Advanced Waterworks Mathematics, 2019a

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Example: What is the area of a cross section of an aqueduct that is 5 feet across the bottom, 7 feet across the top and 6 feet deep? b 1 b2 Area of a Trapezoid = H 2 5 ft 7 ft Area of a Trapezoid = 6 ft = 2 12 ft 2 6 ft 6 ft6 ft 36 ft 2 Example: What is the area of a cross section of an aqueduct that is 8 feet across the bottom, 12 feet across the top and 10 feet deep? b 1 b2 Area of a Trapezoid = H 2 8 ft 12 ft Area of a Trapezoid = 10 ft = 2 20 ft 2 10 ft 10 ft10 ft 100 ft 2 Surface Area Circles, rectangles, and trapezoids are the most common shapes in the water industry. However, large standpipes shaped like a cylinder with a sphere on top or an elevated storage tank shaped like a sphere can be very common in flat areas. Half circles and rectangles can also be found as reservoirs or sedimentation basins. Therefore, understanding how to calculate the area for these types of structures is also important. Cylinder The circumference is the distance around a circle. The circumference is importance in waterworks mathematics as it is used to calculate the surface area of the side of a cylinder or tank. This is especially helpful when painting or coating a tank. The picture below shows a cylinder and the surface area of a cylinder. 30 | A dvanced Waterworks Mathematics
Figure 2.9 9 Circumference of a Circle = π × D 9 Image by Marilyn Hightower is licensed under CC BY 4.0 31 | A dvanced Waterworks Mathematics
Page 1 and 2: 1 | A dvanced Waterworks Mathematic
Page 3 and 4: Acknowledgements College of the Can
Page 5 and 6: Unit 10 201 10.1 Horsepower and Eff
Page 7 and 8: Multiple units may need to be conve
Page 9 and 10: Practice Problems 1.1a Show how eac
Page 11 and 12: Word problems may involve unit conv
Page 13 and 14: 6. A pipe flows at a rate of 6.3 cf
Page 15 and 16: 6. A well flows at a rate of 1,250
Page 17 and 18: Well 2: Total Flow in MGD 1,000 gal
Page 19 and 20: Practice Problems 1.2 1. A water ut
Page 21 and 22: 3. A water utility has 12,300 servi
Page 23 and 24: The shape of a tank is often a cyli
Page 25 and 26: Circles A circle is a round figure
Page 27 and 28: Example: What is the area of an 813
Page 29: Trapezoids Trapezoids are four-side
Page 33 and 34: The formula for the area of a spher
Page 35 and 36: Example: What is the entire interio
Page 37 and 38: Practice Problems 2.1 1. What is th
Page 39 and 40: 8. What is the entire interior surf
Page 41 and 42: 5. A standpipe needs to be painted.
Page 43 and 44: Then, calculate the volume of the t
Page 45 and 46: 2 1 2 Trapezoidal Prism = H L 8.5
Page 47 and 48: Practice Problems 2.2 1. What is th
Page 49 and 50: Exercise 2.2 1. What is the volume
Page 51 and 52: 2.3 AREA AND VOLUME WORD PROBLEMS W
Page 53 and 54: Figure 2.20 19 Step 4: Put the info
Page 55 and 56: Step 3: Make a sketch to clarify th
Page 57 and 58: Figure 2.22 21 When looking at a pr
Page 59 and 60: Calculate the volume of the cylinde
Page 61 and 62: 4. A water tank truck delivered 30
Page 63 and 64: Exercise 2.3 1. A water utility ope
Page 65 and 66: 6. A private contractor needs water
Page 67 and 68: 2.4 FLOW RATE Flow rate is the meas
Page 69 and 70: Key Terms circumference - the dist
Page 71 and 72: 4. What is the diameter of a pipe t
Page 73 and 74: 4. What is the diameter of a pipe t
Page 75 and 76: Substance Specific Gravity Weight C
Page 77 and 78: 5. The specific gravity of 25% Alum
Page 79 and 80: 5. The specific gravity of 25% Alum
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To convert between a percentage and
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And now we are moving to the row fo
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Practice Problems 3.2 1. An 87.5% c
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Exercise 3.2 Solve the following pr
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3.3 MIXING AND DILUTING SOLUTIONS T
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Total Volume of the new solution is
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3. A chlorine storage tank that is
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3. A chlorine storage tank that is
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The following charts or Pie Wheels
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At only a 10% concentration, you wi
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Now the question is asking how many
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Key Terms chlorine demand - the
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3. How many pounds of 24.5% sodium
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7. A water treatment operator adjus
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11. An operator added 422 gallons o
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3. How many pounds of 12.5% sodium
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7. A water treatment operator adjus
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11. An operator added 275 gallons o
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Weirs can either be sharp-crested o
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Weir Overflow Rate (gpm/ft) = ? gpm
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Key Terms weir - an overflow stru
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5. A treatment plant processes 8.4
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5. A treatment plant processes 15 M
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UNIT 6 6.1 DETENTION TIME Detention
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D = t Volume Flow gallons million
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Rearranging the terms in the detent
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3. A water utility engineer is desi
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7. A 70-foot diameter, 35-foot-deep
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3. A water utility engineer is desi
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7. The chlorine residual decay rate
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11. A circular clarifier processes
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Although filtration rates are commo
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Key Terms contact time - detenti
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4. A water treatment plant processe
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Exercise 6.2 1. A water treatment p
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7. An Engineer is designing a circu
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Pin It! Misconception Alert Sometim
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Next, there are two crucial terms t
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Finding the Correct CT Table Typica
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and resulting disinfection inactiva
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plant maintains a chloraminated res
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Practice Problems 7.1 1. What is th
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5. A conventional water treatment p
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7. A direct filtration plant is ope
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6. A direct filtration water treatm
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UNIT 8 8.1 PRESSURE Pressure is the
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From this example, it is clear that
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5. Two houses are served by a nearb
