Math for Water Treatment Distribution Wastewater Treatment Docu… · • Do all the multiplication...

WAT305 Math Part 1

ABC Math

1/17/2013 Wk 5c Math Pt2 DMACC2012

Good to know for certification:

You have used 35 150lb cylinders of Chlorine

in 2011…how many pounds total did you use?

How many pounds per month did you use?

If demand is expected to increase by 10% this

year, how many lbs should you have budgeted

for in 2012?


Disease-causing bacteria are

known as A. Coliforms

B. Non-coliforms

C. Non-pathogenic

D. Pathogenic


Organisms that can cause

disease in humans and that

may be found in water include A. Bacteria

B. Viruses

C. Protozoa

D. All of these


The difference between the

amount of chlorine added and

the amount of residual chlorine

remaining is called

A. Chlorine dosage

B. Free available chlorine

C. Chlorine residual

D. Chlorine demand


After all chlorine demands

have been met, what is the

remaining chlorine called? A. Breakpoint

B. Differential

C. Potential

D. Residual

Adapted from “Math for Water

Distribution”

Steve Moehlmann

Phil Koundakjian

Mark Simms

1/17/2013 WAT 305 WD ABC Formulas and

Conversions

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Agenda & Objectives

• Math Primer & review

• ABC Formula/Conversion Table

• Practice Solving Problems


Conversions

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Let’s look at some tools you

have

• AceOps Web Page www.aceops.org

• ABC Formula/Conversion Table


Conversions

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CSUS Arithmetic

Rules for Solving Equations • Work from left to right

• Do all the multiplication and division above (numerator)

• Do all the multiplication and division below (denominator) the line

• Do all the addition and subtraction above

• Do all the addition and subtraction below the line

• Divide numerator (top) by the denominator (bottom)

• If parentheses, do the calculations within them first using the previous steps, then complete the rest of the equation


Conversions

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ABC Formula/Conversion Table

Combines formulas, conversions, and

abbreviations for:

Water Treatment

Distribution

Lab


Conversions

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Units Are the Key!!! • ABC formulas are generic

• Must watch the units

• Can’t mix units



• C a n ’ t m i x u n i t s

ABC Formula/Conversion Table Area:

[from Bing.com] “measurement of surface: the extent of part of a S U R F A C E enclosed within a B O U N D A R Y , …. The area of a square or rectangle can be calculated by multiplying together the lengths of two adjacent sides.”

ABC Formula/Conversion Table Area of rectangle: L x W = ___ ___ ___

Area of circle: πr2= ___ ___ ___

OR (π/4)(Diameter2)= ___ ___ ___

ABC Formula/Conversion Table Don’t mix units!

ft. only = ft.

in. only = in.

So al l dimensions must be in one unit

(can’t say L= 48 inches and W= 10 feet)

ABC Formula/Conversion Table Let’s give it a try…

What is the area of a rectangle if

the length is 4 feet and the width is 10 feet?

4 x 10 = 40

And what unit of measure will the result be in?

sq. ft. (sf, ft2)

So the answer is 40 sq. ft. (sf, sf2)

ABC Formula/Conversion Table Let’s give it another try…

What is the area of a rectangular tank if

the length is 80 feet and the width is 40 feet?

80 x 40 = 3,200 And what unit of measure will the result be in?

sq. ft. (sf, ft2)

So the answer is 3,200 sq. ft. (sf, sf2)


What is the area of a circle if

the diameter is 40 feet?

Radius “r” is ½ of diameter “D”

½ of 40 is 20

π202 = 1,256 (3.14 x 20 x 20)


sq. ft. (sf, ft2)



What is the area of a circle if the diameter is 40 feet?

Since we already have DIAMETER what if there was a formula we could use so we don’t have to change into

radius??? Walla… 0.785 x D2

0.785 x 402 = 1,256 (0.785 x 40 x 40)

And what unit of measure will the result be in? sq. ft. (sf, ft2)



What is the area of a circular tank if the diameter is 50 feet?

Since we already have DIAMETER what if there was a formula we could use so we don’t have to change into

radius??? Walla… 0.785 x D2

0.785 x 502 = 1,962.5 (0.785 x 50 x 50)

And what unit of measure will the result be in? sq. ft. (sf, ft2)

So the answer is 1,962.5 sq. ft. (sf, sf2)

ABC Formula/Conversion Table REMINDER………………

Don’t mix units! ft. only = ft.

in. only = in.

