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## Clarifier Calculations

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**Clarifier Calculations**Prepared By Michigan Department of Environmental Quality Operator Training and Certification Unit**Clarifier Calculations**Hydraulic Loading Solids Loading**Clarifier Loading Calculations**Tank Volume, MG X 24 Flow into Tank, MGD Detention Time (DT) = Flow, gallons/day = Surface Overflow Rate (SOR) Surface Area, ft2 Flow, gallons/day Weir Overflow Rate (WOR) = Length of Weir, ft Solids, lbs/day Surface Area, ft2 Solids Loading =**Area**and Volume Calculations**Surface Area Calculations**Rectangles Surface Area, ft2 = Length, ft X Width, ft Example 1: If a tank is 10 ft long and5 ft wide, what is the surfacearea? SA, ft2 = 10 ft X 5 ft = 50 ft2**Surface Area Calculations**Rectangles Surface Area, ft2 = Length, ft X Width, ft Example 2: If a tank is 10 ft 6 inches long and5 ft 9 inches wide, what is the surface area in sq. ft.? NOT SA, ft2 = 10.6 ft X 5.9 ft**Converting Inches to Feet**6 inches 12 in/ft = 0.5 ft 6 inches = So: 10 ft 6 inches = 10.5 ft 9 inches 12 in/ft = 0.75 ft 9 inches = So: 5 ft 9 inches = 5.75 ft**Surface Area Calculations**Rectangles Surface Area, ft2 = Length, ft X Width, ft Example 2: If a tank is 10 ft 6 inches long and5 ft 9 inches wide, what is the surface area in sq. ft.? SA, ft2 = 10.5 ft X 5.75 ft = 60.4 ft2**Surface Area Calculations**Rectangles Surface Area, ft2 = Length, ft X Width, ft Work Calculations on Separate Paper Answers Given on Next Slides Practice 1: If a clarifier is 25 ftlong and9 ftwide, what is the surface area in sq. ft.? Practice 2: If a clarifier is 22 ft 3 inches long and7 ft 7 inches wide, what is the surface area in sq. ft.?**Surface Area Calculations**Rectangles Surface Area, ft2 = Length, ft X Width, ft Practice 1: If a clarifier is 25 ftlong and9 ftwide, what is the surface area in sq. ft.? SA, ft2 = 25 ft X 9 ft = 225 ft2**Surface Area Calculations**Rectangles Surface Area, ft2 = Length, ft X Width, ft Practice 2: If a clarifier is 22 ft 3 inches long and7 ft 7 inches wide, what is the surface area in sq. ft.?**Converting Inches to Feet**3 inches 12 in/ft = 0.25 ft 3 inches = So: 22 ft 6 inches = 22.25 ft 7 inches 12 in/ft = 0.58 ft 7 inches = So: 7 ft 7 inches = 7.58 ft**Surface Area Calculations**Rectangles Surface Area, ft2 = Length, ft X Width, ft Practice 2: If a clarifier is 22 ft 3 inches long and7 ft 7 inches wide, what is the surface area in sq. ft.? SA, ft2 = 22.25 ft X 7.58 ft = 60.4 ft2**Diameter**Diameter 2 Radius = Radius Surface Area Calculations Circles Diameter: The distance across a circle, going through the center. Radius: The distance from the center a circle to the perimeter.**Circumference**Diameter Radius Surface Area Calculations Circles Circumference = distance around circle**Diameter**Radius Surface Area Calculations Circles pie**Diameter**Radius Surface Area Calculations Circles pi = Circumference Diameter = = 3.14 for any circle**Diameter**Radius Surface Area Calculations Circles Surface Area = r2 = 3.14 X radius X radius**X D2**= 3.14 22 3.14 4 A = X D2 Surface Area Calculations Circles Surface Area = r2 = 3.14 X r2 OR A = 3.14 X (D/2)2 = 3.14 X D2 4 