Part V Workbook Practice Problems L1675_C34.fm Page 345 Saturday, January 31, 2004 6:09 PM © 2004 by CRC Press LLC 34 Workbook Practice Problems TOPICS • Basic Math Operations (Problems 1 to 43) • Fundamental Operations (Water/Wastewater) (Problems 1 to 342) • Water Treatment Calculations (Problems 1 to 457) • Wastewater Treatment Calculations (Problems 1 to 574) • Laboratory Calculations (Water and Wastewater) (Problems 1 to 80) Note: Answers to practice problems can be found in the Appendix. BASIC MATH OPERATIONS (PROBLEMS 1 TO 43) D ECIMAL O PERATIONS 1. 90.5 ¥ 7.3 = 2. 9.556 ¥ 1.03 = 3. 13 ÷ 14.3 = 4. 8.2 ÷ .96 = 5. 2 ÷.053 = L1675_C34.fm Page 347 Saturday, January 31, 2004 6:09 PM © 2004 by CRC Press LLC 348 Mathematics for Water/Wastewater Treatment Plant Operators 6. Convert 3/4 into a decimal. 7. Convert 1/6 into a decimal. 8. Convert 3/8 into a decimal. 9. Convert .13 into a fraction. 10. Convert .9 into a fraction. 11. Convert .75 into a fraction. 12. Convert .245 into a fraction. P ERCENTAGE C ALCULATIONS 13. Convert 15/100 into a percent. L1675_C34.fm Page 348 Saturday, January 31, 2004 6:09 PM © 2004 by CRC Press LLC Workbook Practice Problems 349 14. Convert 122/100 into a percent. 15. Convert 1.66 into a percent. 16. Convert 4/7 into a percent. 17. A 100% decline from 66 leaves us with how much? F IND X 18. If x – 6 = 2, find x . 19. If x – 4 = 9, find x . 20. If x – 8 = 17, find x . 21. If x + 10 = 15, find x . L1675_C34.fm Page 349 Saturday, January 31, 2004 6:09 PM © 2004 by CRC Press LLC 350 Mathematics for Water/Wastewater Treatment Plant Operators 22. If x /3 = 2, find x . 23. Solve for x when x /4 = 10. 24. If 4 x = 8, find x . 25. If 6 x = 15, find x . 26. If x + 10 = 2, find x . 27. If x – 2 = –5, find x . 28. If x + 4 = –8, find x . 29. If x – 10 = –14, find x . 30. If .5 x – 1 = –6, find x . L1675_C34.fm Page 350 Saturday, January 31, 2004 6:09 PM © 2004 by CRC Press LLC Workbook Practice Problems 351 31. If 9 x + 1 = 0, find x . 32. How much is x 2 if x = 6? 33. If x = 3, find x 4 . 34. If x = 10, find x 0 . R ATIO AND P ROPORTION 35. If an employee was out sick for 6 of 96 workdays, what is the ratio of sick days to days worked? 36. Find x when 2: x = 5:15. A REA OF R ECTANGLES 37. What is the area of the rectangle shown in Figure 34.1? 3 feet 3 feet Figure 34.1 L1675_C34.fm Page 351 Saturday, January 31, 2004 6:09 PM © 2004 by CRC Press LLC 352 Mathematics for Water/Wastewater Treatment Plant Operators 38. What is the area of the rectangle shown in Figure 34.2? 39. What is the area of the rectangle shown in Figure 34.3? C IRCUMFERENCE AND A REA OF C IRCLES 40. Find the circumference of a circle with diameter of 14 ft. 41. If the circumference of a circle is 8 inches, what is the diameter? 42. If the radius of a circle is 7 inches, what is the area? 43. If the diameter of a circle is 10 inches, what is the area? Figure 34.2 5 inches 3 inches 1 yard 5 yards Figure 34.3 L1675_C34.fm Page 352 Saturday, January 31, 2004 6:09 PM © 2004 by CRC Press LLC Workbook Practice Problems 353 FUNDAMENTAL OPERATIONS (WATER/WASTEWATER) (PROBLEMS 1 TO 342) T ANK V OLUME C ALCULATIONS 1. The diameter of a tank is 70 ft. If the water depth is 25 ft, what is the volume of water in the tank (in gallons)? 2. A tank is 60 ft in length, 20 ft wide, and 10 ft deep. Calculate the cubic foot volume of the tank. 3. A tank 20 ft wide and 60 ft long is filled with water to a depth of 12 ft. What is the volume of the water in the tank (in gal)? 4. What is the volume of water in a tank (in gallons) if the tank is 20 ft wide by 40 ft long and contains water to a depth of 12 ft? 5. A tank has a diameter of 60 ft and a depth of 12 ft. Calculate the volume of water in the tank (in gallons). 