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VWEA Operations Challenge Roanoke, VA July 14, 2016
Basic Math Functions
• Addition & Multiplication– Order does not matter
– 2 x 3 or 3 x 2
• Subtraction & Division– Must be done in the order given
– Different order = different answer
– 5-3 = 2, but 3-5 = -2
– 8/4= 2, but 4/8 = 0.5
Wastewater Math
• Involves complex calculations– Based on basic math concepts
8.34)]mg/L?MGD(?8.34)mg/L?MGD[(?
8.34MG)?MG(?mg/L? X
21%,,,,,
Multiple Step Calculations
• Eliminate parentheses then brackets– Work “inside – out”
8.34)6(57)(66)(4
3,150]5.8)[(6,500
250.24224
3,150][37,700
250.266
40,850
368.7250.2618.9
Basic Concepts
.5050%50100= =
DecimalFractionPercent
Percent(%)
• Parts per 100 • Used in
• Expressing plant process performance• Solids treatment calculations
• Unless otherwise stated, convert percent to decimal percent BEFORE using in most wastewater treatment calculations.
Percent to Decimal
• Divide percent (%) by 100
0.50100
5050%
Decimal to Percent
• Move the decimal 2 places to the right and change the decimal to a % sign.
5 0%
Calculator Use
• Select based on needs• Read instructions• Practice using functions• Write down what you are
going to do– Start with small numbers– Do a piece at a time
Remember…
• Exam regulations DO NOT allow:– programmable
calculators
– calculators that have alpha-numeric keyboards
Problem Solving is easy if you follow these steps
Step 1:Understand
the problem
Step 1 - Understand the Problem
• The operator removes 5,400 gallons of sludge. The sludge contains 275 gallons of solids. What is the percent solids?
Percent Solids = ?
-Read the problem carefully-Identify what to solve
Problem Solving is easy if you follow these steps
Step 2:Decide how
you’re going to solve theproblem
• The operator removes 5,400 gallons of sludge. The sludge contains 275 gallons of solids. What is the percent solids?
Step 2 – How to Solve the Problem
Total = 5,400 Quantity =275
-Find the formula
Percent Solids = ?
Step 2 - How to solve the problem
Fill in the required data in the correct positions!
100xQuantity Total
QuantityMeasured%
-Write down the formula
Step 3:Solve The
Problem
Problem Solving is easy if you follow these steps
Step 3 - Solve the problem
% Solids = 0.0509 X 100
% Solids = 5.09 or 5.1%
% Solids =275 gallons
5,400 gallonsX 100
Problem Solving is easy if you follow these steps
Step 4:Double-Check
Your Work
Determining Percent
• Example– Sludge volume = 5,400 gal
– Solids volume = 275 gal
5.1%or%5.09Solids%
100xgal5,400
gal275Solids%
What a % Equals
PercentDecimalxTotalQuantityMeasured
• Given:– %
– Total
• What quantity does the % equal
What does it Equal?
• Example:– Sludge volume = 5,400 gal
– Percent Solids = 5.1%
Quantity = 5,400 gallonsx 0.051
= 275.4 gallons
Determining the Total
• Given– Percent
– What the percent equals
• Find the total
%Decimal
QuantityMeasuredTotal
What is the Total?
• Example:– 275 gallons of solids
– Percent Solids = 5.1%
Total, gallons =275.4 gallons
0.051
= 5,400 gallons
Circumference, Area, Volume
Plants are made up of tanks and channels
It will be necessary to calculate
14163Π
A constant Used for:
Circles Cylinders Cones Spheres
Needed when calculating Circumference Area Volume
Not This
(Pie)
Distance around an object
Expressed in linear units
Circumference & Perimeter
Circumference of a Circle
Diameter
DiameterxΠC
80 ft
ft251ft80x3.1416C
Circumference of a Circle Example
Perimeter of a Rectangle or Square
LW
)Wx2()Lx2(Perimeter
Length & width must be same units
Rectangle PerimeterExample
L =90 ft
W = 45 ft
ft270
ft452ft902Perimeter
The surface of an object
Measured in square units
Requires 2 dimensions
Area
Area of a Circle
DiameterDiameter4
ΠA
Diameter
0.7854
3.1416
Calculation Shortcut
For area & volume calculations
Area of a CircleExample
2ft9,499
ft110ft110x0.785A
110 ft
WxLA
Area –Rectangle/Square
Length & width must be same units!
