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,,,, %, 1 2 X [(? MGD? mg/l? mg/l (? MG? MG) 8.34) (? MGD 8.34? mg/l 8.34)]
Multiple Step Calculations Eliminate parentheses then brackets Work inside out [(6,500 5.8) 3,150] (4 6) (6 7) [37,700 3,150] 24 42 40,850 250.2 66 618.9 250.2 368.7 250.2 (5 6 8.34)
Basic Concepts Percent Fraction Decimal 50% 50 = 100 =.50
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 50 50% 100 0.50
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 -Read the problem carefully -Identify what to solve The operator removes 5,400 gallons of sludge. The sludge contains 275 gallons of solids. What is the percent solids? Percent Solids =?
Problem Solving is easy if you follow these steps Step 2: Decide how you re going to solve the problem
Step 2 How to Solve the Problem -Find the formula The operator removes 5,400 gallons of sludge. The sludge contains 275 gallons of solids. What is the percent solids? Total = 5,400 Quantity =275 Percent Solids =?
Step 2 - How to solve the problem -Write down the formula % Measured Quantity Total Quantity x100 Fill in the required data in the correct positions!
Problem Solving is easy if you follow these steps Step 3: Solve The Problem
Step 3 - Solve the problem % Solids = 275 gallons 5,400 gallons X 100 % Solids = 0.0509 X 100 % Solids = 5.09 or 5.1%
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 %Solids 275gal 5,400gal x 100 %Solids 5.09% or 5.1%
What a % Equals Given: % Total What quantity does the % equal Measured Quantity Total x Decimal Percent
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 Total Measured Quantity Decimal %
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
(Pie) Π 3 1416 A constant Used for: Circles Cylinders Cones Spheres Needed when calculating Circumference Area Volume Not This
Circumference & Perimeter Distance around an object Expressed in linear units
Circumference of a Circle Diameter C Π x Diameter
Circumference of a Circle Example 80 ft C 3.1416 x 80 ft 251 ft
Perimeter of a Rectangle or Square W L Perimeter (2 x L) ( 2 x W) Length & width must be same units
Rectangle Perimeter Example L =90 ft W = 45 ft Perimeter 2 90 ft 2 45 ft 270 ft
Area The surface of an object Measured in square units Requires 2 dimensions
Area of a Circle Diameter A Π 4 Diameter Diameter
Calculation Shortcut For area & volume calculations 3.1416 4 0.785
Area of a Circle Example 110 ft A 0.785 x 110 ft 110 ft 2 9,499 ft
Area Rectangle/Square W L A L x W Length & width must be same units!
Rectangle Area Example W=45 ft L=115 ft A 115 ft 2 5,175 ft 45 ft
Volume How much an object will hold Measured in cubic units Uses 3 dimensions
Volume of a Cylinder Volume 3.1416 Diameter Diameter depth 4 0.785 x Diameter x Diameter x depth
Cylinder Volume Example Depth = 20 ft Diameter =95 ft Volume 0.785 x D 2 0.785 95 ft 95 ft 20 ft 141,693 ft 3 x d
Volume of a Rectangular Tank W d L Volume Length x Width x depth Length, width & depth must be same units!
Rectangle Volume Example 45 ft 22 ft 150 ft Volume Length x Width x depth 150 ft 45 ft 22 ft 3 148,500 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 Page Left Column to Right Column Multiply Right Column to Left Column Divide
Cubic Feet to Gallons From chart: Cubic Feet 7.48 Gallons Gallons = Cubic Feet x 7.48 gal/ft 3
Example How many gallons of sludge can be pumped to a digester with 3,240 cubic feet of volume Type equation here. available? 3,240 ft 3 x 7.48 gal/ft 3 =24,235 gallons
From chart: Gallons to Cubic Feet Cubic Feet 7.48 Gallons Cubic feet = Gallons 7.48 gal/ft 3
Example How many cubic feet of sludge are removed when 15,500 gallons are withdrawn? Cubic feet = 15,500 gallons 7.48 gal/ft 3 = 2,072 ft 3
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 From the chart: Gallons 3.785 Liters Gallons = Liters 3.785 L/gallon
Example Convert 231,500 liters to gallons Gallons = 231,500 Liters 3.785 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 (m 3 /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 Step 2: Divide gallons per day by 1,440 minutes/day Flow, gpm = 2,650,000 gallons per day 1,440 minutes per day = 1,841 gallons per minute
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 Vol./MGD mg/l 8.34 lbs/gallon
Pounds Pounds Volume, MG 8.34 lbs/gallon mg/l Numbers in bottom half are multiplied
Pounds Example Volume = 0.9 MG MLSS= 2,580 mg/l Pounds =?? pounds 19,366 pounds 0.9 MG 2,580mg/L 8.34 lbs/gallon Pounds = 2,580 mg/l x 0.90 MG x 8.34 = 19,366 lbs
Pounds/day lbs per day MGD 8.34 lbs/gallon mg/l Numbers in bottom half are multiplied
Pounds/day Example Flow = 6 MGD Inf. TSS = 260 mg/l lbs./day =?? lbs per day 13,010 lbs/day 6 MGD 260mg/L MGD 8.34 lbs/gallon mg/l 6.0 MGD x 8.34 lbs./gallon x 260 mg/l =13,010.4 lbs/day
MG or MGD or mg/l lbs./lbs. per day MG OR MGD mg/l 8.34 lbs/gallon If lbs./lbs. per day is known Multiply bottom numbers together Divide into top half
Pounds to mg/l Quantity, lbs. = 3,529 Volume = 0.25 MLSS, mg/l=? lbs 3,529 Pounds 0.25 MGD 1,693mg/L? 8.34 lbs./gallon 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 8,956 lbs/day 5.77MGD? 186mg/L 8.34 lbs/gallon 8,956 lbs/day 186 mg/l x 8.34 = 5.77 MGD
In Review Read the question Choose the right formula Make necessary conversions Double check work And relax
Any Questions? DEQ, Operator Training Copyright 2016