Lin S.D. Water and Wastewater Calculations Manual

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Step 2. Determine discharge with 0.72 submergence for (b)

From Fig. 4.14, enter the plot at H

⫽ 0.72 and proceed horizontally to the

line representing H

⫽ 1.1. Drop downward and read a discharge of

⫽ 3.33 ft

Example 2: Determine the discharge of a 2-ft Parshall flume with gage

readings H

⫽1.55 ft and H

⫽ 1.14 ft.

solution:

Step 1. Compute H

ratio

This ratio exceeds 0.7, therefore the flume is submerged.

Step 2. Compute the free discharge of the 2-ft flume

Step 3. Determine the correction discharge for a 1-ft flume from Fig. 4.15,

enter the plot at a value of H

⫽1.55 ft and proceed horizontally to the line

representing the submergence curve of 74 %. Then drop vertically downward

and read a discharge correction for the 1-ft flume of

⫽ 0.40 ft

Step 4. Compute discharge correction for the 2-ft flume

⫽ 1.8 ⫻ 0.40 ft

/s (factor M ⫽ 1.8, Fig. 4.15)

⫽ 0.72 ft

Step 5. Compute the actual discharge

Q ⫽ Q (at Step 2 ⫺ at Step 4)

⫽ 17.78 ft

/s ⫺ 0.72 ft

⫽ 17.06 ft

5 17.78 sft

/sd

5 8 3 2.223

5 4s2ds1.55d

1.522 3 2

0.26

Q 5 4WH

1.522W

0.26

1.14 ft

1.55 ft

5 0.74 or 74%

Fundamental and Treatment Plant Hydraulics 305

References

American Society of Civil Engineers (ASCE) and Water Environment Federation (WEF).

1992. Design and construction of urban stormwater management systems. New York:

ASCE & WEF.

Benefield, L. D., Judkins, J. F. Jr and Parr, A. D. 1984. Treatment plant hydraulics for envi-

ronmental engineers. Englewood Cliffs, New Jersey: Prentice-Hall.

Brater, E. F., King, H. W., Lindell, J. E. and Wei, C. Y. 1996. Handbook of hydraulics 7th

edn. New York: McGraw-Hill.

Brisbin, S. G. 1957. Flow of concentrated raw sewage sludges in pipes. J. Sanitary Eng.

Div., ASCE 83: 201.

Chadwick, A. J. and Morfett, J. C. 1986. Hydraulics in civil engineering. London: Allen &

Unwin.

Chow, V. T. 1959. Open-channel hydraulics, New York: McGraw-Hill.

Cross, H. 1936. Analysis of flow in networks of conduits or conductors. University of

Illinois Bulletin no. 286. Champaign-Urbana: University of Illinois.

Ductile Iron Pipe Research Association. 1997. Ductile Iron Pipe News, fall/winter 1997.

Fair, G. M., Geyer, J. C. and Okun, D. A. 1966. Water and wastewater engineering, Vol. 1:

Water supply and wastewater removal. New York: John Wiley.

Fetter, C. W. 1994. Applied hydrogeology, 3rd edn. Upper Saddle River, New Jersey:

Prentice-Hall.

Horvath, I. 1994. Hydraulics in water and waste-water treatment technology. Chichester:

John Wiley.

Hwang, N. H. C. 1981. Fundamentals of hydraulic engineering systems. Englewood Cliffs,

New Jersey: Prentice-Hall.

Metcalf & Eddy, Inc. 1972. Wastewater engineering: Collection, treatment, disposal. New

York: McGraw-Hill.

Metcalf & Eddy, Inc. 1990. Wastewater engineering: Collection and pumping of wastewater.

New York: McGraw-Hill.

James M. Montgomery, Consulting Engineers, Inc. 1985. Water treatment principles and

design. New York: John Wiley.

Morris, H. M. and Wiggert, J. M. 1972. Applied hydraulics in engineering, 2nd edn. New

York: John Wiley.

Parshall, R. L. 1926. The improved Venturi flume. Trans. Amer. Soc. Civil Engineers 89:

841–851.

Parshall, R. L. 1932. Parshall flume of large size. Colorado Agricultural Experiment

Station, Bulletin 386.

Parshall, R. L. 1950. Measuring water in irrigation channels with Parshall flumes and

small weirs. US Soil Conservation Service, Circular 843.