So all dimensions must be in one unit

(can’t say L= 48 inches and W= 10 feet)


Conversions

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Area of Circle

(.785) (Diameter2)

or

(P)(Radius2)

• Units

– Sq in, sq ft, acres, sq miles

– in2, ft2

• Use

– Pressure (psi), loading rates, velocity


Conversions

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Area of Circle:

Calculate these… 1. The diameter is 20 ft. Calculate the area

of the circle.

2. The diameter is 40 ft. Calculate the area

of the circle.

3. The diameter is 50 ft. Calculate the area

of the circle.


Conversions

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Area of Rectangle

(Length)(Width)

• Units

– Sq in, sq ft, acres, sq miles

– in2, ft2

• Use

– Pressure (psi), loading rates


Conversions

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Area of a Rectangle: Problem

• Formula

• Problem

– The length of a tank is 12 feet and the width is

4 feet. Calculate the area of the tank.


Conversions

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Area of a Rectangle: Formula

• The length of a tank is 12 feet and the

width is 4 feet. Calculate the area of the

tank.

• Formula

Area of Rectangle = (Length)(Width)


Conversions

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Area of a Rectangle: Solution

• The length of a tank is 10 feet and the


tank.

Area of Rectangle = (Length)(Width)

= (10 ft)(5 ft)

= 50 ft2


Conversions

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Area of a Rectangle:

Calculate these… 1. The length of a tank is 20 feet and the


tank.

2. The length of a tank is 40 feet and the


tank.

3. The length of a tank is 50 feet and the


tank.


Conversions

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Circumference of Circle

(3.14)(Diameter)

• Units

– ft

• Use

– Loading rates


Conversions

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The tank is 10 feet in diameter, what is the

circumference?

(3.14)(Diameter)

(3.14)(10) = 31.4 feet


Conversions

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1. The tank is 20 feet in diameter, what is the

circumference?

2. The tank is 40 feet in diameter, what is the

circumference?

3. The tank is 100 feet in diameter, what is

the circumference?


Conversions

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Detention Time

Volume

Flow

• Volume

– cubic feet or gallons

• Flow

– cfs, cfm, gpm, gpd, mgd

• Use

– Loadings


Conversions

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Detention Time

The volume of a tank is 100,000 gallons and

the flow is 100,000 gallons per day (gpd).

Volume

Flow

100,000

100,000

= 1 day


Conversions

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Detention Time:

Calculate these… The volume of a tank is 100,000 gallons and


The volume of a tank is 200,000 gallons and


The volume of a tank is 1,000,000 gallons

and the flow is 100,000 gallons per day

(gpd).


Conversions

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Leakage

Volume

Time

• Volume

– cubic feet or gallons or million gallons

• Time

– Seconds, minutes, hours, days

• Use

– Loadings

ABC Formula/Conversion Table Have you ever heard of Mass or Mass Flux?

“rate of flow of mass through a unit area”

Do you know what it is and how to use it in operations and on certification exams?

ABC Formula/Conversion Table Mass or Mass Flux

Do you know what it is and how to use it in operations and on certification exams?

Mass, lbs = (Volume, gal)(Concentration, mg/l)(8.34 lbs/Gal)

Mass Flux, lbs = (Flow, gal)(Concentration, mg/l)(8.34 lbs/Gal)


Conversions

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Mass or Dosage, lbs or lbs/day

(mg/L)(8.34)(MGD)

or

Davidson Pie


Conversions

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Davidson Pie Method

• Gerald Davidson, Manager of the Clear

Lake Oaks, CA Water District

• California State University Manuals


Conversions

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Davidson Pie Method #1

lbs/day = (Concentration)(8.34)(Flow)

lbs/day = (mg/L)(8.34)(MGD)


Conversions

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Conversions

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Calculate the lbs/day needed for a dosage

of 3 mg/L and a flow of 0.75 MGD.


Conversions

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Conversions

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= 3 mg/L x 8.34 x 0.75 MGD

= 18.8 lbs/day


Conversions

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lbs = (Concentration)(8.34)(Volume)

lbs = (mg/L)(8.34)(MG)


Conversions

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lbs = (mg/L)(8.34)(MG)


Conversions

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Calculate the pounds needed for a dosage

of 50 mg/L for a tank that holds 2 million

gallons.


Conversions

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Conversions

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Pounds = (mg/L)(8.34)(MG)

= 50 mg/L x 8.34 x 2 MG

= 834 lbs


Conversions

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Davidson Pie Method

The beauty of the Davidson Pie

Method is how easy it is to use to

calculate mg/L.