OR = 0.785 X D2 Any on the Three Formulas Can Be Used**Diameter**Radius Surface Area Calculations Circles Surface Area = r2 Example 1: If a tank has a radius of 15 feet, what is the surfacearea? S A = r2 = 3.14 X 15 ft. X 15 ft. = 707 ft2**Diameter**Radius Surface Area Calculations Circles Surface Area = r2 Example 2: If a tank has a diameter of 25 feet, what is the surfacearea? S A = r2 = 3.14 X 12.5 ft. X 12.5 ft. = 491 ft2**Diameter**Radius Surface Area Calculations Circles Surface Area = r2 Work Calculations on Separate Paper Answers Given on Next Slides Practice 1: If a tank has a diameter of 50.5 feet, what is the surfacearea? Practice 2: If a tank has a diameter of 50 feet 7 inches, what is the surfacearea?**Diameter**Radius Surface Area Calculations Circles Surface Area = r2 Practice 1: If a tank has a diameter of 50.5 feet, what is the surfacearea? S A = r2 = 3.14 X 25.25 ft. X 25.25 ft. = 2002 ft2**Diameter**Radius Surface Area Calculations Circles Surface Area = r2 Practice 2: If a tank has a diameter of 50 feet 7 inches, what is the surfacearea? 7 inches 12 in/ft = 0.58 ft 7 inches = 50 feet 8 inches = 50.58 ft Radius = 50.58 ft ÷ 2 = 25.29 ft**Diameter**Radius Surface Area Calculations Circles Surface Area = r2 Practice 2: If a tank has a diameter of 50 feet 7 inches, what is the surfacearea? S A = r2 = 3.14 X 25.29 ft. X 25.29 ft. = 2008 ft2**Volume Calculations**Volume – Three D**Volume Calculations**Volume – Three Dimensions Depth Width Length**Volume Calculations**Rectangular Tanks Volume = Length X Width X Height (or Depth) Example 1: If a tank is 10 feet long, 5 feet wide, and 5 feet deep, what is the volume in cubic feet? Vol. = 10 ft X 5 ft X 5 ft = 250 ft3**Volume Calculations**Rectangular Tanks Volume = Length X Width X Height (or Depth) Example 2: If a tank is 20 ft. long, 7 ft. wide, and 5.5 ft. deep, what is the volume in cubic feet? Vol. = 20 ft X 7 ft X 5.5 ft = 770 ft3**Volume Calculations**Rectangular Tanks Volume = Length X Width X Height (or Depth) Example 3: If a tank is 25 ft. long, 9 ft. 3 inches wide, and 7.5 ft. deep, what is the volume in gallons? Vol. = 25 ft X 9.25 ft X 7.5 ft = 1734 ft3**Volume Calculations**Rectangular Tanks Volume = Length X Width X Height (or Depth) Example 3: If a tank is 25 ft. long, 9 ft. 3 inches wide, and 7.5 ft. deep, what is the volume in gallons? There are 7.48 gallons in one cubic foot OR 7.48 gal/ft3**Volume Calculations**Rectangular Tanks Volume = Length X Width X Height (or Depth) Example 3: If a tank is 25 ft. long, 9 ft. 3 inches wide, and 7.5 ft. deep, what is the volume in gallons? Vol. = 25 ft X 9.25 ft X 7.5 ft = 1734 ft3 1734ft3 7.48 gal/ft3 = 12,970 gallons X**Volume Calculations**Rectangular Tanks Work Calculations on Separate Paper Answers Given on Next Slides Practice 1: If a tank is 21 feet long, 9 feet wide, and 7 feet deep, what is the volume in cubic feet? Practice 2: If a tank is 22 ft. long, 9 ft. wide, and 7.5 ft. deep, what is the volume in cubic feet? Practice 3: If a tank is 35 ft. long, 12 ft. 3 inches wide, and 9.5 ft. deep, what is the volume in gallons?