VWEA Operations Challenge Roanoke, VA July 14, 2016

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1 VWEA Operations Challenge Roanoke, VA July 14, 2016

2 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

3 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)]

4 Multiple Step Calculations Eliminate parentheses then brackets Work inside out [(6, ) 3,150] (4 6) (6 7) [37,700 3,150] , ( )

5 Basic Concepts Percent Fraction Decimal 50% 50 = 100 =.50

6 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.

7 Percent to Decimal Divide percent (%) by %

8 Decimal to Percent Move the decimal 2 places to the right and change the decimal to a % sign. 5 0%

9 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

10 Remember Exam regulations DO NOT allow: programmable calculators calculators that have alpha-numeric keyboards

12 Problem Solving is easy if you follow these steps Step 1: Understand the problem

13 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 =?

14 Problem Solving is easy if you follow these steps Step 2: Decide how you re going to solve the problem

15 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 =?

16 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!

17 Problem Solving is easy if you follow these steps Step 3: Solve The Problem

18 Step 3 - Solve the problem % Solids = 275 gallons 5,400 gallons X 100 % Solids = X 100 % Solids = 5.09 or 5.1%

20 Problem Solving is easy if you follow these steps Step 4: Double-Check Your Work

21 Determining Percent Example Sludge volume = 5,400 gal Solids volume = 275 gal %Solids 275gal 5,400gal x 100 %Solids 5.09% or 5.1%

22 What a % Equals Given: % Total What quantity does the % equal Measured Quantity Total x Decimal Percent

23 What does it Equal? Example: Sludge volume = 5,400 gal Percent Solids = 5.1% Quantity = 5,400 gallonsx = gallons

24 Determining the Total Given Percent What the percent equals Find the total Total Measured Quantity Decimal %

25 What is the Total? Example: 275 gallons of solids Percent Solids = 5.1% Total, gallons = gallons = 5,400 gallons

26 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

27 (Pie) Π A constant Used for: Circles Cylinders Cones Spheres Needed when calculating Circumference Area Volume Not This

28 Circumference & Perimeter Distance around an object Expressed in linear units

29 Circumference of a Circle Diameter C Π x Diameter

30 Circumference of a Circle Example 80 ft C x 80 ft 251 ft

31 Perimeter of a Rectangle or Square W L Perimeter (2 x L) ( 2 x W) Length & width must be same units

32 Rectangle Perimeter Example L =90 ft W = 45 ft Perimeter 2 90 ft 2 45 ft 270 ft

33 Area The surface of an object Measured in square units Requires 2 dimensions

34 Area of a Circle Diameter A Π 4 Diameter Diameter

35 Calculation Shortcut For area & volume calculations

36 Area of a Circle Example 110 ft A x 110 ft 110 ft 2 9,499 ft

37 Area Rectangle/Square W L A L x W Length & width must be same units!

38 Rectangle Area Example W=45 ft L=115 ft A 115 ft 2 5,175 ft 45 ft

39 Volume How much an object will hold Measured in cubic units Uses 3 dimensions

40 Volume of a Cylinder Volume Diameter Diameter depth x Diameter x Diameter x depth

41 Cylinder Volume Example Depth = 20 ft Diameter =95 ft Volume x D ft 95 ft 20 ft 141,693 ft 3 x d

42 Volume of a Rectangular Tank W d L Volume Length x Width x depth Length, width & depth must be same units!

43 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

44 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

45 Basic Conversions Conversion by multiplying or dividing by a conversion factor Feet x 12 inches/foot Gallons x 8.34 lbs./gal

46 Reference Chart Handout Back Page Left Column to Right Column Multiply Right Column to Left Column Divide

47 Cubic Feet to Gallons From chart: Cubic Feet 7.48 Gallons Gallons = Cubic Feet x 7.48 gal/ft 3

48 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

49 From chart: Gallons to Cubic Feet Cubic Feet 7.48 Gallons Cubic feet = Gallons 7.48 gal/ft 3

50 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

51 Gallons to Pounds From chart: Gallon 8.34 Pounds Pounds = Gallons x 8.34 lbs/gallon

52 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

53 Pounds to gallons From chart: Gallon 8.34 Pounds Gallons = pounds 8.34 pounds/gallon

54 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

55 Liters to Gallons From the chart: Gallons Liters Gallons = Liters L/gallon

56 Example Convert 231,500 liters to gallons Gallons = 231,500 Liters L/gallon = 61,163 gallons

57 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)

58 cfs to MGD From the table: MGD 1.55 Cubic feet/second MGD = Flow, CFS 1.55 cfs/mg

59 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

60 MGD to cfs From the table: MGD 1.55 Cubic feet/second cfs = MGD x 1.55 cfs/mgd

61 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

62 MGD to gpd From the chart: MGD 1,000,000 Gallons gpd = MGD x 1,000,000 gallons/mg

63 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

64 gpd to MGD From the chart: MGD 1,000,000 Gallons MGD = Flow, gpd 1,000,000 gallons/mgd

65 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 = MGD

66 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

67 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

68 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

69 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

70 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

71 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

72 Davidson Pie Think inside the circle lbs./ lbs. per day Vol./MGD mg/l 8.34 lbs/gallon

73 Pounds Pounds Volume, MG 8.34 lbs/gallon mg/l Numbers in bottom half are multiplied

74 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

75 Pounds/day lbs per day MGD 8.34 lbs/gallon mg/l Numbers in bottom half are multiplied

76 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

77 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

78 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

79 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

80 In Review Read the question Choose the right formula Make necessary conversions Double check work And relax

Water Utility Science Water Math and Hydraulics 050. Name: Date:

Water Utility Science Water Math and Hydraulics 050 Name: Date: Note: Please show all of your calculations for each problem no matter how simple the problem may seem. Please use the accompanying pieces