Lin S.D. Water and Wastewater Calculations Manual

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Streams and Rivers 105

Figure 1.14 Plot of (⌺t/⌺DO

)

1/3

versus ⌺t.

TABLE 1.19 DO Proﬁle Computation at 27ⴗC and a 7-Day, 10-Year Low Flow

(1) (2) (3) (4) (5) (6) (7) (8)

Flow, cfs Total Subreach

t, ⌺t,DO

,DO

Station at station mean days days lb/d lb/d

1 660 0

2 666 663 0.750 0.750 0.242 6218 6218

3 670 668 1.076 1.826 0.491 12603 6385

Dam

4 670

5 674 672 0.345 2.171 0.551 14168 1565

6 682 678 0.626 2.797 0.645 16544 2376

7 696 689 1.313 4.110 0.781 20052 3508

8 702 699 1.370 5.48 0.868 22282 2230

9 704 703 0.938 6.418 0.907 23272 990

10 708 706 0.845 7.263 0.932 23913 941

Tributary 96

11 804

12 810 806 0.608 7.871 0.946 24265 351

1 2 e

⌺

0.030

0.032

0.034

0.036

0.038

0.040

0.042

0.044

0.046

01234567

(Σt/ΣDO

)

1/3

Time of Travel, Σt, days

106 Chapter 1

TABLE 1.19 (contd.)

(10) (11) (12) (13) (14)

(9) Mean DO

Mean (15)

– DO

,DO

, depth M,

Station lb/d lb/d mg/L lb/d H, ft min

1 21084

2 14866 17975 7.87 28124 0.361 5.9 17.4

3 11977 15170 7.87 28336 0.465 6.1 17.5

Dam

5 21584 22366 7.87 28506 0.215 2.5 4.1

6 23895 25083 7.87 28760 0.128 3.4 9.6

7 22908 24662 7.87 29227 0.165 4.6 13.8

8 24556 25671 7.87 29651 0.134 5.5 16.2

9 26367 26862 7.87 29821 0.099 5.7 16.6

10 27093 27404 7.87 29948 0.085 6.0 17.4

Tributary

12 30924 31100 7.87 34190 0.090 6.5 18.6

TABLE 1.19 (concluded)

(16) (20) (21)

t⬘⫽ (19) DO

(or DO

)

1440t, (17) (18) DO

Station min t⬘/MR

/100 lb/d lb/d Remark

1 21084 5.90

2 1080 62.1 0.00555 3696 18362 5.14

3 1549 88.5 0.00545 6353 18330 5.09 Above dam

Dam

4 23148 6.41 Below dam

5 497 121.2 0.00630 4687 26271 7.25

6 901 93.9 0.00730 2521 26416 7.23

7 1891 137.0 0.00620 3878 26786 7.21

8 1973 121.8 0.00578 2802 27357 7.26

9 1351 81.4 0.00568 1367 27734 7.32

10 1217 69.9 0.00550 975 28067 7.38 Above trib.

Tributary

11 31276 Below trib.

12 876 47.1 0.00521 788 31682 7.29

Notes: Col 7 ⫽ L

⫻ Col 6 ⫽ 25,660 ⫻ Col 6

Col 8

⫽ Col 7

– Col 7

n–1

Col 9

⫽ Col 20

n–1

–Col 8

Col 10

⫽ (Col 20

n–1

⫹ Col 9

)/2

Col 11 ⫽ DO

at T of 27⬚C

Col 12 ⫽ 5.39 ⫻ Col 3 ⫻ Col 11

Col 15 ⫽ Calculated or from monogram Fig. 1.12

Col 18 ⫽ Calculated or from monogram Fig. 1.12

Col 19 ⫽ Col 12 ⫻ Col 13 ⫻ Col 17 ⫻ Col 18

Col 20 ⫽ initial value is 663 ⫻ 5.90 ⫻ 5.39 and thereafter ⫽ col 9 ⫹ col 19

Col 21 ⫽ Col 20/Col 3/5.39

trib. ⫽ tributary

1 2

For columns 9, 10, 13, 19, 20, and 21, calculate iteratively from station by

station from upstream downward. The other columns can be calculated inde-

pendently. At station 4 (below the dam), the dam aeration ratio is given as

Eqs. (1.117) and (1.118)

This DO value of 6.45 mg/L is inserted into column 21 at station 4. The cor-

responding DO

(in lb/d) is computed by multiplying 5.39Q to obtain 23,148

lb/d, which is inserted into column 20 at station 4.

