Lin S.D. Water and Wastewater Calculations Manual

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7.3 Estimation of runoff

The quantity of stormwater runoff can be estimated by the rational method

or by the empirical formula. Each method has its advantages. The rational

formula for the determination of the quantity of stormwater runoff is

Q ⫽ CIA (6.12a)

where Q ⫽ peak runoff from rainfall, ft

C ⫽ runoff coefficient, dimensionless

I ⫽ rainfall intensity, in rain/h

A ⫽ drainage area, acres

The formula in SI units is

Q ⫽ 0.278 CIA (6.12b)

where Q ⫽ peak runoff, m

C ⫽ runoff coefficient, see Table 6.2

I ⫽ rainfall intensity, mm/h

A ⫽ drainage area, km

The coefficient of runoff for a specific area depends upon the charac-

ter and the slope of the surface, the type and extent of vegetation, and

other factors. The approximate values of the runoff coefficient are shown

in Table 6.2. There are empirical formulas for the runoff coefficient.

However, the values of C in Table 6.2 are most commonly used.

Example: In a suburban residential area of 1000 acres (4.047 km

), the

rainfall intensity–duration of a 20-min 25-year storm is 6.1 in/h (155 mm/h).

Find the maximum rate of runoff.

Wastewater Engineering 555

TABLE 6.2 Coefﬁcient of Runoff for Various Surfaces

Flat Rolling Hilly

Type of surface slope ⬍2% slope 2–10% slope ⬍10%

Pavements, roofs 0.90 0.90 0.90

City business areas 0.80 0.85 0.85

Dense residential areas 0.60 0.65 0.70

Suburban residential areas 0.45 0.50 0.55

Earth areas 0.60 0.65 0.70

Grassed areas 0.25 0.30 0.30

Cultivated land

clay, loam 0.50 0.55 0.60

sand 0.25 0.30 0.35

Meadows and pasture lands 0.25 0.30 0.35

Forests and wooded areas 0.10 0.15 0.20

SOURCE: Perry (1967)

solution: From Table 6.2, C ⫽ 0.50 (for rolling suburban)

Using Eq. (6.12a)

Q ⫽ CIA

⫽ 0.5 ⫻ 6.1 in/h ⫻ 1000 acre

Note: In practice, a factor of 1.0083 conversion is not necessary. The answer

could be just 3050 ft

/s.

8 Stormwater Quality

The quality and quantity of stormwaters depend on several factors—

intensity, duration, and area extent of storms. The time interval between

successive storms also has significant effects on both the quantity and

quality of stormwater runoff. Land contours, urban location perme-

ability, land uses and developments, population densities, incidence and

nature of industries, size and layout of sewer systems, and other factors

are also influential.

Since the 1950s, many studies on stormwater quality indicate that

runoff quality differs widely in pattern, background conditions, and

from location to location. Wanielista and Yousef (1993) summarized

runoff quality on city street, lawn surface, rural road, highway, and by

land-use categories. Rainwater quality and pollutant loading rates are

also presented.

8.1 National urban runoff program

In 1981 and 1982, the US EPA’s National Urban Runoff Program

(NURP) collected urban stormwater runoff data from 81 sites located

in 22 cities throughout the United States. The data covered more

than 2300 separate storm events. Data was evaluated for solids,

oxygen demand, nutrients, metals, toxic chemicals, and bacteria. The

median event mean concentrations (EMC) and coefficients of vari-

ance for ten standard parameters for four different land use cate-

gories are listed in Table 6.3 (US EPA 1983a). It was found that lead,

copper, and zinc are the most significant heavy metals found in urban

runoff and showed the highest concentrations. The EMC for a storm

is determined by flow-weighted calculation.