LW
2ft5,175
ft45ft115A
Rectangle AreaExample
L=115 ft
W=45 ft
How much an object will hold
Measured in cubic units
Uses 3 dimensions
Volume
Volume of a Cylinder
depthxDiameterxDiameterx0.785
depthDiameterDiameter4
3.1416Volume
Cylinder VolumeExample
3
2
ft141,693
ft20ft95ft950.785
dxDx0.785Volume
Depth = 20 ft
Diameter =95 ft
Volume of aRectangular Tank
depthxWidthxLengthVolume
Length, width & depth must be same units!
W
L
d
Rectangle VolumeExample
3ft148,500
ft22ft45ft150
depthxWidthxLengthVolume
45 ft
150 ft
22 ft
Conversion Factors
• Type 1 - Conversion from one unit to another– Feet to inches
– Gallons to pounds
– Cubic feet to gallons
• Type 2 - Conversion to metric system– Gallons to liters
– Pounds to grams
Basic Conversions
• Conversion by multiplying or dividing by a conversion factor– Feet x 12 inches/foot
– Gallons x 8.34 lbs./gal
Reference Chart Handout
Back PageLeft Column to Right Column
Multiply
Right Column to Left ColumnDivide
Cubic Feet to Gallons
From chart:
Cubic Feet 7.48 Gallons
Gallons = Cubic Feet x 7.48 gal/ft3
Example
How many gallons of sludge can be pumped to a digester with 3,240 cubic feet of volume available?
3,240 ft3x 7.48 gal/ft3
=24,235 gallons
Type equation here.
Gallons to Cubic Feet
From chart:
Cubic Feet 7.48 Gallons
Cubic feet = Gallons7.48 gal/ft3
Example
• How many cubic feet of sludge are removed when 15,500 gallons are withdrawn?
Cubic feet = 15,500 gallons7.48 gal/ft3
= 2,072 ft3
Gallons to Pounds
From chart:
Gallon 8.34 Pounds
Pounds = Gallons x 8.34 lbs/gallon
Example
If 1,235 gallons of solids are removed from the primary settling tank, how many pounds of solids are removed?
Pounds = 1,235 gallons x 8.34 lbs/gallon
= 10,300 pounds
Pounds to gallons
From chart:
Gallon 8.34 Pounds
Gallons = pounds
8.34 pounds/gallon
Example
• How many gallons of water are required to fill a tank which holds 6,458 pounds of water?
Gallons = 6,458 lbs
8.34 pounds/gallons
= 774 gallons
Liters to Gallons
Gallons 3.785 Liters
From the chart:
Gallons = Liters
3.785 L/gallon
Example
Convert 231,500 liters to gallons
Gallons = 231,500 Liters3.785 L/gallon
= 61,163 gallons
Flow Rates
• Use conversion chart
• Million Gallons per Day (MGD)– Gallons per day (gpd)
– Gallons per hour (gph)
– Gallons per minute (gpm)
– Cubic feet per second (cfs)
– Liters per second (Lps)
– Cubic meters per day (m3/day)
cfs to MGD
From the table:
MGD 1.55 Cubic feet/second
MGD =Flow, CFS
1.55 cfs/MG
Example
The flow in a channel is 3.45 cfs. What is the flow rate in MGD?
MGD =3.45 cfs
1.55 cfs/MG
= 2.23 MGD
MGD to cfs
From the table:
MGD 1.55 Cubic feet/second
cfs = MGD x 1.55 cfs/MGD
Example
The flow entering the grit channel is 2.95 MGD. What is the flow rate in cubic feet per second?