6. What is the volume of water in a tank (in gallons) if the tank is 20 ft wide by 50 ft long and contains water to a depth of 16 ft? C HANNEL AND P IPELINE C APACITY C ALCULATIONS 7. A rectangular channel is 340 ft long, 4 ft deep, and 6 ft wide. What is the volume of water (in cubic feet)? L1675_C34.fm Page 353 Saturday, January 31, 2004 6:09 PM © 2004 by CRC Press LLC 354 Mathematics for Water/Wastewater Treatment Plant Operators 8. A replacement section of 10-inch pipe is to be sandblasted before it is put into service. If the length of pipeline is 1600 ft, how many gallons of water will be needed to fill the pipeline? 9. A trapezoidal channel is 800 ft long, 10 ft wide at the top, and 5 ft wide at the bottom, with a distance of 4 ft from the top edge to bottom along the sides. Calculate the gallon volume. 10. A section of 8-inch diameter pipeline is to be filled with treated water for distribution. If the pipeline is 2250 ft in length, how many gallons of water will be distributed? 11. A channel is 1200 ft in length, carries water 4 ft deep, and is 5 ft wide. What is the volume of water (in gallons)? M ISCELLANEOUS V OLUME C ALCULATIONS 12. A pipe trench is to be excavated that is 4 ft wide, 4 ft deep, and 1200 ft long. What is the volume of the trench (in cubic yards)? 13. A trench is to be excavated that is 3 ft wide, 4 ft deep, and 500 yds long. What is the cubic yard volume of the trench? 14. A trench is 300 yards long, 3 ft wide, and 3 ft deep. What is the volume of the trench (in cubic feet)? L1675_C34.fm Page 354 Saturday, January 31, 2004 6:09 PM © 2004 by CRC Press LLC Workbook Practice Problems 355 15. A rectangular trench is 700 ft long, 6.5 ft wide, and 3.5 ft deep. What is the volume of the trench (in cubic feet)? 16. The diameter of a tank is 90 ft. If the water depth in the tank is 25 ft, what is the volume of water in the tank (in gallons)? 17. A tank is 80 ft long, 20 ft wide, and 16 ft deep. What is the volume of the tank (in cubic feet)? 18. How many gallons of water are required to fill an 8-inch-diameter pipe that is 4000 ft in length? 19. A trench is 400 yards long, 3 ft wide, and 3 ft deep. What is the volume of the trench (in cubic feet)? 20. A trench is to be excavated. If the trench is 3 ft wide, 4 ft deep, and 1200 ft long, what is the volume of the trench (in cubic yards)? 21. A tank is 30 ft wide and 80 ft long. If the tank contains water to a depth of 12 ft, how many gallons of water are in the tank? 22. What is the volume of water (in gallons) contained in a 3000-ft section of channel if the channel is 8 ft wide and the water depth is 3.5 ft? L1675_C34.fm Page 355 Saturday, January 31, 2004 6:09 PM © 2004 by CRC Press LLC [...]...L16 75_ C34.fm Page 356 Saturday, January 31, 2004 6:09 PM 356 Mathematics for Water/ Wastewater Treatment Plant Operators 23 A tank has a diameter of 70 ft and a depth of 19 ft What is the volume of water in the tank (in gallons)? 24 If a tank is 25 ft in diameter and 30 ft deep, how many gallons of water will it hold? FLOW, VELOCITY, AND CONVERSION CALCULATIONS 25 A channel 44 inches wide has water. .. what is the velocity in the 10-inch pipeline (in ft/sec)? © 2004 by CRC Press LLC L16 75_ C34.fm Page 358 Saturday, January 31, 2004 6:09 PM 358 Mathematics for Water/ Wastewater Treatment Plant Operators AVERAGE FLOW RATES 37 The following flows were recorded for the week: Monday, 4.8 MGD; Tuesday, 5. 1 MGD; Wednesday, 5. 2 MGD; Thursday, 5. 4 MGD; Friday, 4.8 MGD; Saturday, 5. 2 MGD; Sunday, 4.8 MGD What... of 5. 5 MGD if the chlorine demand is 7.7 mg/L and a chlorine residual of 2 mg/L is desired? 