8.2 Event mean concentration

Individual pollutants are measured on the flow-weighted composite to

determine the event mean concentrations. The event mean concentration

5 3050

acre

1 h

3600 s

1 ft

12 in

43,560 ft

1 acre

5 3075 ft

556 Chapter 6

is defined as the event loading for a specific constituent divided by the

event stromwater volume. It is expressed as

(6.13)

where C ⫽ event mean concentration, mg/L

W ⫽ total loading per event, mg

V ⫽ volume per event, L

The total loading for a storm event is determined by the sum of the

loadings during each sampling period, the loading being the flow rate

(volume) multiplied by the concentration. The loading per event is

(6.14)

where W ⫽ loading for a storm event, mg

n ⫽ total number of samples taken during a storm event

⫽ volume proportional to flow rate at time i, L

⫽ concentration at time i, mg/L

Example: An automatic sampler was installed at the confluence of the main

tributary of a lake. The following sampling time and tributary flow rate were

measured in the field and the laboratory. The results are shown in Table 6.4.

W 5

⌺

i51

C 5

Wastewater Engineering 557

TABLE 6.3 Mean EMCS and Coefﬁcient of Variance for all NURP Sites by Land

Use Category

Residential Mixed Commercial Open/Nonurban

Pollutant Median CV Median CV Median CV Median CV

BOD (mg/L 10.0 0.41 7.8 0.52 9.3 0.31 – –

COD (mg/L) 73 0.55 65 0.58 57 0.39 40 0.78

TSS (mg/L) 101 0.96 67 1.14 69 0.35 70 2.92

Total lead (␮g/L) 144 0.75 114 1.35 104 0.68 30 1.52

Total copper (␮/L) 33 0.99 27 1.32 29 0.81 – –

Total zinc (␮g/L) 135 0.84 154 0.78 226 1.07 195 0.66

Total kjeldahl 1900 0.73 1288 0.50 1179 0.43 965 1.00

nitrogen (␮g/L)

⫺N⫹NO

⫺N 736 0.83 558 0.67 572 0.48 543 0.91

(␮g/L)

Total P (␮g/L) 383 0.69 263 0.75 201 0.67 121 1.66

Soluble P (␮g/L) 143 0.46 56 0.75 80 0.71 26 2.11

Notes: EMC ⫽ event mean concentration

NURP ⫽ National urban runoff program

CV ⫽ coefficient of variance

SOURCE: US EPA (1983a)

The watershed covers mainly agricultural lands. The flow rate and total

phosphorus (TP) concentrations listed are the recorded values subtracted by

the dry flow rate and TP concentration during normal flow period. Estimate

the EMC and TP concentration for this storm event.

solution:

Step1. Calculate sampling interval ⌬t ⫽ time intervals of 2 successive sam-

plings in column 1 of Table 6.5.

Step 2. Calculate mean flow q (col. 2 of Table 6.5)

q ⫽ average of 2 successive flows measured in column 2 of Table 6.4

Step 3. Calculate mean runoff volume, ⌬V

In Table 6.5, col. 3 ⫽ col. 1 ⫻ 60 ⫻ col. 2

558 Chapter 6

TABLE 6.4 Data Collected from Stormwater Sampling

Time of collection Creek flow, L/s Total phosphorus, mg/L

(1) (2) (3)

19:30 0 0

19:36 44 52

19:46 188 129

19:56 215 179

20:06 367 238

20:16 626 288

20:26 752 302

20:36 643 265

20:46 303 189

20:56 105 89

21:06 50 44

TABLE 6.5 Calculations for Total Phosphorus Loading

Sampling interval, Mean flow, Mean runoff Mean TP, Loading

⌬t min L/s volume ⌬V, L ␮g/L ⌬W, mg

(1) (2) (3) (4) (5)

6 22 7,920 26 206

10 116 69,600 90.5 6,300

10 202 121,200 153.5 18,604

10 291 174,600 288 50,285

10 497 298,200 263 78,427

10 689 413,400 295 121,953

10 638 382,800 283.5 108,524

10 473 283,800 227 64,423

10 204 122,400 139 17,014

10 78 46,800 66.5 2,713

⌺ ⫽ 1,920,720 ⌺ ⫽ 468,449

Step 4. Calculate total volume of the storm

V ⫽ ⌺⌬V ⫽ 1,920,720 L

Step 5. Calculate mean total phosphorus, TP (col. 4 of Table 6.5)