**Volume Calculations**Rectangular Tanks Volume = Length X Width X Height (or Depth) Practice 1: If a tank is 21 feet long, 9 feet wide, and 7 feet deep, what is the volume in cubic feet? Vol. = 21 ft X 9 ft X 7 ft = 1323 ft3**Volume Calculations**Rectangular Tanks Volume = Length X Width X Height (or Depth) Practice 2: If a tank is 22 ft. long, 9 ft. wide, and 7.5 ft. deep, what is the volume in cubic feet? Vol. = 22 ft X 9 ft X 7.5 ft = 1485 ft3**Volume Calculations**Rectangular Tanks Volume = Length X Width X Height (or Depth) Practice 3: If a tank is 35 ft. long, 12 ft. 3 inches wide, and 9.5 ft. deep, what is the volume in gallons? Vol. = 35 ft X 12.25 ft X 9.5 ft = 4073 ft3**Volume Calculations**Rectangular Tanks Volume = Length X Width X Height (or Depth) Practice 3: If a tank is 35 ft. long, 12 ft. 3 inches wide, and 9.5 ft. deep, what is the volume in gallons? There are 7.48 gallons in one cubic foot OR 7.48 gal/ft3**Volume Calculations**Rectangular Tanks Volume = Length X Width X Height (or Depth) Practice 3: If a tank is 35 ft. long, 12 ft. 3 inches wide, and 9.5 ft. deep, what is the volume in gallons? Vol. = 35 ft X 12.25 ft X 9.5 ft = 4073 ft3 4073ft3 7.48 gal/ft3 = 30,466 gallons X**Volume Calculations**Round (Cylinder) Tanks Volume – Three Dimensions V = π r2h = 3.14 r = Radius of circle h = Height (or Depth)**Volume Calculations**Round (Cylinder) Tanks Example 1 Find the Volume in cubic feet of a tank having a radius of 10 feet and a depth of 8 feet. V = r2h = 3.14 X 10 ft X 10 ft X 8 ft = 3.14 X 800 ft3 = 2512 ft3**Volume Calculations**Round (Cylinder) Tanks Example 2 Find the Volume in cubic feet of a tank having a diameter of 30 feet and a depth of 8 feet. V = r2h = 3.14 X 15 ft X 15 ft X 8 ft = 3.14 X 1800 ft3 = 5652 ft3**Volume Calculations**Round (Cylinder) Tanks Example 3 Find the Volume in gallons of a tank having a diameter of 50 feet and a depth of 9 feet. V = r2h = 3.14 X 25 ft X 25 ft X 9 ft = 17,662.5 ft3 X 7.48 gal/ft3 = 132,116 gallons**Volume Calculations**Round (Cylinder) Tanks Volume – Three Dimensions = 3.14 r = Radius of circle h = Height (or Depth)**Volume Calculations**Round (Cylinder) Tanks Work Calculations on Separate Paper Answers Given on Next Slides Practice 1 Find the Volume in cubic feet of a tank having a radius of 22 feet and a depth of 10 feet. Practice 2 Find the Volume in cubic feet of a tank having a diameter of 28 feet and a depth of 7.5 feet. Practice 3 Find the Volume in gallons of a tank having a diameter of 48 feet and a depth of 7 feet.**Volume Calculations**Round (Cylinder) Tanks Practice 1 Find the Volume in cubic feet of a tank having a radius of 22 feet and a depth of 10 feet. V = r2h = 3.14 X 22 ft X 22 ft X 10 ft = 3.14 X 4840 ft3 = 15,198 ft3**Volume Calculations**Round (Cylinder) Tanks Practice 2 Find the Volume in cubic feet of a tank having a diameter of 28 feet and a depth of 7.5 feet. V = r2h = 3.14 X 14 ft X 14 ft X 7.5 ft = 3.14 X 1470 ft3 = 4616 ft3**Volume Calculations**Round (Cylinder) Tanks Practice 3 Find the Volume in gallons of a tank having a diameter of 48 feet and a depth of 7 feet. V = r2h = 3.14 X 24 ft X 24 ft X 7 ft = 12,660 ft3 X 7.48 gal/ft3 = 94,700 gallons**Volume Calculations**What about a Round Tank with a Cone Bottom ?**r2h2**3 Vcone = 1/3 r2h or Volume Calculations Cylinder with Cone Bottom h1 Vcylinder = r2h1 h2 Vtotal = Vcylinder + Vcone