Hidrologi #2

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EnvironmentalEngineeringInstitut Teknologi BandungEnvE


STORM SEWER DESIGN


STORM SEWER DESIGN


• Adequate and properly functioning storm water drainage system.

• Construction of houses, commercial buildings, parking lots, paved

roads, and streets increases the impervious cover in a watershed

and reduces infiltration.

• urbanization changes the spatial pattern of flow in the watershed; • urbanization changes the spatial pattern of flow in the watershed;

there is an increase in the hydraulic efficiency of flow through

artificial channels, curbing, gutters, and storm drainage and

collection systems.

• These increase the volume and velocity of runoff and produce

larger peak flood discharges from urbanized watersheds.


STORM SEWER DESIGN


• The urban drainage system can be considered

as consisting of two major types of elements:

LOCATION ELEMENTS and TRANSFER

ELEMENTS.

• LOCATION ELEMENTS: places where the • LOCATION ELEMENTS: places where the

water stops and undergoes changes as a result

of humanly controlled processes e.g. Water

storage, water treatment, water use, WWTP

• TRANSFER ELEMENTS: connect the location

elements e.g. Channels, pipelines, storm

sewers, sanitary sewers, and strrets.


STORM SEWER DESIGN


• Complex urban problems involve distributed systems requiring

analysis of spatial and temporal variations.

• Urban watersheds vary in space in that the ground surface slope

and cover, and the soil type, change from place to place in the and cover, and the soil type, change from place to place in the

watershed.

• They vary in time in that hydrologic characteristics change with

the process of urbanization.


DESIGN PHILOSOPHY


The design of storm sewer systems involves the determination of DIAMETERS,

SLOPES, and CROWN/INVERT elevation for each pipe in the system.

• Selection of a layout/network of pipe locations.

• Once a layout has been selected, the RATIONAL METHOD can be used to select • Once a layout has been selected, the RATIONAL METHOD can be used to select

pipe diameters.

Storm drainage design can be divided into two aspects:

• RUNOFF PREDICTION

• SYSTEM DESIGN

In recent years, rainfall-runoff modeling for urban watersheds has been a

popular activity and a variety of such rainfall-runoff models are now available.

Rational Method


• Still probably the most widely used method for design of storm sewers

[Pilgrim, 1986; Linsley, 1986].

• The idea behind the rational method is that if a rainfall of intensity i begins

instantaneously and continues indefinitely, the rate of runoff will increase until the

time of concentration tc, when all of the watershed is contributing to flow at the time of concentration tc, when all of the watershed is contributing to flow at the

outlet.

• The product of rainfall intensity i and watershed area A is the inflow rate for the

system, iA, and the ratio of this rate to the rate of peak discharge Q (which occurs at

time tc) is termed the runoff coefficient C (0<C<1). This is expressed in the rational

formula:

Q = C i A

• the duration used for the determination of the design precipitation intensity i is the

time of concentration of the watershed.

Rational Method


• a composite analysis for various surface characteristics is required for the

drainage area with subareas.

• The peak runoff:

Q = i ΣCjAj

Assumption associated with the rational method:

• The computed peak rate of runoff at the outlet point is a function of the

average rainfall rate during the time of concentration, that is, the peak

discharge does not result from a more intense storm of shorter duration,

during which only a portion of the watershed is contributing to runoff at the

outlet.

• The time of concentration employed is the time for the runoff to become

established and flow from the most remote part of the drainage area to the

inflow point of the sewer being designed.

• Rainfall intensity is constant throughout the storm duration

Runoff Coefficient


• The proportion of the total rainfall that will reach the storm drains depends

on the percent imperviousness, slope, and ponding character of the surface.

• impervious surfaces, such as asphalt pavements and roofs of buildings, will

produce nearly 100% runoff after the surface has become thoroughly wet,

regardless of the slope.regardless of the slope.

• Field inspection and aerial photographs are useful in estimating the nature of

the surface within the drainage area.

• The runoff coefficient is also dependent on the character and condition of

the soil. The infiltration rate decreases as rainfall continues, and is also

influenced by the antecedent moisture condition of the soil.