2.95 MGD x 1.55 cfs/MGD
= 4.57 cfs
MGD to gpd
From the chart:
MGD 1,000,000 Gallons
gpd = MGD x 1,000,000 gallons/MG
Example
The flow meter reads 27.5 MGD. What is the flow in gallons per day?
gpd = 27.5 MGD x 1,000,000 gallons/MG
= 27,5000,000 gpd
gpd to MGD
From the chart:
MGD 1,000,000 Gallons
MGD =Flow, gpd
1,000,000 gallons/MGD
Example
The return pump flow meter reads 45, 700 gallons per day. What is the current flow rate in million gallons per day?
MGD =45,700 gpd
1,000,000 gallons/MGD
= 0.0457 MGD
MGD to gpm
• Two steps– Convert million gallons to gallons
(x 1,000,000)
– Convert days to minutes (/1,440)
gpm =MGD x 1,000,000 gallons/MG
1,440 minutes per day
Example
The current pump rate is 2.65 MGD. What is the flow rate in gallons per minute?
Step 1:Million gallons per day must be converted to gallons per day
Flow, gpd = 2.65 MGD x 1,000,000 = 2,650,000 gpd
Example
Flow, gpm =2,650,000 gallons per day
1,440 minutes per day
= 1,841 gallons per minute
Step 2:Divide gallons per day by 1,440 minutes/day
gpm to MGD
• Two steps– Convert gallons/minute to gallons/day
(x 1,440)
– Convert gallons to million gallons (/1,000,000)
MGD =gpm x 1,440 minutes per day
1,000,000 gal/MG
Example
The current flow is 1,259 gpm. What is the flow in million gallons per day?
MGD =1,259 gpm x 1,440 minutes per day
1,000,000 gal/MG
= 1.81 MGD
Complex Conversions
• Using weight, concentration & flow
• Two or more measurements
• One or more conversion factors
• Can be rearranged to solve for any of the measured items
Davidson Pie• Think “inside the circle”
lbs./ lbs. per day
8.34
lbs/gallon
Vol./MGD mg/L
Pounds
• Numbers in bottom half are multiplied
Pounds
8.34
lbs/gallon
Volume, MG mg/L
Pounds Example
• Volume = 0.9 MG
• MLSS= 2,580 mg/L
• Pounds = ?
? pounds
8.34 lbs/gallon
0.9 MG 2,580mg/L
19,366 pounds
Pounds = 2,580 mg/L x 0.90 MG x 8.34= 19,366 lbs
Pounds/day
• Numbers in bottom half are multiplied
lbs per day
8.34 lbs/gallon
MGD mg/L
Pounds/day Example
• Flow = 6 MGD
• Inf. TSS = 260 mg/L
• lbs./day = ?
? lbs per day
8.34 lbs/gallon
MGD mg/L6 MGD 260mg/L
13,010 lbs/day
6.0 MGD x 8.34 lbs./gallon x 260 mg/L=13,010.4 lbs/day
MG or MGD or mg/L
• If lbs./lbs. per day is known
• Multiply bottom numbers together
• Divide into top half
lbs./lbs. per day
8.34 lbs/gallon
MG OR MGD mg/L
Pounds to mg/L
• Quantity, lbs. = 3,529
• Volume = 0.25
• MLSS, mg/L= ?
lbs
8.34
lbs./gallon
MGD ? mg/L0.25 MG 1,693mg/L
3,529 Pounds
Conc., mg/L =3,529 lbs
0.25 MG x 8.34= 1,693 mg/L
Pounds/day to MGD
• Inf. BOD = 186 mg/L
• BOD, lbs/day = 8,956
• Flow = ? MGD
lbs per day
8.34 lbs/gallon
? MGD mg/L186mg/L
8,956 lbs/day
5.77MGD
8,956 lbs/day186 mg/L x 8.34
= 5.77 MGD
• Read the question
• Choose the right formula
• Make necessary conversions
• Double check work
• And relax…
In Review
Any Questions?
DEQ, Operator Training Copyright 2016
