UNIT CONVERSIONS Key Concepts • Units are labels that distinguish one measurable quantity from other measurable quantities • A given value divided by an equivalent value is equal to 1 • Any number multiplied by 1 remains the same • By using equivalents, units can be changed to the desired units • Same units above and below the division line cancel each other out Example A: 1 acre = 1 2 43,560 ft Example B: 87,120 ft2 x 1 acre 43,560 ft2 = 2 acres Monorail Method of Converting Units Step 1 – Draw a horizontal line with a vertical line in the middle of it Step 2 – Write down your known number with appropriate units in the upper left space Step 3 – Choose an appropriate equivalent and write in the next space (make sure the value with the same units as your starting number is below the line so that the units will cancel each other out) Step 4 – Cross out units that appear above and below the division line Step 5 – Do the math by multiplying your beginning number by all numbers above the line and dividing by all numbers below the line 1 © American Water College UNIT CONVERSIONS Example 1: Convert 50 feet of head to psi. Example 2: Convert 100,000 ft2 to acres. Example 3: Convert 10 liters of water to pounds. Example 4: Convert 6 lb/day of polymer to mg/sec. 2 © American Water College UNIT CONVERSIONS Convert between acres and square feet: 1 acre = 43,560 square feet 1. 150,000 square ft = _____________ acres 2. 23,000 square ft = _____________ acres 3. 500,000 square ft = _____________ acres 4. 5 acres = _____________ square feet 5. 3.5 acres = _____________ square feet 6. Find the acreage of a pond surface with an average width of 150 feet and a length of 200 feet. 7. Find the area in acres of a reservoir that is 1,000 feet long by 900 feet wide. 3 © American Water College UNIT CONVERSIONS Convert the following volumes: 1 cubic foot of water = 7.48 gallons 8. A basin that measures 20 ft wide by 40 ft long by 10 ft deep = _____________ gallons 9. A basin that measures 20 ft wide by 30 ft long by 12 ft deep = _____________ gallons 10. A basin that measures 15 ft wide by 60 ft long by 13 ft deep = _____________ gallons 11. 250,000 gallons of water = _____________ cubic feet 12. 500,000 gallons of water = _____________ cubic feet 13. 150,000 gallons of water = _____________ cubic feet 14. 75,000 gallons of water = _____________ cubic feet 4 © American Water College UNIT CONVERSIONS Convert the following volume/weight relationships: 1 gallon of water = 8.34 pounds 15. 1,500 gallons of water = _____________ pounds 16. 120,000 gallons of water = _____________ pounds 17. 50 gallons of water = _____________ pounds 18. 30,000 pounds of water = _____________ gallons 19. 5,000 pounds of water = _____________ gallons Convert between English and Metric volumes: 1 gallon = 3.785 liters 20. 7 gallons = _____________ liters 21. 25 gallons = _____________ liters 5 © American Water College UNIT CONVERSIONS 22. 125 gallons = _____________ liters 23. 19 liters = _____________ gallons 24. 50 liters = _____________ gallons Convert the following concentrations: 1 mg/L = 1 ppm and 1% = 10,000 ppm 25. 5 ppm = _____________ mg/L 26. 58 mg/L = _____________ ppm 27. 5% = _____________ mg/L 28. 12.5% = _____________ mg/L 6 © American Water College UNIT CONVERSIONS 29. 5,000 mg/L = _____________ % 30. 90,000 mg/L = _____________ % Convert between feet of Head and psi: 1 foot of water = 0.433 psi 1 psi = 2.31 feet of Head 31. 100 feet of water = _____________ psi 32. 525 feet of water = _____________ psi 33. 375 feet of water = _____________ psi 34. 55 psi = _____________ feet of head 35. 125 psi = _____________ feet of head 7 © American Water College UNIT CONVERSIONS 36. 250 psi = _____________ feet of head Convert the following power relationships: 1 HP = .746 Kw = 550 ft-lb/sec = 33,000 ft-lb/min 37. 3 HP = _____________ Kw 38. 18 HP = _____________ Kw 39. 65 Kw = ____________ HP 40. 20 Kw = _____________ HP 41. 6,000 ft-lb/sec = _____________ HP 42. 17,000 ft-lb/sec = _____________ HP 8 © American Water College UNIT CONVERSIONS 43. 23,000 ft-lb/sec = _____________ Kw 44. 42,000 ft-lb/sec = _____________ Kw Perform the following complex conversions: 45. 8 lb/day = _____________ mg/sec 46. 4 MGD = _____________ CFS (cubic feet per second) 47. 10 MG = ______________ acre-feet 9 © American Water College UNIT CONVERSIONS 1. 3.4 acres 2. 0.53 acres 3. 11.5 acres 4. 217,800 sq ft 5. 152,460 sq ft 6. 0.7 acres 7. 20.7 acres 8. 59,840 gallons 9. 53,856 gallons 10. 87,516 gallons 11. 33,422 cu ft 12. 66,845 cu ft 13. 20,053 cu ft 14. 10,027 cu ft 15. 12,510 lb 16. 1,000,800 lb 17. 417 lb 18. 3,597 gallons 19. 600 gallons 20. 26.5 L 21. 94.6 L 22. 473 L 23. 5 gallons 24. 13.2 gallons 25. 5 mg/L 26. 58 ppm 27. 50,000 mg/L 28. 125,000 mg/L 29. 0.5% 30. 9% 31. 43 psi 32. 227 psi 33. 162 psi 34. 127 ft of head 35. 289 ft of head 36. 577 ft of head 37. 2.2 Kw 38. 13.4 Kw 39. 87 HP 40. 26.8 HP 41. 10.9 HP 42. 30.9 HP 43. 31.2 Kw 44. 57 Kw 45. 42 mg/sec 46. 6.2 CFS 47. 30.7 acre-ft 10 © American Water College