Runoff Coefficient for use in the rational method [Chow et al., 1988]


Character of surface Return Period (years)

5 25

DEVELOPED

Asphaltic 0.77 0.86

Concrete/roof 0.80 0.88

Grass area (lawns, parks)

- Poor condition (grass cover less than 50% of the area)

- Flat (0-2%)

- Steep (over 7%)

0.34

0.43

0.40

0.49

- Good condition (grass cover larger than 75% of the area)

- Flat

- Steep

0.23

0.37

0.29

0.44

UNDEVELOPED

Cultivated land

- Flat

- Steep

0.34

0.42

0.40

0.48

Forest/Woodlands

- Flat

- Sttep

0.25

0.39

0.31

0.45

Rainfall Intensity


•The rainfall intensity i is the average rainfall rate (in/hr) for a particular drainage basin.

• The intensity is selected on the basis of the design rainfall duration and return period.

• The design duration is equal to the time of concentration for the drainage area under

consideration.

• The return period is established by design standards.• The return period is established by design standards.

• the time of concentration to any point in a storm drainage system is the sum of the

inlet time to (the time it takes for flow from the remotest point to reach the sewer inlet),

and the flow time tf in the upstream sewers connected to the outer point:

tc = to + tf

tf = ΣLi/ViLi is the length of the ith pipe along the flow path, Vi is the flow velocity in the pipe.

• inlet time decreases as the slope and imperviousness of the surface increases.


Time of Concentration Summary [Source Chow et al., 1988][Source Chow et al., 1988][Source Chow et al., 1988][Source Chow et al., 1988]


Time of Concentration Summary

Waktu Konsentrasi Travel Time


Table Approximate average velocities in ft/s of runoff flow for calculating time of concentration

Description of water course Slope

Calculate the time of concentration of a watershed in which the longest flow path covers

100 feet of pastures at a 5% slope, then enters a 1000-foot-long rectangular channel having

width 2 ft, roughness n = 0.015, and slope 2.5%, and receiving a lateral flow of 0.00926

cfs/ft.

Description of water course Slope

0-3 4-7 8-11 12-...

Woodlands

Pastures

Cultivated

Pavements

0-1.5

0-2.5

0-3.0

0-8.5

1.5-2.5

2.5-3.5

3.0-4.5

8.5-13.5

2.5-3.25

3.5-4.25

4.5-5.5

13.5-17

3.25-

4.25-

5.5-

17-

Outlet channel (Natural channel not well-defined) 0-2 2-4 4-7 7-

Distance along channel, l (ft) 0 200 400 600 800 1000

Δl 200 200 200 200 200

Calculated velocity (ft/s) 0 4.63 5.97 6.86 7.56 8.02

Average velocity , V (ft/s)

Travel time t= l/V (s)

Waktu Konsentrasi


Table Approximate average velocities in ft/s of runoff flow for calculating time of concentration

Description of water course Slope (%)

0-3 4-7 8-11 12-...

Woodlands

Pastures

Cultivated

Pavements

0-1.5

0-2.5

0-3.0

0-8.5

1.5-2.5

2.5-3.5

3.0-4.5

8.5-13.5

2.5-3.25

3.5-4.25

4.5-5.5

13.5-17

3.25-

4.25-

5.5-

17-Pavements 0-8.5 8.5-13.5 13.5-17 17-

Outlet channel (Natural channel not well-defined) 0-2 2-4 4-7 7-

Average velocity: 3.0 ft/s

Distance along channel, l (ft) 0 200 400 600 800 1000

Δl 200 200 200 200 200

Calculated velocity (ft/s) 0 4.63 5.97 6.86 7.56 8.02

Average velocity , V (ft/s) 2,315 5,3 6,415 7,21 7,79

Travel time t= l/V (s) 86,4 37,7 31,2 27,7 25,7

Pipe Capacity


•Once the design discharge Q entering the sewer pipe has been calculated by the

rational formula, the diameter of pipe D required to carry this discharge is determined.

• it is usually assumed that the pipe is flowing full under gravity but is not pressurized, so

the pipe capacity can be calculated by the Manning or Darcy-Weisbach equations for

open-channel flow. open-channel flow.

D = (2.16 Qn/√So)3/8

where Q in cfs, D in ft.

Rational Method Assessment


Example A hypothetical drainage basin

comprising seven subcatchments is shown.

Determine the required capacity of the storm

sewer EB draining subarea III for a five-year

return period storm. This subcatchment has

an area of 4 acres, a runoff coefficient of 0.6,

and an inlet time of 10 minutes.

A

I II

III IV V and an inlet time of 10 minutes.

The design precipitation intensity for this

location is given by i = 120 T 0.175/(Td+27),

where i is the intensity in in/hr, T is the return

period, and Td is the duration in minutes.