Perry, R. H. 1967. Engineering manual: A practical reference of data and methods in

architectural, chemical, civil, electrical, mechanical, and nuclear engineering. New York:

McGraw-Hill.

Streeter, V. L. and Wylie, E. B. 1975. Fluid mechanics, 6th edn. New York: McGraw-Hill.

US Department of the Interior, Bureau of Reclamation. 1997. Water measurement manual,

3rd edn. Denver, Colorado: US Department of the Interior.

Williams, G. S. and Hazen, A. 1933. Hydraulic tables, 3rd edn. New York: John Wiley.

Zipparro, V. J. and Hasen, H. 1993. Davis handbook of applied hydraulics. New York:

McGraw-Hill.

306 Chapter 4

Chapter

Public Water Supply

1 Sources and Quantity of Water 308

2 Population Estimates 311

2.1 Arithmetic method 312

2.2 Constant percentage growth rate method 312

2.3 Declining growth method 313

2.4 Logistic curve method 313

3 Water Requirements 315

3.1 Fire demand 315

3.2 Leakage test 320

4 Regulations for Water Quality 321

4.1 Safe drinking water act 321

4.2 Two major rules updated in 2006 336

4.3 Compliance with standards 340

4.4 Atrazine 342

5 Water Treatment Processes 342

6 Aeration and Air Stripping 343

6.1 Gas transfer models 347

6.2 Diffused aeration 355

6.3 Packed towers 357

6.4 Nozzles 365

7 Solubility Equilibrium 368

8 Coagulation 371

8.1 Jar test 375

8.2 Mixing 377

9 Flocculation 380

10 Sedimentation 384

10.1 Overﬂow rate 388

10.2 Inclined settlers 390

11 Filtration 392

11.1 Filter medium size 394

11.2 Mixed media 395

11.3 Hydraulics of ﬁlter 396

11.4 Washwater troughs 401

11.5 Filter efﬁciency 403

12 Water Softening 404

12.1 Lime-soda softening 404

12.2 Pellet softening 411

307

13 Ion Exchange 417

13.1 Leakage 425

13.2 Nitrate removal 426

14 Iron and Manganese Removal 435

14.1 Oxidation 436

15 Activated Carbon Adsorption 440

15.1 Adsorption isotherm equations 440

16 Membrane Processes 444

16.1 Process description and operations 445

16.2 Design considerations 449

16.3 Membrane performance 450

16.4 Silt density index 458

17 Residual from Water Plant 458

17.1 Residual production and density 461

18 Disinfection 463

18.1 Chemistry of chlorination 464

18.2 Ozonation 473

18.3 Disinfection kinetics 474

18.4

CT values 475

18.5 Disinfection by-products 491

19 Water Fluoridation 506

19.1 Fluoride chemicals 507

19.2 Optimal ﬂuoride concentrations 508

19.3 Fluoride feed rate (dry) 509

19.4 Fluoride feed rate for saturator 511

19.5 Fluoride dosage 511

20 Health Risks 513

20.1 Risks 514

20.2 Risk assessment 515

20.3 Risk management 520

References 525

1 Sources and Quantity of Water

The sources of a water supply may include rainwater, surface waters,

and groundwater. During the water cycle, rainwater recharges the sur-

face waters and groundwater. River, stream, natural pond, impoundment,

reservoir, and lake waters are major surface water sources. Some com-

munities use groundwater, such as galleries, wells, aquifers, and springs

as their water supply sources.

Water supplies may be drawn from a single source or from a number

of different ones. The water from multiple sources could be mixed

before distribution or separately distributed. Any new source water

has to be approved by the federal, state, and related authorities. The

quantity of water needed varies with season, geography, size and type

of community, and culture. A water supply system may provide for

domestic, industrial and commercial, public services, ﬁre demands,

unaccounted losses as well as farm uses. The design ﬂow for a water

supply system is discussed in the sections of water requirements and

ﬁre demands. The design engineers should examine the availabilities

308 Chapter 5

of water sources and quantities in the area. The prediction of the

nature population should be made for design purpose. Based on long-

term meteorological data, the amount of water stored in the lake or

reservoirs can be estimated.

Runoff refers to the precipitation that reaches a stream or river.

Theoretically, every unit volume of water passing the observation

station should be measured and the sum of all these units passing in

a certain period of time would be the total runoff. However, it is not

available due to cost. Observations should be carried out at reason-

ably close intervals so that the observed flow over a long period of time

is the sum of flows for the individual shorter periods of observation

and not the sum of the observed rates of flow multiplied by the total

period.