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8.2 HEAD LOSS As water travels thro
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Friction will need to be added at t
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3. A well located at 200 feet above
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UNIT 9 9.1 WELL YIELD, SPECIFIC CAP
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Cone of Depression The triangular s
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Practice Problems 9.1 1. A well has
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7. A well has a specific capacity o
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4. A well has an hour meter attache
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UNIT 10 10.1 HORSEPOWER AND EFFICIE
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The above equation is used to calcu
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Practice Problems 10.1 1. What is t
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Exercise 10.1 Calculate the require
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10.2 HEAD LOSS AND HORSEPOWER As di
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Practice Problems 10.2 1. A well is
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Exercise 10.2 Calculate the followi
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10.3 CALCULATING POWER COSTS It is
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93.25 kW $ 0.088 8.33 hr $ 68.35
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Practice Problems 10.3 1. A well fl
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4. A well draws water from an aquif
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7. Complete the table below based o
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Exercise 10.3 Solve the following p
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4. A well draws water from an aquif
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7. Complete the table below based o
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UNIT 11 11.1 PER CAPITA WATER USE A
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That’s a lot of gallons. This is
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Green Building Code) has resulted i
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7. A water district has a goal of 1
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4. How much water would a family of
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UNIT 12 12.1 BLENDING AND DILUTING
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To determine the percentage of Sour
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Practice Problems 12.1 1. A well ha
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5. Two wells need to achieve a dail
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3. A well with a PCE level of 7.5 u
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UNIT 13 13.1 SCADA AND THE USE OF M
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ottom to what is referred to as the
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mA (reading) - mA (offset) = percen
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4. A water tank is 52 ft tall and h
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8. A chemical injection system is m
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4. A water tank is 45 ft tall and h
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8. A chemical injection system is m
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mean extra funds to pay for securit
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Per the table, the total annual bud
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Pumps and Motors: $72,000 x% $6,2
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Variable Costs Reason 273 | A dvanc
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Practice Problems 14.1 1. A utility
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3. A utility has annual operating e
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7. A small water company has a tota
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2. A pump that has been in operatio
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5. A 250 hp well operates 9 hours a
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PRACTICE PROBLEM SOLUTIONS Practice
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3.1 cf 3,600 sec 10 hr 7.48 gal 30
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1,346,400 gal 1 AF 365 day day 3
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Practice Problems 2.3 1. A water ut
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3 22 ft 217,800.13 ft = depth ft
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Q (cfs) 3.18 cfs A (ft ) = = = 1.17
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5. The specific gravity of 25% Alum
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To convert ppb to ppm, you divide p
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Practice Problems 3.3 1. How many g
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Practice Problems 4.1 1. How many g
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6.35 MG 8.34 lbs 2,914.5 lbs ppm
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8. A water utility produced 6,000 A
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72,327.816 lbs 72,327.816 lbs 72,32
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Weir Length (ft) = 4,791.67 gpm 41
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quality objectives of a certain tre
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12 MG 1,000,000 gal 1 day 1 hour
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8. A circular clarifier processes 9
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4. A water treatment plant processe
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4,700,000 gal 1 day ? min = 1,554.
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Now look at Table C-7 Inactivation
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500 mg/L min CT is required. Locati
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Location and Type of Disinfection T
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2 2 D = 0.33121019 ft 12 in D = 0.5
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5. A water utility has two differen
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gpm Specific Capacity = ft 717.5 gp
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3. A well with pumps located 46 ft
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(630 gpm)(130 ft) 65 hp = (3,960)(?
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electrical rate of $0.111 per kW-Hr
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(flow rate in gallons per minute)(t
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2 flushes per family member 6 famil
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Practice Problems 12.1 1. A well ha
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-137.5 mg/L ? mg/L = = 275 mg/L - (
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Practice Problems 13.1 1. A 4-20 mA
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7. A water utility uses a 4-20 mA s
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NEW PUMP: (450 gpm)(65 ft) Motor hp
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Total operational cost per year. $2
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CT TABLES APPENDIX 367 | A dvanced
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Advanced Waterworks Mathematics, 2019a

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