Meriam, Kraige & Bolton — Distributed Forces: Centroids and Centers of Gravity: Problem 5_72

⚡ Mecademy AIENG정역학 · ch5  Problem Statement The water storage tank is a shell of revolution and is to be sprayed with two coats of paint which has a coverage of per gallon. The engineer (who remembers mechanics) consults a scale drawing of the tank and determines that the curved line has a length of and that its centroid is from the centerline of the tank. How many gallons of paint will be used for the tank including the vertical cylindrical column? Problem 5/72 (a) Calculation of the total amount of paint required 1. Formula: The total surface area of the tank is the sum of the surface area of the main shell and the lateral surface area of the cylindrical column . According to the first theorem of Pappus-Guldinus, the area of a surface of revolution is: The lateral area of a cylinder is: The total volume of paint needed for two coats is: 2. Substitution: For the main shell (): , , radians. For the column: , . Coverage: . 3. Calculation: 500 ft 2 ABC 34 ft8.2 ft S total S 1 S 2 S = 1 θLrˉ S = 2 πDh G G= Coverage 2×S total ABCL=34 ft=rˉ8.2 ftθ=2π D=8 fth=18 ft 500 ft/gallon 2 S = 1 2π×8.2×34 S = 2 π×8×18 S = 1 557.6π≈ 1751.73 ft 2 S = 2 144π≈ 452.39 ft 2 Total Surface Area: Total area for 2 coats: Gallons of paint: 4. Result: ● Final Conclusion: Approximately of paint will be used for the tank considering two coats of paint. ✨ Final Answer Summary (a) 8.82 gallons Mecademy AI Solution · ENGProblem 5/72 S = total S + 1 S = 2 (557.6+144)π=701.6π≈ 2204.12 ft 2 A = paint 2×2204.