Example 1: Records of observations during a month (30 days) period

show that a flow rate 2.3 cfs (0.065 m

/s) for 8 days, 3.0 cfs (0.085 m

/s) for

10 days, 56.5 cfs (16.0 m

/s) for 1 day, 12.5 cfs (0.354 m

/s) for 2 days, 5.3 cfs

(0.150 m

/s) for 6 days, and 2.65 cfs (0.075 m

/s) for 3 days. What is the

mean flow rate?

solution:

Example 2: If the mean annual rainfall is 81 cm (32 in). A horizontal pro-

jected roof area is 300 m

(3230 ft

). Make a rough estimate of how much water

can be caught.

solution:

Step 1. Calculate annual gross yield, V

Step 2. Estimate net yield V

According to Fair et al. (1966), V

⫽ V

s243 m

/yrd 5 162 m

/yr

5 0.444 m

5 300 m

3 0.81 m/yr 5 243 m

/yr

5 0.666 m

Q 5

2.3 3 8 1 3.0 3 10 1 56.5 3 1 1 12.5 3 2 1 5.3 3 6 1 2.65 3 3

5 5.66 ft

5 0.160 m

Public Water Supply 309

Step 3. Estimate the water that can be stored and then be used, V

Example 3: Determine the rainfall-runoff relationship.

Using a straight line by method of average. The given values are as follows:

Year Rainfall, in Runoff, cfs/miles

1988 15.9 26.5

1989 19.4 31.2

1990 23.9 38.6

1991 21.0 32.5

1992 24.8 37.4

1993 26.8 40.2

1994 25.4 38.7

1995 24.3 36.4

1996 27.3 39.6

1997 22.7 34.5

solution:

Step 1. Write a straight line equation as y ⫽ mx ⫹ b in which m is the slope

of the line, and b is the intercept on the Y axis.

Step 2. Write a equation for each year in which the independent variable is

X (rainfall) and the dependent variable is Y (runoff). Group the equations, in

two groups, and alternate the years. Then total each group.

5 7.83 ft

5 0.5s0.444 m

/dd 5 0.222 m

5 2860 ft

/yr

5 0.5V

5 0.5s162 m

/yrd 5 81 m

/yr

310 Chapter 5

1988 26.5 ⫽ 15.9 m ⫹ b 1989 31.2 ⫽ 19.4 m ⫹ b

1990 38.6 ⫽ 23.9 m ⫹ b 1991 32.5 ⫽ 21.0 m ⫹ b

1992 37.4 ⫽ 24.8 m ⫹ b 1993 40.2 ⫽ 26.8 m ⫹ b

1994 38.7 ⫽ 25.4 m ⫹ b 1995 36.4 ⫽ 24.3 m ⫹ b

1996 39.6 ⫽ 27.3 m ⫹ b 1997 34.5 ⫽ 22.7 m ⫹ b

180.8 ⫽ 117.3 m ⫹ 5b 174.8 ⫽ 114.2 m ⫹ 5b

Step 3. Solve the total of each group of equations simultaneously for m and b

180.8 5 117.3m 1 5b

2 s174.8 5 114.2m 1 5bd

6.0 5 3.1m

m 5 1.94

Step 4. Substituting for m and solving for b

Step 5. The equation of straight line of best ﬁt is

Y ⫽ 1.94X ⫺ 9.35

where X ⫽ rainfall, in

Y ⫽ runoff, cfs/miles

Example 4: A watershed has a drainage area of 1000 ha (2470 acres). The

annual rainfall is 927 mm (36.5 in). The expected evaporation loss is 292 mm

(11.5 in) per year. The estimated loss to groundwater is 89 mm (3.5 in) annu-

ally. Estimate the amount of water that can be stored in a lake and how

many people can be served, assuming 200 L(c ⋅ d) is needed.

solution:

Step 1. Using a mass balance

R (rainfall excess) ⫽ P (precipitation) ⫺ E (evaporation) ⫺

G (loss to groundwater)