Conversions

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Davidson Pie

What is the chlorine dose if you add

20 lbs/day to a flow of 1.5 MGD?


Conversions

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Davidson Pie


Conversions

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Davidson Pie

mg/L = lbs/day 8.34 MGD

= 20 lbs/day 8.34 1.5 MGD

= 1.6 mg/L


Conversions

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Davidson Pie Method

This works the same way for tanks!

Back to the Formula Sheet


Conversions

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Removal (Efficiency), %

(In - Out)(100%)

In

• Units

– mg/L or lbs/day

• Use

– Removal, pumps, motors


Conversions

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Slope

Drop or Rise x 100 Distance

• Units: ft/ft

– Decimals or %

• Uses:

– Pipe laying


Conversions

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Slope Drop or Rise x100

Distance

• Calculate the slope of a pipeline 300 feet long with a beginning elevation of 1200.00 and an ending elevation of 1197.00.

(1200.00-1197.00) x 100 300 ft

= 1% drop (or 0.01 decimal equivalent)


Conversions

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Velocity

Flow or Distance

Area Time

• Units: feet per second, fps, ft/sec

– Flow must be in cubic feet per second

– Area must be in square feet


Conversions

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Volume of Cone

(1/3)(.785)(Diameter2)(Height)

• Units: feet

• Height = SWD

• Hopper

Volume of a Cylinder

• (.785)(D2)(Height)

Cylinder:

–100 ft Height 2 ft Dia

–.785 x 2 x 2 x 100 = 314 cf


Conversions

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Conversions

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Volume of Cylinder

(.785)(Diameter2)(Height)

• Units: feet

• Height = SWD


Conversions

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Volume of Cylinder: Problem

• Problem

– The diameter is 40 ft and the height is 20 ft.

Calculate the volume of the cylinder.

• Formula


Conversions

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Volume of Cylinder: Formula

• The diameter is 40 ft and the height is 20

ft. Calculate the volume of the cylinder.

• Formula

Volume of Cylinder = (.785)(Diameter2)(Height)


Conversions

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Volume of Cylinder : Solution

• The diameter is 40 ft and the height is 20 ft.

Calculate the volume of the cylinder.

Volume of Cylinder = (.785)(Diameter2)(Height)

Area of Circle = (.785) (40 ft)2(20 ft)

= (.785)(40 ft)(40 ft) (20 ft)

= .785 x 1600 ft2 x 20 ft

= 25,120 ft3


Conversions

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Volume of Rectangle

(Length)(Width)(Height)

• Units: feet

• Height = SWD

S W D

ABC Formula/Conversion Table Volume of rectangle: L x W x ___ = ___ ___ Volume of circle: πr2 x __= ___ ___ OR (π/4)(Diameter2)(__)= ___ ___

ABC Formula/Conversion Table Volume of rectangle:

L x W x H = cu ft.

Volume of circle CYLINDER: πr2 x h= cu ft.

OR (π/4)(Diameter2)(h)= cu ft.


What is the volume of a rectangular tank if

the length is 50 feet, the width is 50 feet,

and the height is 10 ft.?

50 x 50 x 10 = 25,000


cu ft. (cf, ft3)

So the answer is 25,000 cu ft. (cf, ft3)


Conversions

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Volume of a Rectangle: Problem

• Problem

– The length of a tank is 12 feet, the width is 4

feet, and the height is 3 feet. Calculate the

volume of the tank.

• Formula


Conversions

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Volume of a Rectangle: Formula

• The length of a tank is 12 feet, the width is

4 feet, and the height is 3 feet. Calculate

the volume of the tank.

• Formula

Volume of Rectangle = (Length)(Width)(Height)


Conversions

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Volume of a Rectangle: Solution

• The length of a tank is 12 feet, the width is

4 feet, and the height is 3 feet. Calculate

the volume of the tank.

Volume of Rectangle = (Length)(Width)(Height)

= (12 ft)(4 ft)(3 ft)

= 144 ft3


What is the volume of a circular tank if

the diameter is 50 feet

and the height or length is 10 ft.?

0.785 x 502 x 10 = 19,625 (0.785 x 50 x 50 x 10)


cu ft. (cf, ft3)

So the answer is 19,625 cu ft. (cf, ft3)

ABC Formula/Conversion Table Good enough, but we may need to know how

many gallons these tanks hold

There are ____ gallons in ONE Cubic Foot?