TP ⫽ average of 2 successive TP values in Table 6.4

Step 6. Calculate loading (col. 5 of Table 6.5)

⌬W ⫽ (⌬V in L)(TP in mg/L)(1 mg/1000 mg)

Step 7. Calculate total load by Eq. (6.14)

W ⫽ ⌺⌬W ⫽ 468,449 mg

Step 8. Calculate EMC

C ⫽ W/V ⫽ 468,449 mg/1,920,720 L

⫽ 0.244 mg/L

Note: If the TP concentrations are not flow weighted, the mathematic mean

of TP is 0.183 mg/L which is less than the EMC.

8.3 Street and road loading rate

Rainfall will carry pollutants from the atmosphere and remove deposits

on impervious surfaces. The rainfall intensity, duration, and storm

runoff affect the type and the amount of pollutants removed. According

to the estimation by the US EPA(1974a), the times required for 90% par-

ticle removal from impervious surfaces are 300, 90, 60, and 30 min,

respectively for 0.1, 0.33, 0.50, and 1.00 in/h storms. Average loading of

certain water quality parameters and some heavy metals from city

street, highway, and rural road are given in Table 6.6. Loading rates vary

Wastewater Engineering 559

TABLE 6.6 Average Loads (kg/curb ⭈ km ⭈ d) of Water Quality Parameters and Heavy

Metals on Streets and Roads

Parameter Highway City street Rural road

BOD

0.900 0.850 0.140

COD 10.000 5.000 4.300

0.080 0.060 0.150

0.015 0.015 0.025

N (total) 0.200 0.150 0.055

Cr 0.067 0.015 0.019

Cu 0.015 0.007 0.003

Fe 7.620 1.360 2.020

Mn 0.134 0.026 0.076

Ni 0.038 0.002 0.009

Pb 0.178 0.093 0.006

Sr 0.018 0.012 0.004

Zn 0.070 0.023 0.006

SOURCE: Wanielista and Youset (1993).

with local conditions. Loads from highways are larger than those from

city streets and rural roads. Loading is related to daily traffic volume.

Example: A storm sewer drains a section of a downtown city street 260 m

(850 ft) and 15 m (49 ft) wide with curbs on both sides. Estimate the BOD

level in the stormwater following a 60-min storm of 0.5 in/h. Assume there is

no other source of water contribution or water losses; also, it has been 4 days

since the last street cleansing.

solution:

Step 1. Determine BOD loading

From Table 6.6, average BOD loading for a city street is 0.850 kg/(curb km ⭈ d)

⫽ 850,000 mg/(curb km ⭈ d)

Total street length ⫽ 0.26 km ⫻ 2 curb ⫽ 0.52 km

⭈ curb

Total BOD loading ⫽ 850,000 mg/(curb km ⭈ d) ⫻ 0.52 km ⭈ curb ⫻ 4d

⫽ 1,768,000 mg

A 0.5 in/h storm of 60 min duration will remove 90% of pollutant; thus

Runoff BOD mass ⫽ 1,768,000 mg ⫻ 0.9

⫽ 1,591,000 mg

Step 2. Determine the volume of runoff

Area of street ⫽ 260 m ⫻ 15 m ⫽ 3900 m

Volume ⫽ 0.5 in/h ⫻ 1 h ⫻ 0.0254 m/in ⫻ 3900 m

⫽ 49.53 m

⫽ 49,530 L

Step 3. Calculate BOD concentration

BOD ⫽ 1,591,000 mg ⫼ 49,530 L

⫽ 32.1 mg/L

8.4 Runoff models

Several mathematical models have been proposed to predict water qual-

ity characteristics from storm runoffs. A consortium of research con-

structions proposed an urban runoff model based on pollutants deposited

on street surfaces and washed off by rainfall runoff. The amount of pol-

lutants transported from a watershed (dP) in any time interval (dt)is

proportional to the amount of pollutants remaining in the watershed (P).

