WAT305 Math Part 1 ABC Math
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1 WAT305 Math Part 1 ABC Math
2 Good to know for certification: You have used lb 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
3 Disease-causing bacteria are known as A. Coliforms B. Non-coliforms C. Non-pathogenic D. Pathogenic 1/17/2013 Wk 5c Math Pt2 DMACC2012
4 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
5 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
6 After all chlorine demands have been met, what is the remaining chlorine called? A. Breakpoint B. Differential C. Potential D. Residual 1/17/2013 Wk 5c Math Pt2 DMACC2012
7 Adapted from Math for Water Distribution Steve Moehlmann Phil Koundakjian Mark Simms
8 Agenda & Objectives Math Primer & review ABC Formula/Conversion Table Practice Solving Problems 1/17/2013 WAT 305 WD ABC Formulas and 8 of 74
9 Let s look at some tools you have AceOps Web Page ABC Formula/Conversion Table 1/17/2013 WAT 305 WD ABC Formulas and 9 of 74
10 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 1/17/2013 WAT 305 WD ABC Formulas and 10 of 74
11 ABC Formula/Conversion Table Combines formulas, conversions, and abbreviations for: Water Treatment Distribution Lab 1/17/2013 WAT 305 WD ABC Formulas and 11 of 74
12 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 1/17/2013 WAT 305 WD ABC Formulas and 12 of 74
13 Area: ABC Formula/Conversion Table [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.
14 ABC Formula/Conversion Table Area of rectangle: L x W = Area of circle: πr 2 = OR (π/4)(diameter 2 )=
15 ABC Formula/Conversion Table 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)
16 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, ft 2 ) So the answer is 40 sq. ft. (sf, sf 2 )
17 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, ft 2 ) So the answer is 3,200 sq. ft. (sf, sf 2 )
18 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 π20 2 = 1,256 (3.14 x 20 x 20) And what unit of measure will the result be in? sq. ft. (sf, ft 2 ) So the answer is 1,256 sq. ft. (sf, sf 2 )
19 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 x D x 40 2 = 1,256 (0.785 x 40 x 40) And what unit of measure will the result be in? sq. ft. (sf, ft 2 ) So the answer is 1,256 sq. ft. (sf, sf 2 )
20 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 x D x 50 2 = 1,962.5 (0.785 x 50 x 50) And what unit of measure will the result be in? sq. ft. (sf, ft 2 ) So the answer is 1,962.5 sq. ft. (sf, sf 2 )
21 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)
22 Area of Circle (.785) (Diameter 2 ) or (P)(Radius 2 ) Units Sq in, sq ft, acres, sq miles in 2, ft 2 Use Pressure (psi), loading rates, velocity 1/17/2013 WAT 305 WD ABC Formulas and 22 of 74
23 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. 1/17/2013 WAT 305 WD ABC Formulas and 23 of 74
24 Area of Rectangle (Length)(Width) Units Sq in, sq ft, acres, sq miles in 2, ft 2 Use Pressure (psi), loading rates 1/17/2013 WAT 305 WD ABC Formulas and 25 of 74
25 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. 1/17/2013 WAT 305 WD ABC Formulas and 26 of 74
26 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) 1/17/2013 WAT 305 WD ABC Formulas and 27 of 74
27 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 ft 2 1/17/2013 WAT 305 WD ABC Formulas and 28 of 74
28 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. 1/17/2013 WAT 305 WD ABC Formulas and 29 of 74
29 Circumference of Circle (3.14)(Diameter) Units ft Use Loading rates 1/17/2013 WAT 305 WD ABC Formulas and 30 of 74
30 Circumference of Circle The tank is 10 feet in diameter, what is the circumference? (3.14)(Diameter) (3.14)(10) = 31.4 feet 1/17/2013 WAT 305 WD ABC Formulas and 31 of 74
31 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? 1/17/2013 WAT 305 WD ABC Formulas and 32 of 74
32 Volume Detention Time cubic feet or gallons Flow Volume Flow cfs, cfm, gpm, gpd, mgd Use Loadings 1/17/2013 WAT 305 WD ABC Formulas and 33 of 74
33 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 = 1 day 1/17/2013 WAT 305 WD ABC Formulas and 34 of 74
34 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). 1/17/2013 WAT 305 WD ABC Formulas and 35 of 74
35 Leakage Volume Volume Time cubic feet or gallons or million gallons Time Seconds, minutes, hours, days Use Loadings 1/17/2013 WAT 305 WD ABC Formulas and 36 of 74
36 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?