The ground elevations at points E and B are

498.43 and 495.55 ft above mean sea level,

respectively, and the length of pipe EB is 450

ft. Assume Manning’s n is 0.015. Calculate

the flow time in the pipe.

BE

C

D

III IV V

VI VII



i = 120 T 0.175/(Td+27)

= 120 (5) 0.175/(10+27)

= 4.30 in/h

The design discharge:

Q = C i A

= 0.6 x 4.30 x 4

A

BE

C

I II

III IV V

VI VII

= 0.6 x 4.30 x 4

= 10.3 cfs

The slope of the pipe EB is the difference between the

ground elevations at points E and B divided by the length of

the pipe: So = (498.43 – 495.55)/450 = 0.0064

The required pipe diameter is:

D = (2.16 Qn/√So)3/8

D = (2.16 x 10.3 x 0.015/√0.0064)3/8

= 1.71 ft

The diameter is rounded up to the next commercially

available pipe size, 1.75 ft or 21 in.

D



i = 120 T 0.175/(Td+27)

= 120 (5) 0.175/(10+27)

= 4.30 in/h

The design discharge:

Q = C i A

= 0.6 x 4.30 x 4

A

BE

C

I II

III IV V

VI VII

= 0.6 x 4.30 x 4

= 10.3 cfs

The slope of the pipe EB is the difference between the

ground elevations at points E and B divided by the length of

the pipe: So = (498.43 – 495.55)/450 = 0.0064

The required pipe diameter is:

D = (2.16 Qn/√So)3/8

D = (2.16 x 10.3 x 0.015/√0.0064)3/8

= 1.71 ft

The diameter is rounded up to the next commercially

available pipe size, 1.75 ft or 21 in.

D



Determine The diameter for pipes AB, BC,

and CD in the 27-acre drainage basin shown

in the figure. The area, runoff coefficients,

and inlet time for each subcatchment are

shown in Table, and the length and slope for

each pipe are in columns 2 and 3 of Table .

Use the same rainfall intensity equation and

A

I II

III IV V

Use the same rainfall intensity equation and

assume the pipes have Manning’s n = 0.015. BE

C

D

VI VIICatchment Area, A

(acres)

Runoff

coefficient,

C

Inlet time,

ti (min)

I

II

III

IV

V

VI

VII

2

3

4

4

5

4.5

4.5

0.7

0.7

0.6

0.6

0.5

0.5

0.5

5

7

10

10

15

15

15

Sewer pipe Length , L (ft) Slope, So

EB

AB

BC

CD

450

550

400

450

0.0064

0.0081

0.0064

0.0064


The same method is used for each pipe, except that now the

time of concentration must include both inlet time and flow

time through upstream sewers. The results obtained for pipe

EB the previous case is shown in table.

A

BE

C

D

I II

III IV V

VI VII

Sewer

pipe

L (ft) So Total

area

ΣCA tc (min) i (in/hr) Design

dischar

Comput

ed

Pipe

size

Flow

velocity

Flow

time


pipe area

drained

(acres)

dischar

ge, Q

(cfs)

ed

sewer

diamet

er (ft)

size

used

(ft)

velocity

Q/A

(ft/s)

time

L/V

(min)

EB 450 0.0064 4 2.4 10.0 4.30 10.3 1.71 1.75 4.28 1.75

AB 550 0.0081 5 3.5 7.0 4.68 16.4 1.94 2.00 5.21 1.76

This pipe drains subcatchments I and II. From Table, A1=2 acres, C1=0.7, and the inlet time is

t1=5min, while AII=3 acres, CII=0.7, and tII=7 min. Hence, the toal area drained by pipe AB is

5 acres and ΣCA=CIAI + CIIAII = 0.7x2 + 0.7x3 = 3.5. The time concentration used is 7 min, the

larger of the two inlet times. The calculations for the required diameter are carried out in

the same way; the results are shown in the second row of the table. The calculated

diameter, 1.94 ft, is rounded up to a commercial size of 2.0 ft (24 in) for pipe AB.

IDF Curve Intensity-Duration-Frequency


Periode

Inte

nsita

s h

ujan

( in

/jam

)

Periode

Ulang

100 tahun

50

25

10

5

2

Inte

nsita

s h

ujan

( in

/jam

)

Durasi (menit)

IDF Curve Intensity-Duration-Frequency


Determine the design precipitation intensity and depth for a 20-minute duration

storm with a 5-year return period.