This assumption is a first-order reaction (discussed in Chapter 1):

(6.15)

5 kP

560 Chapter 6

Integrating Eq. (6.15) to form an equation for mass remaining

P ⫽ P

⫺kt

(6.16)

The amount removed (proposed model) is

⫺ P ⫽ P

(1 ⫺ e

⫺

) (6.17)

where P

⫽ amount of pollutant on the surface initially present, lb

P ⫽ amount of pollutant remaining after time t, lb

⫺ P ⫽ amount of pollutant washed away in time t, lb

k ⫽ transport rate constant, per unit time

t ⫽ time

The transport rate constant k is a factor proportional to the rate of

runoff. For impervious surfaces,

k ⫽ br

where b ⫽ constant

r ⫽ rainfall excess

To determine b, it was assumed that a uniform runoff of 0.5 in/h would

wash 90% of the pollutant in 1 h (as stated above). We can calculate b

from Eq. (6.16)

P/P

⫽ 0.1 ⫽ e

⫺

brt

⫽ e

⫺

b(0

5 in/h) (1h)

⫽ e

⫺

0.5b

2.304 ⫽ 0.5b (in)

b ⫽ 4.6 in

Substituting b into Eq. 6.17 leads to the equation for impervious

surface areas

⫺ P ⫽ P

(1 ⫺ e

⫺

4.6rt

) (6.18)

Certain modifications to the basic model (Eq. (6.18)) for predicting total

suspended solids and BOD have been proposed to refine the agreement

between the observed and predicted values for these parameters. The

University of Cincinnati Department of Civil Engineering (1970) devel-

oped a mathematical model for urban runoff quality based essentially

on the same principles and assumptions as in Eq. (6.18). The major dif-

ference is that an integral solution was developed by this group instead

of the stepwise solution suggested by the consortium. The amount of a

pollutant remaining on a runoff surface at a particular time, the rate of

runoff at that time, and the general characteristics of the watershed

were found to be given by the following relationship

P ⫽ P

⫺

(6.19)

Wastewater Engineering 561

where P

⫽ amount of pollutant initially on the surface, lb

P ⫽ amount of pollutant remaining on the surface at time t, lb

⫽ accumulated runoff water volume up to time t

q ⫽ runoff intensity at time t

k ⫽ constant characterizing the drainage area

Many computer simulation models for runoff have been proposed and

have been discussed by McGhee (1991).

9 Sewer Hydraulics

The fundamental concepts of hydraulics can be applied to both sanitary

sewers and stormwater drainage systems. Conservation of mass,

momentum, energy, and other hydraulic characteristics of conduits are

discussed in Chapter 4 and elsewhere (Metcalf and Eddy, Inc. 1991;

WEF and ASCE, 1992) WEF and ASCE, (1992) also provide the design

guidelines for urban stormwater drainage systems, including system

layout, sewer inlets, street and intersection, drainage ways (channels,

culverts, bridges), erosion control facilities, check dams, energy dissi-

pators, drop shaft, siphons, side-overflow weirs, flow splitters, junc-

tions, flap gates, manholes, pumping, combined sewer systems,

evaluation and mitigation of combined sewer overflows, stormwater

impoundments, and stormwater management practices for water qual-

ity enhancement, etc.

10 Sewer Appurtenances

The major appurtenances used for wastewater collection systems include

street (stormwater) inlets, catch basins, manholes, building connection,

flushing devices, junctions, transitions, inverted siphons, vertical drops,

energy dissipators, overflow and diversion structure, regulators, outlets,

and pumping stations.

10.1 Street inlets

Street inlets are structures to transfer stormwater and street cleansing

wastewater to the storm sewers. The catch basin is an inlet with a basin

which allows debris to settle. There are four major types of inlet, and

multiple inlets. Location and design of inlets should consider traffic

safety (for both pedestrian and vehicle) and comfort. Gutter inlet is

more efficient than curb inlet in capturing gutter flow, but clogging by

qdt

562 Chapter 6

debris is a problem. Combination inlets are better. Various manufactured

inlets and assembled gratings are available.