There are 7.48 gallons in ONE Cubic Foot

ABC Formula/Conversion Table Good enough, but we may need to know how

many gallons these tanks hold


So, cu ft. x 7.48 = gallons of capacity

ABC Formula/Conversion Table If our tank has 25,000 cu ft. how many gallons

does it hold?


25,000 cu ft. x 7.48 = 187,000 gallons of capacity

ABC Formula/Conversion Table If our tank has 187,000 gallons of capacity, how

many millions of gallons of capacity does it have?

187,000/1,000,000 = 0.187 Million Gallons (MG)

ABC Formula/Conversion Table If our tank has 187,000 of capacity, how many

pounds (lbs) of capacity does it have?

There are ___ lbs in each gallon

There are 8.34 lbs in each gallon

187,000 gal x 8.34lbs/gal = 1,559,580 lbs

ABC Formula/Conversion Table If our tank has 187,000 of capacity, how many pounds (lbs) of GAS chlorine would we need to

achieve a concentration of 50 mg/l?

Are you ready for some pie?


Conversions 82 of 74

Convert Temperature

• Problem

– Calculate the temperature in Celsius for a water temperature of 4oC.

• Conversion


Conversions

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Convert Celsius to Fahrenheit

• Problem

– Calculate the temperature in Fahrenheit for a

water temperature of 4oC.

• Conversion


Conversions

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• Calculate the temperature in Fahrenheit

for a water temperature of 4oC.

• Conversion Degrees Fahrenheit = (Degrees Celsius) (9/5) + 32


Conversions

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• Calculate the temperature in Fahrenheit

for a water temperature of 4oC. Degrees Fahrenheit = (Degrees Celsius) (9/5) + 32

= (4oC)(9/5) + 32

= (4oC)(1.8) + 32

= 7.2 + 32

= 39.2oF


Conversions

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ABC Conversions

1 acre = 43,560 square feet

1 cubic foot = 7.48 gallons

1 foot = 0.305 meters

1 gallon = 3.79 liters


Conversions

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ABC Conversions

1 gallon = 8.34 pounds

1 grain per gallon = 17.1 mg/L

1 horsepower = 0.746 kilowatts


Conversions

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ABC Conversions

1 million gallons per day

= 694 gallons per minute

1 pound = 0.454 kilograms

1 pound per square inch

= 2.31 feet of water


Conversions

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ABC Conversions

Degrees Celsius = (Degrees Fahrenheit - 32) (5/9)

Degrees Fahrenheit = (Degrees Celsius) (9/5) + 32

1% = 10,000 mg/L


Conversions

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ABC Abbreviations

ft feet

gpd gallons per day

gpg grains per gallon


Conversions

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ABC Abbreviations

gpm gallons per minute

lbs pounds

mg/L milligrams per liter

MGD million gallons per day


Conversions

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ABC Abbreviations

mL milliliter


Conversions

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Review

• Generic formulas

– Listed alphabetically

• Must watch the units

– Can’t mix units

• Conversions and abbreviations


Conversions

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Summary

• Math can help you pass your certification

exams

• Math is important for your operations,

troubleshooting, reports, and records

• And your paycheck!


Conversions

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What to do before next session

• Practice some basic math on

your own (4-5 pipe math)

• REVIEW the SDWA Chart in

your CSUS book

• Take a break!


Conversions

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Conversions

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Math

Design flow= Population x Design Factor for

Flow

Population Equivalent (gpcd)= Flow (gpd)

Population

Drawdown (ft)=

Static Water Depth (ft) - Depth after Pumping (ft)

Specific Capacity (gpm/ft)= Flow (gpm)

Drawdown (ft)


Conversions

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Clear Wells, Storage Tanks, and

Reservoirs Math

Detention Time (hrs)=Capacity (gal) x 24 hrs/day

Flow (gpd)

Filling Time (min)=Capacity (gal)

Flow (gpm)

Filling Time with Inflow (min)=Capacity (gal)

Inflow (gpm) - Outflow (gpm)

Emptying Time with Inflow (min)=Capacity (gal)

Outflow (gpm) - Inflow (gpm)


Conversions

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Flushing

Flow (gpm)=

Pipe Area (sf) x Velocity (ft/sec) x 448 gpm/cfs

or Flow (gpm)=

Pipe Area (sf) x Velocity (ft/sec) x 7.48 gal/cf x

60 sec/min

Total Gallons Used=

Flow (gpm) x Flushing Time (min)

Math for Water Treatment Distribution Wastewater Treatment Docu… · • Do all the multiplication...

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