Answer:

From the IDF curves, the design intensity for a 5-year, 20-minute storm is

i = 3.5 in/h.

The corresponding precipitation depth is

i = P/Td with Td = 20 min = 0.333 h.

P = i Td = 3.50 x 0.333 = 1.17 in.

Design STORM

Determine the design rainfall depth for a 25-year 30-minute storm in City X.

P 10-min = 0.51 P5-min + 0.49 P15-min

P 30-min = 0.51 P15-min + 0.49 P60-min

For T=2 years, P2,30= 0.51x1.02 + 0.45x1.85 = 1.43 in

For T=100 years, P100,30= 0.51 x 1.86 +0.49x3.80 = 2,81 in

Coefficient a and b are 0.293 and 0.669, respectively (from Table)Coefficient a and b are 0.293 and 0.669, respectively (from Table)

P25,30 = aP2,30 + bP100,30

= 0.293 x 1.43 + 0.669x2.81

= 2.30 in

Return period T,

years

a b

5

10

25

50

0.674

0.496

0.293

0.146

0.278

0.449

0.669

0.835

Hydroeconomic Analysis

Use the maps and equations to plot IDF curves for City-O for return periods of 2, 5, 10,

25, 50, and 100 years. Consider rainfall durations ranging from 5 minutes to 1 hour.

0.850.90 0.90

0.85

0.80

Design STORM

Use the National Weather Service maps to plot IDF curves for City X, for return period 2, 5, 10,

25, 50, and 100 years. Consider rainfall duration ranging from 5 minutes to 1 hour.

Answer:

The six maps presented in the figure show precipitation for 5-, 15-, and 60-minute durations and

2- and 100-year return periods. The six values for this City X are:

P2,5 = 0.48 in P100,5 0.87 in P2,15 1.02 in P100,15 1.86 in P2,60 1.85 in P100,60 3.80 in

The results are shown in the table in terms of precipitation depth, and are converted into intensity

map

The results are shown in the table in terms of precipitation depth, and are converted into intensity

by dividing by duration.

For example P25,30 = 2.30 in � 4.60 in/hr.

P 10-min = 0.51 P5-min + 0.49 P15-min

P 30-min = 0.51 P15-min + 0.49 P60-min P25,30 = aP2,30 + bP100,30

Coefficient a and b are 0.293 and 0.669, respectively (from Table)

Return period T,

years

a b

5

10

25

50

0.674

0.496

0.293

0.146

0.278

0.449

0.669

0.835

Return period

T (year)

Duration, Td (min)

5 10 15 30 60

2

5

10

25

50

100

0.48

0.57

0.63

0.72

0.80

0.87

0.80

0.94

1.05

1.21

1.33

1.45

1.02

1.20

1.34

1.54

1.70

1.86

1.43

1.74

1.97

2.30

2.56

2.81

1.85

2.30

2.62

3.08

3.44

3.80

Design precipitation

depths (in) at City X for

various Td and T

Design STORM

Return period

T (year)

Duration, Td (min)

5 10 15 30 60

2

5

10

25

50

100

0.48

0.57

0.63

0.72

0.80

0.87

0.80

0.94

1.05

1.21

1.33

1.45

1.02

1.20

1.34

1.54

1.70

1.86

1.43

1.74

1.97

2.30

2.56

2.81

1.85

2.30

2.62

3.08

3.44

3.80

Design precipitation

depths (in) at City X for

various Td and T

11.0

10.0

9.0

Inte

nsi

ty (

in/h

)

Duration (min)

9.0

8.0

7.0

6.0

5.0

4.0

3.0

2.5

2.0

1.5

1.01 5 10 15 30 60

Return Period (years)

100

50

25

10

5

2

Kurva Intensitas Hujan


Dari data hujan yang dihasilkan oleh penakar hujan otomatis di Lokasi X dapat

dilihat besaran intensitas hujan ‘ekstrim’ seperti tampak pada tabel.

Tahun 5 10 15 30 45 60 120 360 720 1440

1985 122 138 118 122 87 70 50 20 9 71985

1986

1987

1988

1989

1990

1991

1992

1993

122

156

138

147

126

192

129

142

133

138

134

149

125

174

120

164

118

159

118

124

129

160

154

132

149

134

140

122 87 70 50 20 9 7



Dari data hujan yang dihasilkan oleh penakar hujan otomatis di Lokasi X dapat

dilihat besaran intensitas hujan ‘ekstrim’ seperti tampak pada tabel.

