinematic Wave- IDF Curve is neededneeded

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Example: Kinematic Example: Kinematic Wave EquationWave Equation ttcoco=[56(L=[56(Loo)).6 .6 (n)(n).6.6]/[S]/[Soo

.3 .3 ii.4.4]] Assume 1-hr; 2-yr frequency (i=1”/hr)Assume 1-hr; 2-yr frequency (i=1”/hr) ttcoco=[56(200)=[56(200).6 .6 (.24)(.24).6.6]/[.03]/[.03.3*.3*11.4.4]]

ttcoco=1640 seconds = 27 minutes=1640 seconds = 27 minutes Intensity for 30-min; 2-yr storm Intensity for 30-min; 2-yr storm

=1.6”/hr=1.6”/hr Intensities don’t match; try againIntensities don’t match; try again

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Kinematic Kinematic Wave-Trial/Error Wave-Trial/Error (Tc=9 minutes)(Tc=9 minutes)Assumed Assumed II

Time of Conc.Time of Conc. Actual iActual i

1 in/hr1 in/hr 28 minutes28 minutes 1.6 in/hr1.6 in/hr

1.61.6 1717 2.4 2.4

2.42.4 1111 3.13.1

3.13.1 99 3.13.1

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Example: FAA EquationExample: FAA Equation

t=[1.8(1.1-C)(Lt=[1.8(1.1-C)(Loo)).5 .5 ]/[S]/[S.333.333]] t=[1.8(1.1-.2)(200)t=[1.8(1.1-.2)(200).5 .5 ]/[.03]/[.03.333.333]] C=.2C=.2 LLoo=200 ft=200 ft

SSoo = .03 = .03 t =t = 41 min41 min

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Example: Nomograph Example: Nomograph

From nomograph C-2From nomograph C-2

Concentration timeConcentration time == 21 minutes21 minutes– Length=200 ftLength=200 ft– Dense Grass Dense Grass – Slope=3%Slope=3%– Note: had to extend pivot lineNote: had to extend pivot line

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Example ResultsExample Results

Man. KinematicMan. Kinematic Kinematic WaveKinematic Wave FAAFAA NomographNomograph

24 minutes24 minutes 9 minutes9 minutes 41 minutes41 minutes 21 minutes21 minutes

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Shallow Concentrated Shallow Concentrated Flow Flow TR-55TR-55

– page 3-2; Figure 3-1page 3-2; Figure 3-1– page 3-3; Explanationpage 3-3; Explanation– Appendix F - formulasAppendix F - formulas

Derived from Manning’s equationDerived from Manning’s equation Determine average velocity (Fig 3-Determine average velocity (Fig 3-

1)1) Divide flow length by average Divide flow length by average

velocity to obtain travel timevelocity to obtain travel time

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Shallow Concentrated Shallow Concentrated FlowFlow EquationsEquations

– Velocity=16.1345*SVelocity=16.1345*S0.5 0.5 UnpavedUnpaved– Velocity=20.8282*SVelocity=20.8282*S0.5 0.5 PavedPaved

AssumptionsAssumptions– Unpaved: n=.05; hydraulic radius=0.4Unpaved: n=.05; hydraulic radius=0.4– Paved: n=.025; hydraulic radius=0.2Paved: n=.025; hydraulic radius=0.2

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Open Channel FlowOpen Channel Flow

Manning’s Equation (TR-55, page Manning’s Equation (TR-55, page 3-4)3-4)

Calculate average velocityCalculate average velocity Divide flow length by average Divide flow length by average

velocity to obtain travel timevelocity to obtain travel time

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Manning’s EquationManning’s Equation

Irish Engineer Irish Engineer ““On the Flow of Water in Open On the Flow of Water in Open

Channels and Pipes” 1891Channels and Pipes” 1891 Empirical equationEmpirical equation See more:See more:

– http://manning.sdsu.edu/\– http://el.erdc.usace.army.mil/elpubs/pdf/sr10.

pdf#search=%22manning%20irish%20engineer%22

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Uniform Flow in Open Uniform Flow in Open ChannelsChannels Water depth, flow area, discharge Water depth, flow area, discharge

and velocity distribution at all and velocity distribution at all sections throughout the entire sections throughout the entire channel reach remains unchanged.channel reach remains unchanged.

