Unit Hydrographs 2011

7/22/2019 Unit Hydrographs 2011

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RUNOFFHYDROGRAPHSThe Unit Hydrograph Approach


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STORMWATERHYDROGRAPHS

Graphically represent runoff rates vs. time

Peak runoff rates

Volume of runoff

Measured hydrographs are best

But not often available

Methods are available to develop a synthetic hydrograph

Use a unit hydrograph (UHG)


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DEVELOPMENTOFRO HYDROGRAPHS

Most often interested in hydrographs at the watershedoutlet (and possibly some selected points in thewatershed).

We modify the rainfall hyetograph to reflect watershed

characteristics. The volume under the effective rainfall hyetograph is equal

to the volume of surface runoff.


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HYDROGRAPHCOMPONENTS

qpis the maximumflow rate on the

hydrograph

tp(time to peak) is the

time from the start of

they hydrograph to qp.

tb(base time) is the

total time duration ofthe hydrograph.


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HYDROGRAPHCOMPONENTS

tc(time of concentration) time it takes water to flow fromthe hydraulically most remote point in a watershed tothe watershed outlet

tL(lag time) is the average of the flow times from all

locations in the watershed and can be estimated as thelength of time from the center of mass of the firsteffective rainfall block, to the peak of the runoffhydrograph.

If each block of effective rainfall has a duration of D

2

Dtt Lp


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UNITHYDROGRAPH

Hydrograph of runoff resulting from a unit of rainfall

excess occurring at a uniform rate, uniformly

distributed over a watershed in a specified duration

of time.


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UNITHYDROGRAPHS

Assumptions: Rainfall intensity is not considered Linear relationship between stormwater runoff and rainfall UHG is independent of antecedent conditions Uniform rainfall distribution


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DURATIONOFTHEUNITHYDROGRAPH

Each unit hydrograph has a duration that is the

same as the duration of the rainfall excess that

produced it.

Conceptually can have an infinite # of hydrographs

corresponding to different durations.

Practically, a unit hydrograph is applied to rainfall

excesses of duration as much as 25% different than the

duration of the unit hydrograph.


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HOWISTHEUNITHYDROGRAPHUSED?

For a unit hydrograph ofduration, D, the volumeunderneath the hydrographis always 1, produced by 1unit of excess rainfall.

A hydrograph for a block ofrainfall excess of any depthis obtained by multiplyingthe ordinates of the unithydrograph by the depth ofthe rainfall excess block.

The result is the ordinatesof the runoff hydrograph.


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HOWISTHEUNITHYDROGRAPHUSED?

Rainfall excess is divided intoblocks, each of a uniformduration, D.

A component hydrograph for

each block of rainfall iscalculated.

The starting time for eachhydrograph coincides to thestarting time of the appropriateblock of rainfall excess.

All the component hydrographsare added vertically to obtainthe total runoff hydrograph for

the storm.

1ij

mj

1i

ij urq

ni0u

mi0r

i

i


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CHECKINGTHEVOLUMEUNDERAUNIT

HYDROGRAPH.

A5.60qtV i

Where:

t is the duration time

increment of the

hydrograph (min)

Sqiis the sum of theordinates of the runoff

hydrograph (cfs)

A is the area (acres)


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DERIVINGUNITHYDROGRAPHS

Unit hydrographs can be derived from

records of observed rainfall and streamflow

BUT

For small watersheds, synthetic unithydrographs are generally used.

Synthetic unit hydrographs provide

ordinates of the unit hydrograph as afunction of tp, qpand a mathematical or

empirical shape description.


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ESTIMATINGTHETIMEPARAMETERS

Time of concentration (tc)

For some areas, we can sum the time for various

flow segments as the water flows toward the

watershed outlet.

Segments

Overland flow

Shallow channel flow

Flow in open channels.

n

1ii

ic

vLt


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LAGTIME, TL

SCS Equation to calculate

time lagL = hydraulic length of

watershed (feet)

S = curve number parameter(inches)

Y = average land slope of the

watershed (%)

tl= time lag (hours)

5.0

7.08.0

LY1900)1S(Lt


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TIMETOPEAKANDDURATION

Duration of rainfall excessshould be 1/5 to 1/3 tp.

Base time, tb

tb=2.67 tp.

Some use tb= 5tp Some use tb=

2

Dtt Lp


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ESTIMATIONOFPEAKFLOWPARAMETERS

General form

For a triangular unithydrograph withtb=2.67 tp

Where: tpis the time to peak (hrs)

qpis peak flow (cfs)

A is watershed area (squaremiles)

p

pt

KAq

p

pt

A484q


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SHAPESOFUNITHYDROGRAPHS

SCS uses a dimensionless unit hydrograph

(Figure 3.34).

Also have a triangular unit hydrograph derived

to have the same tpand qpas the

dimensionless hydrograph.

If either of these are used the qpand tpare

related through

p

pt

A484q


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TRIANGULARHYDROGRAPHS

Good approximation for peak and duration.

Find the qpand tpof the unit hydrograph.

Multiply qpby the depth of the rainfall excess block.

Use the tbapproximation to find the duration of thehydrograph.