At station 11, immediately below the tributary, DO contribution is 3208

lb/d (i.e. 5.39 ⫻ 6.2 ⫻ 96). This value plus 28,068 lb/d (31,276 lb/d) is inserted

into column 20. Then computations continue with iterative procedures for

station 12.

It should be noted that the parameters H, M, t⬘, t⬘/M, and R/100 can be com-

puted earlier (i.e. in earlier columns). Therefore, the other DO computations

will be in the latter part of Table 1.19. It seems easier for observation. Also,

these steps of computation can be easily programmed using a computer.

The results of computations for solving equation, DO

⫽ DO

⫺DO

⫹

⫹ DO

are given in Table 1.19, and the DO concentrations in column 21

of Table 1.19 are the predictive DO values for 7-day, 10-year low flow with sec-

ondary wastewater treatment. All DO values are above the regulatory stan-

dard of 5.0 mg/L, owing to expanded wastewater treatment and dam aeration.

18 Biological Factors

18.1 Algae

Algae are most commonly used to assess the extent that primary pro-

ductivity (algal activity) affects the DO resources of surface waters.

Many factors affect the distribution, density, and species composition of

algae in natural waters. These include the physical characteristics of the

water, length of storage, temperature, chemical composition, in situ

reproduction and elimination, floods, nutrients, human activities, trace

elements, and seasonal cycles.

Of the many methods suggested for defining the structure of a bio-

logical community, the most widely used procedure has been the diver-

sity index. A biological diversity index provides a means of evaluating

522.78/1.96 1 7.87 5 6.45 smg/Ld

1.96 5 s7.87 2 5.09d/s7.87 2 C

r 5 sC

2 C

d/sC

2 C

5 1.960

5 1 1 0.11 3 1.1 3 0.58s1 1 0.046 3 27d 3 6.1

r 5 1 1 0.11qbs1 1 0.046Tdh

Streams and Rivers 107

the richness of species within a biological community using a mathe-

matical computation. Although different formulas have been used, the

one determined by the information theory formula, the Shannon⫺Weiner

diversity index, is widely used for algal communities or communities of

other organisms. The formula is (Shannon and Weaver, 1949):

(1.121)

where D ⫽ diversity index

⫽ n

⫽ the number (density) of the ith genera or species

N ⫽ total number (density) of all organisms of the sample

i ⫽ 1, 2,..., m

m ⫽ the number of genera or species

log

⫽ 1.44 ln P

(1.122)

The index D has a minimum value, when a community consisting

solely of one (m ⫽ 1) species has no diversity or richness and takes on

a value of unity. As the number of species increases and as long as each

species is relatively equal in number, the diversity index increases

numerically. It reaches a maximum value when m ⫽ N.

Example: Seven species of algae are present in a stream water sample. The

numbers of seven species per mL are 32, 688, 138, 98, 1320, 424, and 248,

respectively. Compute the diversity index of this algal community.

solution: Using formula (Eq. (1.122))

and construct a table of computations (Table 1.20). Answer: D ⫽ 2.15

18.2 Indicator bacteria

Pathogenic bacteria, pathogenic protozoan cysts, and viruses have been

isolated from wastewaters and natural waters. The sources of these

pathogens are the feces of humans and of wild and domestic animals.

Identification and enumeration of these disease-causing organisms in

water and wastewater are not recommended because no single technique

D 521.44

⌺

i21

/Nd lnsn

/Nd

D 521.44

⌺

i21

/Nd lnsn

/Nd

D 52

⌺

i51

log

108 Chapter 1

is currently available to isolate and identify all the pathogens. In fact,

concentrations of these pathogens are generally low in water and waste-

water. In addition, the methods for identification and enumeration of

pathogens are labor-intensive and expensive.

Instead of direct isolation and enumeration of pathogens, total coliform

(TC) has long been used as an indicator of pathogen contamination of a

water that poses a public health risk. Fecal coliform (FC), which is more

fecal-specific, has been adopted as a standard indicator of contamina-

tion in natural waters in Illinois, Indiana, and many other states. Both

TC and FC are used in standards for drinking-water and natural waters.

Fecal streptococcus (FS) is used as a pollution indicator in Europe.

FC/FS ratios have been employed for identifying pollution sources in the

United States. Fecal streptococci are present in the intestines of warm-

blooded animals and of insects, and they are present in the environment

(water, soil, and vegetation) for long periods of time. Escherichia coli bac-

teria have also been used as an indicator.

