Mathematics Manual
for
WATER AND WASTEWATER
TREATMENT PLANT OPERATORS
2004 by CRC Press LLC
Mathematics Manual
for
WATER AND WASTEWATER
TREATMENT PLANT OPERATORS
Frank R. Spellman
CRC PR E S S
Boca Raton London New York Washington, D.C.
2004 by CRC Pres

L1675_C28.fm Page 275 Saturday, January 31, 2004 5:57 PM
28 Chemical Dosage Calculations
TOPICS
Chemical Dosing
Chemical Feed Rate
Chlorine Dose, Demand, and Residual
Hypochlorite Dosage
Chemical Solutions
Mixing Solutions of Different Strength
Solut

L1675_C26.fm Page 257 Saturday, January 31, 2004 5:53 PM
26 Activated Biosolids
TOPICS
Activated Biosolids Process Control Calculations
Moving Averages
BOD or COD Loading
Solids Inventory
Food-to-Microorganism Ratio (F/M Ratio)
Gould Biosolids Age
M

L1675_C25.fm Page 251 Saturday, January 31, 2004 5:52 PM
25 Rotating Biological
Contactors (RBCs)
TOPICS
RBC Process Control Calculations
Hydraulic Loading Rate
Soluble BOD
Organic Loading Rate
Total Media Area
The rotating biological contactor (RBC)

L1675_C24.fm Page 245 Saturday, January 31, 2004 5:50 PM
24 Trickling Filter Calculations
TOPICS
Trickling Filter Process Calculations
Hydraulic Loading Rate
Organic Loading Rate
BOD and SS Removal
Recirculation Ratio
The trickling lter process (see F

L1675_C21.fm Page 211 Saturday, January 31, 2004 5:45 PM
21 Water Softening
TOPICS
Water Hardness
Calculating Calcium Hardness as CaCO3
Calculating Magnesium Hardness as CaCO3
Calculating Total Hardness
Calculating Carbonate and Noncarbonate Hardness

L1675_C19.fm Page 187 Saturday, January 31, 2004 5:41 PM
19 Water Chlorination
Calculations
Chlorine is the most commonly used substance for disinfection of water in the U.S. The addition
of chlorine or chlorine compounds to water is referred to as chlori

L1675_C18.fm Page 173 Saturday, January 31, 2004 5:39 PM
18 Filtration Calculations
I was always aware, I think, of the water in the soil, the way it travels from particle to particle, molecules
adhering, clustering, evaporating, heating, cooling, freezin

L1675_C15.fm Page 135 Saturday, January 31, 2004 5:33 PM
15 Water Source and
Storage Calculations
TOPICS
Water Sources
Water Source Calculations
Well Drawdown
Well Yield
Specic Yield
Well-Casing Disinfection
Deep-Well Turbine Pump Calculations
Verti

L1675_C14.fm Page 119 Saturday, January 31, 2004 5:31 PM
Part II
Applied Math Concepts:
Water Treatment
2004 by CRC Press LLC
L1675_C14.fm Page 121 Saturday, January 31, 2004 5:31 PM
14 Pumping Calculations
TOPICS
Pumping
Basic Water Hydraulics Calculati

L1675_C10.fm Page 43 Saturday, January 31, 2004 5:18 PM
10 Units of Measurement,
Conversions, and
Electrical Calculations
TOPICS
Units of Measurement
Conversion Factors
Weight, Concentration, and Flow
Conversions
Typical Water/Wastewater Conversion Exam

L1675_C13.fm Page 113 Saturday, January 31, 2004 5:29 PM
Balance and
13 Mass Performance Measuring
Plant
TOPICS
Mass Balance for Settling Tanks
Mass Balance Using BOD Removal
Measuring Plant Balance
Plant Performance/Efciency
Unit Process Performance/Ef

L1675_C12.fm Page 105 Saturday, January 31, 2004 5:28 PM
Pressure, and
12 Force,Calculations
Head
TOPICS
Force and Pressure
Head
Static Head
Friction Head
Velocity Head
Total Dynamic Head
Pressure/Head
Head/Pressure
Force, Pressure, and Head Example

L1675_C11.fm Page 93 Saturday, January 31, 2004 5:25 PM
11 Measurements: Area,
Circumference,
and Volume
TOPICS
Perimeter and Circumference
Perimeter
Circumference
Area
Area of a Rectangle
Area of a Circle
Surface Area of a Circular or Cylindrical Ta

L1675_C09.fm Page 37 Saturday, January 31, 2004 5:16 PM
9 Dimensional Analysis
TOPIC
Dimensional Analysis in Problem Solving
DIMENSIONAL ANALYSIS IN PROBLEM SOLVING
Dimensional analysis is a problem-solving method that uses the fact that the number 1 can

L1675_C07.fm Page 27 Saturday, January 31, 2004 5:13 PM
7 Solving for the Unknown
TOPICS
Equations
Axioms
Solving Equations
Setting Up Equations
Many water/wastewater calculations involve the use of formulae and equations; for example,
calculations used i

L1675_C08.fm Page 33 Saturday, January 31, 2004 5:15 PM
8 Ratio and Proportion
TOPICS
Ratio
Proportion
Working with Ratio and Proportion
RATIO
A ratio is the established relationship between two numbers. For example, if someone says, Ill
give you four to

L1675_C06.fm Page 23 Saturday, January 31, 2004 5:12 PM
6 Averages (Arithmetic Mean)
and Median
TOPICS
Averages
Median
Whether we speak of harmonic mean, geometric mean, or arithmetic mean, each gure is designed to
nd the center (or middle) of a set of nu

L1675_C02.fm Page 7 Saturday, January 31, 2004 5:03 PM
2 Sequence of Operations
TOPICS
Sequence of Operations Rules
Sequence of Operations Examples
Mathematical operations such as addition, subtraction, multiplication, and division are usually
performed i