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EXAMPLE5.10 INTEXT(MODIFIED)

Solution:

HSG = D / CommercialT. 5.1CN = 95

S = 0.53 in.

Assume AMC = IIQ = 1.96 in. of runoff

Find points to develop the unit hydrograph

tl= 0.75 hr (45 min)

tp= 1.25 hr (75 min)

tb= 3.33 hr (200 min) qp= 302 cfs / 1 in. of runoff

Plot unit hydrograph

Check area under the triangle1 in.


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Q(

cfs)

T(min)

600

100

300

150 tb= 200tp= 7550

200

400qp= 302.5 cfs


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Volume under triangle = (302.5 cfs x 4,500 sec) / 2 +

[(302.5 x (12,0004,500 sec)] / 2 = 1,812,000 ft3

Surface runoff depth = 1,812,000 ft3/ 21,780,000 ft2=

0.08 ft = 1.0 in. ok


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EXAMPLE5.10 INTEXT

Solution:

qp 2.5 rain= 302.5 cfs x 1.96 in. of SRO

qp 2.5 rain= 592.9 cfs

Plot storm hydrographCheck area under the triangle1.96 in.


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T(min)

Q (cfs)

Surface runoff depth

= 1.96 in. ok

600

100

300

150 tb= 200tp= 7550

200

400

qp= 592.9 cfs

Volume under triangle= 3,557,400 ft3


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AGSM 335

Homework #6


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SCS DIMENSIONLESSUNITHYDROGRAPH

K

t

t1

p

pett

)p(q)t(q

92.1

pp

V

tq5.6K

Haan equation

Where:

qpis peak flow (in/hr)

To convert from cfs to in/hr

divide by A (acres) and

1.008.

tpis time to peak (hrs)V is volume under the

hydrograph (V=1 for unit

hydrograph)

For a unit hydrograph K should

be close to 3.77


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EXAMPLE5.11 INTEXTUSINGSCS UHG

Rainfall excess for each time block of

duration 15 minutes 0.17, 1.10, 0.84

tp=52.5 minutes qp= 432 cfs

Convert qpto in/hr.

Calculate K

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875.86.05.65.6

92.192.1

V

tqK

pp


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COORDINATESOFTHEUHG

For each time block of duration D, calculate q(t)

using:

These are the ordinates of the UHG.

For each excess rainfall block multiply the depth of

the excess rainfall by all the ordinates of the unit

hydrograph. Each hydrograph should begin at the time the

rainfall excess block begins. i.e. If the rainfall

excess block occurred at 30 minutes, the

hydrograph should start at 30 minutes.

432875.

)(

76.3

875.1

t

et

tq


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CREATINGTHETOTALRUNOFFHYDROGRAPH

Add the contents of each row (not including the UH

ordinates) to get the total runoff at each time t.

Plot t vs. Q.


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UNITANDRUNOFFHYDROGRAPH

CALCULATIONSExample of a Unit Hydrograph

qp 432 cfs

K 3.76

tp 0.875 hr

Excess Runoff (in)

t q(t) 0.17 0.84 0.71 0.24 Runoff (cfs)

0.00 0.00 0.00 0.00

0.25 57.04 9.70 0.00 9.70

0.50 263.93 44.87 47.91 0.00 92.78

0.75 414.04 70.39 221.70 40.50 0.00 332.59

1.00 417.11 70.91 347.79 187.39 13.69 619.79

1.25 329.67 56.04 350.38 293.97 63.34 763.73

1.50 223.48 37.99 276.92 296.15 99.37 710.44

1.75 136.27 23.17 187.73 234.07 100.11 545.07

2.00 76.90 13.07 114.47 158.67 79.12 365.34

2.25 40.90 6.95 64.59 96.75 53.64 221.93

2.50 20.76 3.53 34.35 54.60 32.71 125.18

2.75 10.14 1.72 17.44 29.04 18.45 66.65

3.00 4.81 0.82 8.52 14.74 9.82 33.89

3.25 2.22 0.38 4.04 7.20 4.98 16.60

3.50 1.00 0.17 1.86 3.41 2.43 7.88

3.75 0.44 0.08 0.84 1.57 1.15 3.64

4.00 0.19 0.03 0.37 0.71 0.53 1.65

4.25 0.08 0.01 0.16 0.31 0.24 0.73

4.50 0.04 0.01 0.07 0.14 0.11 0.32

4.75 0.01 0.00 0.03 0.06 0.05 0.14

5.00 0.01 0.00 0.01 0.02 0.02 0.06

1.00 0.01 0.01 0.01 0.02

1.25 0.00 0.00 0.01

0.00 0.00

0.00


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PLOTSOFUNITANDRUNOFFHYDROGRAPHS

0.00

100.00

200.00

300.00

400.00

500.00

600.00

700.00

800.00

900.00

0.00 1.00 2.00 3.00 4.00 5.00 6.00

Runoff(cfs)

Time (hrs)

Unit and Total Runoff Hydrographs

Unit Hydrograph

Total Runoff Hydrograph


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BAEN 460

Homework #6

Documents

Unit Hydrographs 2011