Calculation of bacterial density. The determination of indicator bacteria,

total coliform, fecal coliform, and fecal streptococcus or enterococcus is

very important for assessing the quality of natural waters, drinking-

waters, and wastewaters. The procedures for enumeration of these

organisms are presented elsewhere (APHA et al., 1995). Examinations

of indicator bacterial density in water and in wastewater are generally

performed by using a series of four-decimal dilutions per sample, with

3 to 10, usually 5, tubes for each dilution. Various special broths are used

for the presumptive, confirmation, and complete tests for each of the bac-

teria TC, FC, and FS, at specified incubation temperatures and periods.

MPN method. Caliform density is estimated in terms of the most prob-

able number (MPN). The multiple-tube fermentation procedure is often

called an MPN procedure. The MPN values for a variety of inoculation

series are listed in Table 1.21. These values are based on a series of five

tubes for three dilutions. MPN values are commonly determined using

Streams and Rivers 109

TABLE 1.20 Values for Eq. (2.122)

/N ⫺1.44 ln (n

/N) ⫺1.44(n

/N) ln (n

/N)

1 32 0.0109 6.513 0.071

2 688 0.2334 2.095 0.489

3 138 0.0468 4.409 0.206

4 98 0.0332 4.902 0.163

5 1320 0.4478 1.157 0.518

6 424 0.1438 2.792 0.402

7 248 0.0841 3.565 0.300

⌺ 2948(N ) 1.0000 2.149

Table 1.21 and are expressed as MPN/100 mL. Only two significant fig-

ures are used for the reporting purpose. Other methods are based on five

20 mL or ten 10 mL of the water sample used.

Table 1.21 presents MPN index for combinations of positive and neg-

ative results when five 10-mL, five 1-mL, and five 0.1-mL volumes of

sample are inoculated. When the series of decimal dilution is different

from that in the table, select the MPN value from Table 1.21 for the com-

bination of positive tubes and compute the MPN index using the fol-

lowing formula:

110 Chapter 1

TABLE

1.21 MPN Index for Various Combinations of Positive Results When Five

Tubes Are Used per Dilution (10, 1.0, 0.1 mL)

Combination of MPN index Combination of MPN index

positives 100 mL positives 100 mL

4-2-0 22

0-0-0 ⬍2 4-2-1 26

0-0-1 2 4-3-0 27

0-1-0 2 4-3-1 33

0-2-0 4 4-4-0 34

5-0-0 23

1-0-0 2 5-0-1 30

1-0-1 4 5-0-2 40

1-1-0 4 5-1-0 30

1-1-1 6 5-1-1 50

1-2-0 6 5-1-2 60

2-0-0 4 5-2-0 50

2-0-1 7 5-2-1 70

2-1-0 7 5-2-2 90

2-1-1 9 5-3-0 80

2-2-0 9 5-3-1 110

2-3-0 12 5-3-2 140

3-0-0 8 5-3-3 170

3-0-1 11 5-4-0 130

3-1-0 11 5-4-1 170

3-1-1 14 5-4-2 220

3-2-0 14 5-4-3 280

3-2-1 17 5-4-4 350

5-5-0 240

4-0-0 13 5-5-1 300

4-0-1 17 5-5-2 500

4-1-0 17 5-5-3 900

4-1-1 21 5-5-4 1600

4-1-2 26 5-5-5 ⱖ1600

SOURCE: APHA, AWWA, and WEF (1995)

(1.123)

For the MPN index for combinations not appearing in Table 1.21 or for

other combinations of dilutions or numbers of tubes used, the MPN can

be estimated by the Thomas equation:

(1.124)

Although the MPN tables and calculations are described for use in the

coliform test, they are equally applicable for determining the MPN of

any other organisms for which suitable test media are available.

Example 1: Estimate the MPN index for the following six samples.

solution:

Positive/five tubes, mL used

Combination of MPN index/

Sample 1 0.1 0.01 0.001 positive 100 mL

A-raw 5/5 5/5 3/5 1/5 5-3-1 11000

B ⫻ 10

⫺3

5/5 5/5 3/5 1/5 5-3-1 11000000

C 5/5 3/5 2/5 0/5 5-3-2 1400

D 5/5 3/5 1/5 1/5 5-3-2 1400

E 4/5 3/5 1/5 0/5 4-3-1 330

F 0/5 1/5 0/5 0/5 0-1-0 20

Step 1. For sample A

For 5-3-1; from Table 1.21, MPN ⫽ 110. Using Eq. (1,123)

Step 2. For sample B

Same as sample A; however, it is a polluted water and a 10

⫺3

dilution is used.