The energy grade line, water The energy grade line, water surface line, and the channel bottom surface line, and the channel bottom lines are all parallel to each otherlines are all parallel to each other

No acceleration (or deceleration)No acceleration (or deceleration)

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Manning’s Equation: Manning’s Equation: Flow---EnglishFlow---English Q=A(Q=A(1.491.49/n)(R/n)(Rhh

2/32/3)(S))(S).5 .5

Q is flow rate (cfs)Q is flow rate (cfs) n-Manning’s coefficient n-Manning’s coefficient

(dimensionless)(dimensionless) Rh is hydraulic radius (ft)Rh is hydraulic radius (ft)

– Wetted area / wetted perimeterWetted area / wetted perimeter S is slope (decimal format)S is slope (decimal format)

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Manning’s Equation: Manning’s Equation: Flow---MetricFlow---Metric Q=A(Q=A(11/n)(R/n)(Rhh

2/32/3)(S))(S).5 .5

Q is flow rate (cms)Q is flow rate (cms) n-Manning’s coefficient n-Manning’s coefficient

(dimensionless)(dimensionless) RRh h is hydraulic radius (m)is hydraulic radius (m)

– Wetted area / wetted perimeterWetted area / wetted perimeter S is slope (decimal format)S is slope (decimal format)

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Manning’s Equation: Manning’s Equation: Velocity----EnglishVelocity----English Divide both sides by areaDivide both sides by area V=(V=(1.491.49/n)(R/n)(Rhh

2/32/3)(S))(S).5 .5

V is velocity (fps)V is velocity (fps) n-Manning’s coefficient n-Manning’s coefficient

(dimensionless)(dimensionless) Rh is hydraulic radius (ft)Rh is hydraulic radius (ft)

– Wetted area / wetted perimeterWetted area / wetted perimeter S is slope (decimal format)S is slope (decimal format)

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Manning’s Equation: Manning’s Equation: Velocity-----MetricVelocity-----Metric Divide both sides by areaDivide both sides by area V=(V=(11/n)(R/n)(Rhh

2/32/3)(S))(S).5 .5

V is velocity (meter/sec)V is velocity (meter/sec) n-Manning’s coefficient n-Manning’s coefficient

(dimensionless)(dimensionless) Rh is hydraulic radius (m)Rh is hydraulic radius (m)

– Wetted area / wetted perimeterWetted area / wetted perimeter S is slope (decimal format)S is slope (decimal format)

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Manning’s CoefficientManning’s CoefficientTypical ValuesTypical Values

Appendix A-1 from your bookAppendix A-1 from your book Other ref:Other ref:

– http://www.fhwa.dot.gov/bridge/wsp2339.pdf– http://www.lmnoeng.com/manningn.htm

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Hydraulic RadiusHydraulic Radius

Wetted area / wetted perimeterWetted area / wetted perimeter Easy to calculate for circular Easy to calculate for circular

pipes full or half-fullpipes full or half-full Use trig to calculate triangular or Use trig to calculate triangular or

trapezoidal channelstrapezoidal channels

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Example-Find VExample-Find V

Find the velocity of a rectangular Find the velocity of a rectangular channel 5’ wide w/ a 5% grade, channel 5’ wide w/ a 5% grade, flowing 1’ deep. The channel has flowing 1’ deep. The channel has a stone and weed bank (n=.035). a stone and weed bank (n=.035).

A=5 sf; WP=7’; RA=5 sf; WP=7’; Rhh=0.714 ft=0.714 ft

S=.05S=.05

V=7.6 fpsV=7.6 fps

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Example-Find timeExample-Find time

If velocity = 7.6 ft per second and If velocity = 7.6 ft per second and length of channel = 500 feet then length of channel = 500 feet then time traveled in channel time traveled in channel =l/v=500/7.6==l/v=500/7.6=

Time travelled=66 seconds = 1.1 Time travelled=66 seconds = 1.1 minutesminutes

FlowmasterFlowmaster

Use flowmaster to solve previous Use flowmaster to solve previous example and to solve homework example and to solve homework channel:channel:

3’ Depth3’ Depth 12’ top width and 6’ channel width12’ top width and 6’ channel width Assume slope =3%Assume slope =3% Manning’s coefficient n=.032Manning’s coefficient n=.032

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Time of Concentration Time of Concentration CalculationsCalculations For this class (homework, For this class (homework,

projects, etc.) use worksheet from projects, etc.) use worksheet from the the TR-55 Document

Page D-3 (to print out blank form)Page D-3 (to print out blank form) Also show picture of lengthsAlso show picture of lengths

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Next LectureNext Lecture

Rational Method for Determining Rational Method for Determining Peak FlowPeak Flow