Tabel Perhitungan Periode Ulang dan Probabilits (untuk durasi 5 menit)

T=(n+1)/m

Tahun Intensitas Hujan

ekstrim (mm/jam)

Ranking,

m

Periode

ulang, T

Proba-

bilitas, P

1985

1986

1987

1988

1989

1990

1991

1992

1993

122

156

138

147

126

192

129

142

133

9

2

5

3

8

1

7

4

6

1.11

5

2

3.33

1.25

10

1.43

2.5

1.66

90

20

50

30

80

10

70

40

60



Tabel Intensitas ekstrim (mm/jam) untuk Periode Ulang 5 dan 10 tahun

X, Durasi

(menit)

Y, Intensitas hujan ekstrim,

periode ulang 5 tahun

Y, ntensitas hujan ekstrim,

periode ulang 10 tahun

5

10

156

138

192

17410

15

30

45

60

120

360

720

1440

138

132

104

80

73

40

16

8

5

174

160

122

100

80

50

20

12

7



Tabel Kurva Interpolasi Least Square

X,

Durasi

(menit)

Y XY Y2 XY2 logX logY LogX.

LogY

(Log

X)2

Y √X Y2√X

5 156 780 24336 121680 0.69 2.19 1.53 0.48 348 544165

10

15

30

45

60

120

360

720

1440

156

138

132

104

80

73

40

16

8

5

780 24336 121680 0.69 2.19 1.53 0.48 348 54416

38760 85294 187190 18.4 16.6 26.8 39.9 123 350625



Tiga rumus kurva yang harus dipilih:

- Kurva No. 1: y = a/(x+b) --------� Persamaan Talbot: I = a/(t+b)

a = (Σxy)(Σy2) - (Σxy2)(Σy)

10 (Σy2) - (Σy)(Σy)

b = (Σy)(Σxy) - 10(Σxy2)

10 (Σy2) - (Σy)(Σy)

a = 1625.86 (10=jumlah tahun) b = 121.28

- Kurva No. 2: y = a/Xn -------------� Persamaan Sherman: I = a/Xn

- Kurva No. 3: y = a/((√x) + b) -----� Persamaan Ishiguro: I = a/((√t) + b)

a = 1625.86 (10=jumlah tahun) b = 121.28

log a = (Σlogx)(Σlogx)2 - (Σlogx.logy)(Σy)

10 (Σy2) - (Σlogx)(Σlogx)

n = (Σlogy)(Σlogx) - 10(Σlogx logy)

10 (Σlogx)2 - (Σlogx)(Σlogx)

a = - 8.42 n = - 4.55

a = (Σy√x)(Σy2) - (Σy2√x)(Σy)

10 (Σy2) - (Σy)(Σy)

b = (Σy)(Σy√x) - 10(Σy2√x)

10 (Σy2) - (Σy)(Σy)

a = 746.77 b = 2.732



Selisih intensitas dalam angka mutlak positif dinyatakan dalam dy1, dy2, dy3. Nilai

dy terkecil menunjukkan kurva terbaik untuk dipilih.

No. x y y1 dy1 y2 dy2 y3 dy3

1

2

3

5

10

15

156

138

132

128.64

123.74

119.20

27.35

14.25

12.79

5.8E-06 156 158.57 2.57

3

4

5

6

7

8

9

10

15

30

45

60

120

360

720

1440

132

140

80

73

40

16

8

5

119.20 12.79

Jumlah 153.9 985235 99.2

Mean 15.39 98523.5 9.92

Yang dipilih adalah Kurva no.3, pada dy3 rata-rata terkecil yaitu 9.92.

Determine Areal Rainfall:

� Arithmetic P = ΣP/n

� Thiessen Polygon P = 1/A Σ AjPj

� Isohyet P = 1/A Σ AiPi

Areal RAINFALL

Isohyet P = 1/A Σ AiPi


� Thiessen Polygon

FloodAreal RAINFALL


� Isohyet

Areal RAINFALL

Determine Rainfall:

� Arithmetic

� Thiessen Polygon

� Isohyet

Design FLOWFlood Control Reservoir Design

P5=50 mm

P2=20 mm

P1=10 mm

IsohyetP2=20 mm

P3=30 mmP4=40 mm

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Hidrologi #2