Thus,

MPN ⫽ 11,000 ⫻ 10

⫽ 11,000,000

Step 3. For sample C

For sample: MPN 5 110 3

0.1

5 11,000

MPN

100 mL

No. of positive tubes 3 100

2smL sample in negative tubesdsmL sample in all tubesd

largest volume tested in dilution series used

MPN

100 mL

5 MPN value from table

Streams and Rivers 111

From Table 1.21, MPN ⫽ 140 for 5-3-2 combination

Step 4. For sample D

Since one is positive at 0.001 mL used, add 1 positive into 0.01 dilution.

Therefore, the combination of positive is 5-3-2.

Thus, MPN ⫽ 1400

Step 5. For sample E with a 4-3-1 combination

Step 6. For sample F, 0-1-0 positive

Note: Unit for MPN is the number per 100 mL sample.

Example 2: Calculate the MPN value by the Thomas equation with data

given in Example 1.

solution:

Step 1. For sample A

Number of positive tubes for the last two dilutions ⫽ 3 ⫹ 1 ⫽ 4

mL sample in negative tubes ⫽ 2 ⫻ 0.01 ⫹ 4 ⫻ 0.001 ⫽ 0.024

mL sample in all tubes ⫽ 5 ⫻ 0.01 ⫹ 5 ⫻ 0.001 ⫽ 0.055

With the Thomas equation:

Step 2. For sample B

As Step 1, in addition multiply by 10

MPN

100 mL

5 11,000 3 10

5 11,000,000

5 11,000 sfor 10, 1, and 0.1 mLd

4 3 100

20.024 3 0.055

MPN

100 mL

No. of positive tubes 3 100

2smL sample in negative tubesdsmL sample in all tubesd

MPN 5 2 3

5 20

MPN 5 33 3

5 330

For sample: MPN 5 140 3

5 1400

112 Chapter 1

Step 3. For sample C

Note: Use only two significant figures for bacterial count.

Step 4. For sample D

The answer is exactly the same as for sample C

Step 5. For sample E

Step 6. For sample F

Example 3: The results of positive tubes of 4 tubes with five dilutions (100,

10, 1, 0.1, and 0.01 mL) are 4/4, 3/4, 1/4, 1/4, and 0/4. Estimate the MPN value

of the sample.

solution:

Step 1. Adjust the combination of positive tubes

It will be 4-3-2 at 100, 10, and 1 mL dilutions.

Step 2. Find MPN by the Thomas formula:

5 22

MPN

100 mL

s3 1 2d 3 100

2s10 1 2 3 1d 3 4s10 1 1d

5 18

MPN

100 mL

100

2s5.45 3 5.55d

5 310

5 305

MPN

100 mL

s4 1 3 1 1d 3 100

21.24 3 5.55

MPN

100 mL

5 1400

5 1406

MPN

100 mL

s3 1 2d 3 100

20.23 3 0.55

Streams and Rivers 113

Membrane ﬁlter method. The membrane filtration (MF) method is the

most widely used method. Calculations of MF results for these indica-

tors or other organisms are presented here (Illinois EPA, 1987):

Step 1. Select the membrane filter with the number of colonies in the

acceptable range

The acceptable range for TC is 20 to 80 TC colonies and no more than 200

colonies of all types per membrane. Sample quantities producing MF counts

of 20 to 60 colonies of FC or FS are desired.

Step 2. Compute count per 100 mL, according to the general formula:

Example 1: Counts with the acceptable limits:

Assume that filtration of volumes 75, 25, 10, 3, and 1 mL produced FC colony

counts of 210, 89, 35, 11, and 5, respectively. What is the FC density for the

sample?

solution:

The MF with 35 FC colonies is the best MF for counting.

Thus, the FC density is

which will be recorded as 350 FC/100 mL.

It should be noted that an analyst would not count the colonies on all five

filters. After inspection of five membrane filters, the analyst would select the

MF(s) with 20 to 60 FC colonies and then limit the actual counting to such a

membrane. If there are acceptable counts on replicate filters, count colonies

on each MF independently and determine final reporting densities. Then

compute the arithmetic mean of these densities to obtain the final recorded

density.

Example 2: For duplicate samples:

A duplicate filtration of 2.0 mL of water sample gives plate counts of 48 and

53 TC colonies. Compute the recorded value.

solution:

Step 1. Determine FS densities for two membranes independently, with the

general formula:

100 mL

48 3 100

5 2400

100 mL

35 3 100

5 350

Colonies

100 mL

No. colonies counted 3 100

Volume of sample, mL

114 Chapter 1