Street inlets are generally placed near the corner of the street, depend-

ing on the street length. The distance between inlets depends on the

amount of stormwater, the water depth of the gutter, and the depres-

sion to the gutter. The permissible depth of stormwater in most U.S.

cities is limited to 6 in (15 cm) on residential streets.

Flow in the street gutter can be calculated by the Manning formula,

modified for a triangular gutter cross section (McGhee, 1991):

Q ⫽ K(z/n)s

1/2

8/3

(6.20)

where Q ⫽ gutter flow, m

/s or ft

K ⫽ constant ⫽ 22.61 m

/(min ⭈ m) ⫽ 0.38 m

/(s ⭈ m)

or ⫽ 0.56 ft

/(s ⭈ ft)

z ⫽ reciprocal of the cross transverse slope of the gutter

n ⫽ roughness coefficient

⫽ 0.015 for smooth concrete gutters

s ⫽ slope of the gutter

y ⫽ water depth in the gutter at the curb

The water depth at the curve can be calculated from the flow and the

street cross section and slope. The width over which the water will

spread is equal to yz.

Example 1: A street has a longitudinal slope of 0.81%, a transverse slope of

3.5%, a curb height of 15 cm (6 in), and a coefficient of surface roughness (n)

of 0.016. The width of the street is 12 m (40 ft). Under storm design condi-

tions, 4 m of street width should be kept clear during the storm. Determine

the maximum flow that can be carried by the gutter.

solution:

Step 1. Calculate the street spread limit, w

w ⫽ (12 m ⫺ 4 m)/2 ⫽ 4 m

Step 2. Calculate the curb depth (d) with the spread limit for a transverse

slope of 3.5%

d ⫽ 4 m ⫻ 0.035 ⫽ 0.14 m ⫽ 14 cm

The street gutter flow is limited by either the curb height (15 cm) or the curb

depth with the spread limit. Since

d ⫽ 14 cm

a curb height of 14 cm is the limit factor for the gutter flow.

Wastewater Engineering 563

Step 3. Calculate the maximum gutter flow Q by Eq. (6.20)

z ⫽ 1/0.035 ⫽ 28.57

Q ⫽ K(z/n)s

1/2

8/3

⫽ 0.38 m

/(s ⭈ m)(28.57/0.016) (0.0081)

1/2

(0.14 m)

8/3

⫽ 0.323 m

⫽ 11.4 ft

Example 2: The stormwater flow of a street gutter at an inlet is 0.40 m

(14.1 ft

/s). The longitudinal slope of the gutter is 0.01 and its cross transverse

slope is 0.025. The value of roughness coefficient is 0.016. Estimate the water

depth in the gutter at the curb.

solution:

Step 1. Calculate the value of z

z ⫽ 1/0.025 ⫽ 40

Step 2. Find y by Eq. (6.20)

0.40 m

/s ⫽ 0.38 m

/(s ⭈ m) (40/0.016) (0.01)

1/2

(y m)

8/3

⫽ 0.00421 m

y ⫽ 0.129 m

⫽ 5.06 in

10.2 Manholes

Manholes provide an access to the sewer for inspection and mainte-

nance operations. They also serve as ventilation, multiple pipe inter-

sections, and pressure relief. Most manholes are cylindrical in shape.

The manhole cover must be secured so that it remains in place and

avoids a blow-out during peak flooding period. Leakage from around the

edges of the manhole cover should be kept to a minimum.

For small sewers, a minimum inside diameter of 1.2 m (4 ft) at the

bottom tapering to a cast-iron frame that provides a clear opening usu-

ally specified as 0.6 m (2 ft) has been widely adopted (WEF and ASCE,

1992). For sewers larger than 600 mm (24 in), larger manhole bases are

needed. Sometimes a platform is provided at one side, or the manhole

is simply a vertical shaft over the center of the sewer. Various sizes and

types of manholes are available locally.

Manholes are commonly located at the junctions of sanitary sewers,

at changes in grades or alignment except in curved alignments, and at

locations that provide ready access to the sewer for preventive mainte-

nance and emergency service. Manholes are usually installed at street

intersections (Parcher, 1988).

564 Chapter 6