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TRANSCRIPT
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?
1/17/2013 Wk 5c Math Pt2 DMACC2012
Disease-causing bacteria are
known as A. Coliforms
B. Non-coliforms
C. Non-pathogenic
D. Pathogenic
1/17/2013 Wk 5c Math Pt2 DMACC2012
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
1/17/2013 Wk 5c Math Pt2 DMACC2012
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
1/17/2013 Wk 5c Math Pt2 DMACC2012
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
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Agenda & Objectives
• Math Primer & review
• ABC Formula/Conversion Table
• Practice Solving Problems
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Let’s look at some tools you
have
• AceOps Web Page www.aceops.org
• ABC Formula/Conversion Table
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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
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ABC Formula/Conversion Table
Combines formulas, conversions, and
abbreviations for:
Water Treatment
Distribution
Lab
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Units Are the Key!!! • ABC formulas are generic
• Must watch the units
• Can’t mix units
• Can’t mix 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)
ABC Formula/Conversion Table Let’s give it another try…
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)
And what unit of measure will the result be in?
sq. ft. (sf, ft2)
So the answer is 1,256 sq. ft. (sf, sf2)
ABC Formula/Conversion Table Let’s give it another try…
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)
So the answer is 1,256 sq. ft. (sf, sf2)
ABC Formula/Conversion Table Let’s give it another try…
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)
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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
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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.
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Area of Rectangle
(Length)(Width)
• Units
– Sq in, sq ft, acres, sq miles
– in2, ft2
• Use
– Pressure (psi), loading rates
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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.
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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)
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Area of a Rectangle: Solution
• The length of a tank is 10 feet and the
width is 5 feet. Calculate the area of the
tank.
Area of Rectangle = (Length)(Width)
= (10 ft)(5 ft)
= 50 ft2
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Area of a Rectangle:
Calculate these… 1. The length of a tank is 20 feet and the
width is 10 feet. Calculate the area of the
tank.
2. The length of a tank is 40 feet and the
width is 10 feet. Calculate the area of the
tank.
3. The length of a tank is 50 feet and the
width is 20 feet. Calculate the area of the
tank.
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Circumference of Circle
(3.14)(Diameter)
• Units
– ft
• Use
– Loading rates
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Circumference of Circle
The tank is 10 feet in diameter, what is the
circumference?
(3.14)(Diameter)
(3.14)(10) = 31.4 feet
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Circumference of Circle
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?
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Detention Time
Volume
Flow
• Volume
– cubic feet or gallons
• Flow
– cfs, cfm, gpm, gpd, mgd
• Use
– Loadings
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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
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Detention Time:
Calculate these… The volume of a tank is 100,000 gallons and
the flow is 100,000 gallons per day (gpd).
The volume of a tank is 200,000 gallons and
the flow is 100,000 gallons per day (gpd).
The volume of a tank is 1,000,000 gallons
and the flow is 100,000 gallons per day
(gpd).
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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)
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Mass or Dosage, lbs or lbs/day
(mg/L)(8.34)(MGD)
or
Davidson Pie
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Davidson Pie Method
• Gerald Davidson, Manager of the Clear
Lake Oaks, CA Water District
• California State University Manuals
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Davidson Pie Method #1
lbs/day = (Concentration)(8.34)(Flow)
lbs/day = (mg/L)(8.34)(MGD)
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Davidson Pie Method #1
lbs/day = (mg/L)(8.34)(MGD)
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Davidson Pie Method #1
Calculate the lbs/day needed for a dosage
of 3 mg/L and a flow of 0.75 MGD.
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Davidson Pie Method #1
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Davidson Pie Method #1
lbs/day = (mg/L)(8.34)(MGD)
= 3 mg/L x 8.34 x 0.75 MGD
= 18.8 lbs/day
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Davidson Pie Method #2
lbs = (Concentration)(8.34)(Volume)
lbs = (mg/L)(8.34)(MG)
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Davidson Pie Method #2
lbs = (mg/L)(8.34)(MG)
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Davidson Pie Method #2
Calculate the pounds needed for a dosage
of 50 mg/L for a tank that holds 2 million
gallons.
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Davidson Pie Method #2
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Davidson Pie Method #2
Pounds = (mg/L)(8.34)(MG)
= 50 mg/L x 8.34 x 2 MG
= 834 lbs
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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.
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Davidson Pie
What is the chlorine dose if you add
20 lbs/day to a flow of 1.5 MGD?
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Davidson Pie
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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
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Davidson Pie Method
This works the same way for tanks!
Back to the Formula Sheet
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Removal (Efficiency), %
(In - Out)(100%)
In
• Units
– mg/L or lbs/day
• Use
– Removal, pumps, motors
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Slope
Drop or Rise x 100 Distance
• Units: ft/ft
– Decimals or %
• Uses:
– Pipe laying
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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)
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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
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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
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Volume of Cylinder
(.785)(Diameter2)(Height)
• Units: feet
• Height = SWD
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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
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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)
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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
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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.
ABC Formula/Conversion Table Let’s give it another try…
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
And what unit of measure will the result be in?
cu ft. (cf, ft3)
So the answer is 25,000 cu ft. (cf, ft3)
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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
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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)
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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
ABC Formula/Conversion Table Let’s give it another try…
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)
And what unit of measure will the result be in?
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
There are 7.48 gallons in ONE Cubic Foot
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?
There are 7.48 gallons in ONE Cubic Foot
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?
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Convert Temperature
• Problem
– Calculate the temperature in Celsius for a water temperature of 4oC.
• Conversion
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Convert Celsius to Fahrenheit
• Problem
– Calculate the temperature in Fahrenheit for a
water temperature of 4oC.
• Conversion
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Convert Celsius to Fahrenheit
• Calculate the temperature in Fahrenheit
for a water temperature of 4oC.
• Conversion Degrees Fahrenheit = (Degrees Celsius) (9/5) + 32
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Convert Celsius to Fahrenheit
• 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
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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
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ABC Conversions
1 gallon = 8.34 pounds
1 grain per gallon = 17.1 mg/L
1 horsepower = 0.746 kilowatts
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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
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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
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ABC Abbreviations
ft feet
gpd gallons per day
gpg grains per gallon
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ABC Abbreviations
gpm gallons per minute
lbs pounds
mg/L milligrams per liter
MGD million gallons per day
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ABC Abbreviations
mL milliliter
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Review
• Generic formulas
– Listed alphabetically
• Must watch the units
– Can’t mix units
• Conversions and abbreviations
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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!
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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!
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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)
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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)
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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)