37 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)
38 Mass or Dosage, lbs or lbs/day (mg/l)(8.34)(mgd) or Davidson Pie 1/17/2013 WAT 305 WD ABC Formulas and 39 of 74
39 Davidson Pie Method Gerald Davidson, Manager of the Clear Lake Oaks, CA Water District California State University Manuals 1/17/2013 WAT 305 WD ABC Formulas and 40 of 74
40 Davidson Pie Method #1 lbs/day = (Concentration)(8.34)(Flow) lbs/day = (mg/l)(8.34)(mgd) 1/17/2013 WAT 305 WD ABC Formulas and 41 of 74
41 Davidson Pie Method #1 lbs/day = (mg/l)(8.34)(mgd) 1/17/2013 WAT 305 WD ABC Formulas and 42 of 74
42 Davidson Pie Method #1 Calculate the lbs/day needed for a dosage of 3 mg/l and a flow of 0.75 MGD. 1/17/2013 WAT 305 WD ABC Formulas and 43 of 74
43 Davidson Pie Method #1 1/17/2013 WAT 305 WD ABC Formulas and 44 of 74
44 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 1/17/2013 WAT 305 WD ABC Formulas and 45 of 74
45 Davidson Pie Method #2 lbs = (Concentration)(8.34)(Volume) lbs = (mg/l)(8.34)(mg) 1/17/2013 WAT 305 WD ABC Formulas and 46 of 74
46 Davidson Pie Method #2 lbs = (mg/l)(8.34)(mg) 1/17/2013 WAT 305 WD ABC Formulas and 47 of 74
47 Davidson Pie Method #2 Calculate the pounds needed for a dosage of 50 mg/l for a tank that holds 2 million gallons. 1/17/2013 WAT 305 WD ABC Formulas and 48 of 74
48 Davidson Pie Method #2 1/17/2013 WAT 305 WD ABC Formulas and 49 of 74
49 Davidson Pie Method #2 Pounds = (mg/l)(8.34)(mg) = 50 mg/l x 8.34 x 2 MG = 834 lbs 1/17/2013 WAT 305 WD ABC Formulas and 50 of 74
50 Davidson Pie Method The beauty of the Davidson Pie Method is how easy it is to use to calculate mg/l. 1/17/2013 WAT 305 WD ABC Formulas and 51 of 74
51 Davidson Pie What is the chlorine dose if you add 20 lbs/day to a flow of 1.5 MGD? 1/17/2013 WAT 305 WD ABC Formulas and 52 of 74
52 Davidson Pie 1/17/2013 WAT 305 WD ABC Formulas and 53 of 74
53 Davidson Pie mg/l = lbs/day 8.34 MGD = 20 lbs/day MGD = 1.6 mg/l 1/17/2013 WAT 305 WD ABC Formulas and 54 of 74
54 Davidson Pie Method This works the same way for tanks! 1/17/2013 WAT 305 WD ABC Formulas and 55 of 74
55 Back to the Formula Sheet
56 Removal (Efficiency), % Units mg/l or lbs/day Use (In - Out)(100%) In Removal, pumps, motors 1/17/2013 WAT 305 WD ABC Formulas and 57 of 74
57 Slope Units: ft/ft Decimals or % Uses: Pipe laying Drop or Rise x 100 Distance 1/17/2013 WAT 305 WD ABC Formulas and 58 of 74
58 Slope Drop or Rise x100 Distance Calculate the slope of a pipeline 300 feet long with a beginning elevation of and an ending elevation of ( ) x ft = 1% drop (or 0.01 decimal equivalent) 1/17/2013 WAT 305 WD ABC Formulas and 59 of 74
59 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 1/17/2013 WAT 305 WD ABC Formulas and 61 of 74
60 Volume of Cone (1/3)(.785)(Diameter 2 )(Height) Units: feet Height = SWD Hopper 1/17/2013 WAT 305 WD ABC Formulas and 62 of 74
61 Volume of a Cylinder (.785)(D 2 )(Height) Cylinder: 100 ft Height 2 ft Dia.785 x 2 x 2 x 100 = 314 cf 1/17/2013 WAT 305 WD ABC Formulas and 63 of 74
62 Volume of Cylinder (.785)(Diameter 2 )(Height) Units: feet Height = SWD 1/17/2013 WAT 305 WD ABC Formulas and 64 of 74
63 Volume of Cylinder: Problem Problem The diameter is 40 ft and the height is 20 ft. Calculate the volume of the cylinder. Formula 1/17/2013 WAT 305 WD ABC Formulas and 65 of 74
64 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)(Diameter 2 )(Height) 1/17/2013 WAT 305 WD ABC Formulas and 66 of 74
65 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)(Diameter 2 )(Height) Area of Circle = (.785) (40 ft) 2 (20 ft) = (.785)(40 ft)(40 ft) (20 ft) =.785 x 1600 ft 2 x 20 ft = 25,120 ft 3 1/17/2013 WAT 305 WD ABC Formulas and 67 of 74
66 Volume of Rectangle (Length)(Width)(Height) Units: feet Height = SWD S W D 1/17/2013 WAT 305 WD ABC Formulas and 68 of 74
67 ABC Formula/Conversion Table Volume of rectangle: L x W x = Volume of circle: πr 2 x = OR (π/4)(diameter 2 )( )=
68 ABC Formula/Conversion Table Volume of rectangle: L x W x H = cu ft. Volume of circle CYLINDER: πr 2 x h= cu ft. OR (π/4)(diameter 2 )(h)= cu ft.
