Mathcad - Foster 24-Hour Hyetog

8/19/2019 Mathcad - Foster 24-Hour Hyetog

1/12

Weber Road Job No. 18739

Figure 1

Figure 1 shows the site plan of the proposes construction. The sub-station will be completely enclosed with a berm, for

both landscaping reasons and to prevent the inflow of outside rainfall. The site will maintain a 1% slope for all drainage.

The southwest corner will be used as a detention basin. There will be a 12" pipe leaving to enter an existing catchment.

Stormwater design will be based on the "Will County Stormwater Management Ordinance" Effective January 01, 2004.

203.2 Design Methods

Event hydrograph routing methods or the modified rational mehtod may be used to calculate design runoff

volumes for site runoff facilities. The Methods must be HEC-1, (SCS methodology), HEC-HMS, TR-20, or

TR-55 tabular method. Event methods shall incorporate the following assumptions:

a. Antecedent moisture condition = 2

b. Appropriate Huff rainfall distribution

c. 24-hour duration storm with a 1% probability (100-year frequency) of occurence in any one year as

specified by Illinois State Water Survey Bulletin 70 Northeast Sectional rainfall statistics.

SCS methodology will be used for this design


2/12

Develop SCS Dimensionless Unit Hydrograph

The unit hydrograph is based on the following graph (Figure 2).

1 2 3 4 5 60

.1

.2

.3

.4

.5

.6

.7

.8

.9

1.0

SCS Dimensionless Unit Hydrograph

t/tp

q/qp

Mass Curve

dimensionless unit

hydrograph

Figure 2

From the graph the following time and flow ratios are given

Dimensionless SCS hydrograph values obtained from

Table 9-17 McCuenDATA

0

.4

.7

1

1.5

2

3

4

5

0

.310

.820

1

.680

.28

.055

.011

0

:=

l 0 8..:=

Time_Ratiol

DATAl 0,:= Dimensionless time from SCS dimensionless UH

Flow_Ratiol

DATAl 1,:= Dimensionless flow from SCS dimensionless UH


3/12

t p 0.2hr =t p2

3tc⋅:=

q p 12.4 ft

3

sec=q p

726 A

mi2

⋅ Vol

in⋅

tc

hr

ft3

sec⋅:=

Vol 1in:=

The SCS dimensionless hydrograph depends on the the time to peak (t p ) and the flow at the peak (q p ). These values are

obtained from the triangular unit hydrograph. A depth of runoff of 1inch is used.

D 2.39min=D .133 tc⋅:=

Time Interval For Convolution

This equation is intended for use on watersheds where overland flow predominates and was developed for nonurban

watersheds. This equation was shown by McCuen to provide accurate estimates of t c for catchments up to 4000 acres.

tc 17.95min=Eqn. 3-56 McCuentc .00526 L

ft

0.8

⋅ 1000

CN9−

0.7

⋅ S .5−⋅ min⋅:=

Time of Concentration

Curve Number, Based on Table 3-18 McCuenCN 86:=

Average watershed slope in ft/ft S 0.01:=

Length of the watershed in feet L 630ft:=

Area of catchment in acresA 3.26acre:=

From soil borings, the soil is found to be in Group B, which is Shallow loess; sandy loam.

Land Use Description Treatment Hydrologic Condition

Cultivated agricultural land

Fallow Straight row or bare soil Poor

Land Characteristics


4/12

The values for the unit hydrograph can now be found by multiplying the time to peak and flow at peak times the time ratios

and the flow ratios respectively.

UH_Timel

Time_Ratiol t p⋅:=

UH_Flow

l

Flow_Ratio

l

q p⋅:=

UH_Flow

0

3.831

10.133

12.358

8.403

3.46

0.68

0.136

0

ft3

sec= UH_Time

0

0.08

0.14

0.199

0.299

0.399

0.598

0.798

0.997

hr =

A mathcad function "lspline" is used to create a smooth function connecting all the points. This function will be used to

determine the total flow in later calculations.

t 0 hr ⋅ .01 hr ⋅, 1 hr ⋅..:=

UH t( ) interp lspline UH_Time UH_Flow,( ) UH_Time, UH_Flow, t,( ):=


5/12

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

1.5

3

4.56

7.5

9

10.5

12

13.5

15

Unit Hydrograph Points

SCS Unit Hydrograph

Unit Hydrograph

Time (hr)

F l o w

( c u .

f t .

/ s e c )

U.S. NRCS (SCS) Synthetic Temportal Distribution

This method develops a synthetic distribution of rainfall to produce a 24-hour synthetic design storm. The

dimensionless distribution data from the NRCS is given below in Table 1. This data was found in Table 4.4 of

"Stormwater Conveyance Modeling and Design" By Haestad. The dimensionless distribution data from the NRCS

provides fractions of the total accumulated rainfall depth over time for storms with 24-hour durations. The storms

are classified into various types, depending on the geographic region. For Illinois Type II is appropriate.

The storm specific rain accumulation is found by multiplying the total rainfall for the event times the fractional

accumulations from the NRCS data. The rainfall for this event was found using "Bulletin 70 - Rainfall Distributions

and Hydroclimatic Characteristics of Heavy Rainstorms in Illinois - Illinois State Water Survey" By F. A. Huff. The

100-year, 24-hour storm event in Figure 4.21 yielded a total rainfall of 8 inches for Will County. Table 2 gives the

rain accumulation and Table 3 gives the incrimental change in depth. The incrimental change is used to develop

the hyetograph.