94 The suspended solids concentration of the wastewater entering primary system is 3 05 mg/L If the plant flow is 3 .5 MGD, how many lb/day suspended solids enter the primary system? © 2004 by CRC Press LLC L16 75_ C34.fm Page 366 Saturday, January 31, 2004 6:09 PM 366 Mathematics for Water/ Wastewater Treatment Plant. .. to a 3 . 5- acre wastewater pond is 120,000 gpd The influent BOD concentration is 170 mg/L What is the organic loading to the pond (in lbs BOD/day/ac)? © 2004 by CRC Press LLC L16 75_ C34.fm Page 372 Saturday, January 31, 2004 6:09 PM 372 Mathematics for Water/ Wastewater Treatment Plant Operators 138 An 8 5- ft-diameter trickling filter with a media depth of 6 ft receives a primary effluent flow of 2, 850 ,000... gpm)? 51 An 8-inch diameter pipe flowing full delivers 51 0 gpm What is the velocity of flow in the pipeline (in ft/sec)? 52 Express a flow of 10 cfs in terms of gpm © 2004 by CRC Press LLC L16 75_ C34.fm Page 360 Saturday, January 31, 2004 6:09 PM 360 Mathematics for Water/ Wastewater Treatment Plant Operators 53 The total reading for the month of December was 134.6 MG What was the average daily flow (ADF) for. .. population loading on the pond? © 2004 by CRC Press LLC L16 75_ C34.fm Page 376 Saturday, January 31, 2004 6:09 PM 376 Mathematics for Water/ Wastewater Treatment Plant Operators 163 A 381,000 gpd wastewater flow has a BOD concentration of 17 65 mg/L Using an average of 0.2 lb/day BOD/person, what is the population equivalent of this wastewater flow? 164 A wastewater lb is designed to serve a population of 6000 If... September? 54 What is 5. 2 MGD expressed as cfs? 55 A pump discharges into a 3-ft-diameter container If the water level in the container rises 20 inches in 30 seconds, what is the rate of flow into the container (in gpm)? 56 Convert a flow of 1,8 25, 000 gpd to cfm 57 A 6-inch diameter pipeline has water flowing at a velocity of 2.9 fps) What is the flow rate through the pipeline (in gpm)? 58 The velocity in a 10-inch... by CRC Press LLC L16 75_ C34.fm Page 368 Saturday, January 31, 2004 6:09 PM 368 Mathematics for Water/ Wastewater Treatment Plant Operators 109 What is the hydraulic loading rate (in gpd/sq ft) to a 90-ft-diameter trickling filter if the primary effluent flow to the tickling filter is 3,880,000 gpd and the recirculated flow is 1,400,000 gpd? 110 A 20-acre pond receives a flow of 4.4 acre-feet/day What is the... wide and has wastewater to a depth of 12 ft, The desired F/M ratio is 0 .5 What is the desired MLVSS concentration (in mg/L) in the aeration tank? 176 A sedimentation tank 80 ft by 25 ft receives a flow of 2.0 MGD What is the surface overflow rate (in gpd/da ft)? © 2004 by CRC Press LLC L16 75_ C34.fm Page 378 Saturday, January 31, 2004 6:09 PM 378 Mathematics for Water/ Wastewater Treatment Plant Operators. .. PM 374 Mathematics for Water/ Wastewater Treatment Plant Operators DIGESTER LOADING RATE CALCULATIONS 151 A digester receives a total of 12,110 lb/day volatile solids If the digester volume is 33,100 cu ft, what is the digester loading in the volatile solids added/day/cu ft? 152 A digester, 60 ft in diameter with a water depth of 25 ft, receives 124,000 lb/day raw sludge If the sludge contains 6 .5% total . Operations (Water/ Wastewater) (Problems 1 to 342) • Water Treatment Calculations (Problems 1 to 457 ) • Wastewater Treatment Calculations (Problems 1 to 57 4) • Laboratory Calculations (Water and Wastewater) . Mathematics for Water/ Wastewater Treatment Plant Operators 53 . The total reading for the month of December was 134.6 MG. What was the average daily flow (ADF) for the month of September? 54 feet 3 feet Figure 34.1 L16 75_ C34.fm Page 351 Saturday, January 31, 2004 6:09 PM © 2004 by CRC Press LLC 352 Mathematics for Water/ Wastewater Treatment Plant Operators 38. What is the area