69 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, ft 3 ) So the answer is 25,000 cu ft. (cf, ft 3 )
70 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 1/17/2013 WAT 305 WD ABC Formulas and 72 of 74
71 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) 1/17/2013 WAT 305 WD ABC Formulas and 73 of 74
72 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 ft 3 1/17/2013 WAT 305 WD ABC Formulas and 74 of 74
73 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.? x 50 2 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, ft 3 ) So the answer is 19,625 cu ft. (cf, ft 3 )
74 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
75 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
76 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
77 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 = Million Gallons (MG)
78 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
79 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?
80 Convert Temperature Problem Calculate the temperature in Celsius for a water temperature of 4 o C. Conversion 1/17/2013 WAT 305 WD ABC Formulas and 82 of 74
81 Convert Celsius to Fahrenheit Problem Calculate the temperature in Fahrenheit for a water temperature of 4 o C. Conversion 1/17/2013 WAT 305 WD ABC Formulas and 83 of 74
82 Convert Celsius to Fahrenheit Calculate the temperature in Fahrenheit for a water temperature of 4 o C. Conversion Degrees Fahrenheit = (Degrees Celsius) (9/5) /17/2013 WAT 305 WD ABC Formulas and 84 of 74
83 Convert Celsius to Fahrenheit Calculate the temperature in Fahrenheit for a water temperature of 4 o C. Degrees Fahrenheit = (Degrees Celsius) (9/5) + 32 = (4 o C)(9/5) + 32 = (4 o C)(1.8) + 32 = = 39.2 o F 1/17/2013 WAT 305 WD ABC Formulas and 85 of 74
84 ABC 1 acre = 43,560 square feet 1 cubic foot = 7.48 gallons 1 foot = meters 1 gallon = 3.79 liters 1/17/2013 WAT 305 WD ABC Formulas and 86 of 74
85 ABC 1 gallon = 8.34 pounds 1 grain per gallon = 17.1 mg/l 1 horsepower = kilowatts 1/17/2013 WAT 305 WD ABC Formulas and 87 of 74
86 ABC 1 million gallons per day = 694 gallons per minute 1 pound = kilograms 1 pound per square inch = 2.31 feet of water 1/17/2013 WAT 305 WD ABC Formulas and 88 of 74
87 ABC Degrees Celsius = (Degrees Fahrenheit - 32) (5/9) Degrees Fahrenheit = (Degrees Celsius) (9/5) % = 10,000 mg/l 1/17/2013 WAT 305 WD ABC Formulas and 89 of 74
88 ABC Abbreviations ft gpd feet gallons per day gpg grains per gallon 1/17/2013 WAT 305 WD ABC Formulas and 90 of 74
89 ABC Abbreviations gpm gallons per minute lbs pounds mg/l milligrams per liter MGD million gallons per day 1/17/2013 WAT 305 WD ABC Formulas and 91 of 74
90 ABC Abbreviations ml milliliter 1/17/2013 WAT 305 WD ABC Formulas and 92 of 74
91 Generic formulas Review Listed alphabetically Must watch the units Can t mix units and abbreviations 1/17/2013 WAT 305 WD ABC Formulas and 93 of 74
92 Summary Math can help you pass your certification exams Math is important for your operations, troubleshooting, reports, and records And your paycheck! 1/17/2013 WAT 305 WD ABC Formulas and 94 of 74
93 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! 1/17/2013 WAT 305 WD ABC Formulas and 95 of 74
94 1/17/2013 WAT 305 WD ABC Formulas and 96 of 74
95 Math Design flow= Population x Design Factor for Flow Population Equivalent (gpcd)= Drawdown (ft)= Flow (gpd) Population Static Water Depth (ft) - Depth after Pumping (ft) Specific Capacity (gpm/ft)= Flow (gpm) Drawdown (ft) 1/17/2013 WAT 305 WD ABC Formulas and 97 of 74
96 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) 1/17/2013 WAT 305 WD ABC Formulas and 98 of 74
97 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) 1/17/2013 WAT 305 WD ABC Formulas and 99 of 74
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