6/12

Depth 8in:=

NRCS

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

0

0.011

0.022

0.035

0.048

0.063

0.080

0.099

0.120

0.147

0.181

0.235

0.663

0.772

0.820

0.854

0.880

0.902

0.921

0.938

0.952

0.965

0.977

0.989

1.000

:= i 0 24..:= Timei

NRCSi 0, hr ⋅:= Acci NRCSi 1,:=

Eventi

Acci Depth⋅:=

j 1 24..:=

Incrimental_Depth j

Event j

Event j 1−−:=

Table 1


7/12

Eventi

0

0.088

0.176

0.28

0.384

0.504

0.64

0.792

0.96

1.176

1.448

1.88

5.304

6.176

6.56

6.832

7.04

7.216

7.368

7.504

7.616

7.72

7.816

7.912

8

in

= Incrimental_Depthi

0

0.088

0.088

0.104

0.104

0.12

0.136

0.152

0.168

0.216

0.272

0.432

3.424

0.872

0.384

0.272

0.208

0.176

0.152

0.136

0.112

0.104

0.096

0.096

0.088

in

=

Table 2 Table 3

Figure 1 shows the Hyetograph for the storm event. Figure 2 shows accumulation of precipitation during the storm

event.


8/12

100-Year, 24-Hour Storm Hyetograph

Will County, Illinois

0

0.5

1

1.5

2

2.5

3

3.5

4

1 3 5 7 9 1 1

1 3

1 5

1 7

1 9

2 1

2 3

2 5

Time (hr)

I n t e n s i t y (

i n / h r )

Figure 1

0 3 6 9 12 15 18 21 240

1

2

3

4

5

6

7

8

Event Rainfall Runoff

100-Year, 24-Hour Storm Precipitation

Time (hr)

P r e c i p i t a t i o n ( i n )

Figure 2


9/12

Convolution Of The Unit Hydrograph And The Hyetograph

Compute the maximum possible retention "S" in (in.)

S 1000

CN10−

in:= (Haestad, 5.15) S 1.63in=

The NRCS (SCS) Curve Number Method calculates runoff based seperating the total depth of rainfall into initial

abstractions I a, retention, and effective rainfall (runoff) P e.

Initial abstractions consist of all rainfall losses occurring before the beginning of surface runoff, including

interception, infiltration, and depresstion storage.

Retention refers to the continuing rainfall losses following the initiation of surface runoff, which are mainly continual

infiltration.

The following equation assumes the inital abstractions are 20% of the maximum possible retention (S). Therefore if the

event rainfall is less than 0.2S the runoff will equal zero.

.2 S⋅ 0.326in=

Pei

Eventi

.2 S⋅−( )2

Eventi

0.8 S⋅+:= Pe

iif Event

i .2 S⋅< 0 in⋅, Pe

i,( ):=

Compute the incremental runoff by subtracting sequential values of effective rainfall runoff

Qincremental j

Pe j

Pe j 1−

−:=

Actual_Acc

0

24

j

Qincremental j∑

=

:= Actual_Acc 6.331 in=


10/12

0 3 6 9 12 15 18 21 240

1

2

3

4

5

6

7

8

Event Rainfall Runoff Effective Rainfall Runoff

Incremental Runoff

Effective Rainfall Runoff

Time (hr)

R u n o f f ( i n )

Figure 3

A time interval of 6 minutes will be used for the convolution. Values from the unit hydrograph are taken obtained from the

spline. The incremental runoff is brought in as a text file because of its large size.

∆t 6min:=

Data

C...\Foster Incremental excess runoff.txt

:=

SCS_UH

UH 0min( )

UH 6min( )

UH 12min( )

UH 18min( )

UH 24min( )

UH 30min( )

UH 36min( )

UH 42min( )

UH 48min( )

UH 54min( )

UH 60min( )

1

in⋅:= SCS_UH

0

0

1

2

3

4

5

6

7

8

9

10

0

5.925

12.356

8.361

3.423

1.199

0.676

0.38

0.132

0.023

-2.531·10 -4

ft3

s in⋅=

p 0 249..:=

Qinc p

Data p 0, in⋅:=

rows SCS_UH( ) 11= rows Data( ) 250=

total rows SCS_UH( ) rows Qinc( )+ 1−:=

total 260=


11/12

To multiply these two vectors, both vectors must have the same number of rows. Zeros are added to fill the rows that do not

have any values.

total 260= i 0 total..:=

SCS_UHi if i 11< SCS_UHi, 0 ft

3

sec in⋅⋅,

:=

Qinci

if i 250< Qinci

, 0 in⋅,( ):=

ti

i ∆t⋅:= Vector of times to use when plotting splined DRH

n 1 total..:=

DRHn

0

n

i

Qinci

SCS_UHn i

−

⋅( )

∑=:=

The direct runoff hydrograph is plotted along with a spline

DR time( ) interp lspline t DRH,( ) t, DRH, time,( ):=

time 0 hr ⋅ .1 hr ⋅, 26 hr ⋅..:=

0 2.6 5.2 7.8 10.4 13 15.6 18.2 20.8 23.4 260

1

2

3

4

5

6

7

8

9

10

Direct Runoff Splined Direct Runoff

Direct Runoff Hydrograph

Time (hr)

R u n o f f ( c u .

f t / s e c )


12/12

Actual_Acc A⋅ 7.492 104× ft3=

The area under the spline doesn't match what the volume should be

0hr

26hr

timeDR time( )⌠ ⌡

d 7.402 104× ft3=

Actual_Acc A⋅0hr

26hr

timeDR time( )⌠ ⌡

d−

Actual_Acc A⋅ 0.012=

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Mathcad - Foster 24-Hour Hyetog