R ⫽ 927 mm ⫺ 292 mm ⫺ 89 mm

⫽ 546 mm

Step 2. Convert R from mm to m

(volume) and L

Step 3. Compute the people that can be served

Annual usage per capita ⫽ 200 L/(c ⋅ d) ⫻ 365 days

⫽ 7.3 ⫻ 10

L/c

2 Population Estimates

Prior to the design of a water treatment plant, it is necessary to forecast

the future population of the communities to be served. The plant should

be sufﬁcient generally for 25 to 30 years. It is difﬁcult to estimate the

5 74,800 capita

No. of people served 5

5.46 3 10

7.3 3 10

L/c

R 5 564 mm 3

1 m

1000 mm

3 1000 ha 3

10,000 m

1 ha

5 5.46 3 10

3 10

L/1 m

5 5.46 3 10

180.8 5 117.3s1.94d 1 5b

5b 5246.76

b 529.35

Public Water Supply 311

population growth due to economic and social factors involved. However,

a few methods have been used for forecasting population. They include the

arithmetic method and uniform percentage growth rate method (Clark and

Viessman, 1966; Steel and McGhee, 1979; Viessman and Hammer, 1993).

The ﬁrst three methods are short-term (<10 years) forecasting.

2.1 Arithmetic method

This method of forecasting is based upon the hypothesis that the rate

of increase is constant. It may be expressed as follows:

(5.1)

where p ⫽ population

t ⫽ time, year

⫽ arithmetic growth rate constant

Rearrange and integrate the above equation, p

and p

are the popula-

tions at time t

and t

, respectively.

We get

(5.2a)

⫽ p

⫹ k

t (5.2b)

where p

⫽ population at future time

⫽ present population, usually use p

(recent censused)

2.2 Constant percentage growth rate method

The hypothesis of constant percentage or geometric growth rate assumes

that the rate increase is proportional to population. It can be written as

(5.3a)

Integrating this equation yields

(5.3b)

ln p

2 ln p

5 k

2 t

ln p

2 ln p

2 t

5 k

2 p

5 k

2 t

2 p

2 t

⌬p

⌬t

dp 5

5 k

312 Chapter 5

The geometric estimate of population is given by

ln p ⫽ ln p

⫹ k

(t ⫺ t

) (5.3c)

2.3 Declining growth method

This is a decreasing rate of increase on the basis that the growth rate

is a function of its population deﬁcit. Mathematically it is given as

(5.4a)

where p

⫽ saturation population, assume value

Integration of the above equation gives

Rearranging

(5.4b)

The future population P is

(5.4c)

where P

⫽ population of the base year

2.4 Logistic curve method

The logistic curve-ﬁtting method is used for modeling population trends

with an S-shape for large population center, or nations for long-term

population predictions. The logistic curve form is

(5.5a)

where P

⫽ saturation population

a, b ⫽ constants

They are

(5.5b)P

2 p

1 p

2 p

P 5

1 1 e

a1b⌬t

P 5 P

1 sP

2 P

ds1 2 e

2 t

2 p

s 2

5 k

2 ln

2 p

s 2

5 k

2 t

5 k

2 pd

Public Water Supply 313

(5.6)

(5.7)

where n ⫽ time interval between successive censuses

Substitution of these values in Eq. (5.5a) gives the estimation of future

population on P for any period ∆t beyond the base year corresponding

to P

Example: A mid size city recorded populations of 113,000 and 129,000 in the

April 1980 and April 1990 census, respectively. Estimate the population in

January 1999 by comparing (a) arithmetic method, (b) constant percentage

method, and (c) declining growth method.

solution:

Step 1. Solve with the arithmetic method

Let t

and t

for April 1980 and April 1990, respectively

∆t ⫽ t

⫺ t

⫽ 10 years

Using Eq. (5.2 a)

Predict p

for January 1999 from t

, using Eq. (5.2b)

t ⫽ 8.75 years

⫽ p

⫹ k

⫽ 129,000 ⫹ 1600 ⫻ 8.75

⫽ 143,000

Step 2. Solve with constant percentage method, using Eq. (5.3b)

⫽ 0.013243

Then using Eq. (5.3c) ln P ⫽ ln P

⫹ k

(t ⫺ t

)

⫽ ln 129,000 ⫹ 0.013243 ⫻ 8.75

⫽ 11.8834

p ⫽ 144,800

lnp

2 lnp

2 t

ln 129,000 2 ln 113,000

2 p

2 t

129,000 2 113,000

5 1600

b 5

2 p

a 5 ln

2 p

314 Chapter 5