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Manometer Procedure Procedure for Computing the Force on a Submerged Plane Area 1. 2. 3. 4. Identify Point S (draw an extension of the angled surface) Locate the centroid of the submerged area from its geometry: Determine hc Determine Lc, βπ πΏπ = π πππ 5. Calculate total area A 6. Calculate Resultant Force, πΉπ = πΎβπ π΄ 7. Calculate Ic π΅π» 3 πΌπ = 12 8. Calculate the location of the center of pressure πΏπ = πΏπ + 9. If desired, calculate hp πΏπ πΏππ΄ Procedure for Solving Buoyancy Problems 1. Determine the objective of the problem. Do you want to determine a force, a weight, a volume or a specific weight? 2. Draw a Free Body Diagram. Include all forces and directions 3. Write static equilibrium equation in vertical direction: π΄πΉπ¦ = 0 4. Solve for the desired force, weight, volume or specific weight Notes: a) The buoyant force is calculated from πΉπ = πΎπππ b) The weight of an object is calculated from π€ = πΎπ c) An object with an average specific weight less than that of the fluid will tend to float because π€ < πΉπ with the object submerged d) An object with an average specific weight greater than that of the fluid will tend to sink because π€ > πΉπ with the object submerged e) Neutral buoyancy occurs with a body stays in a given position when it is submerged because π€ = πΉπ Procedure for Determining the Stability of a Floating Object 1. 2. 3. 4. 5. 6. 7. 8. 9. Determine the position of the floating body, using the principles of buoyancy Locate the center of buoyance, cb. Compute the distance from the bottom of the object, (ycb) Locate the center of gravity, cg. Compute the distance from the bottom of the object, (ycg) Determine the shape of the area at the fluid surface and compute the smallest moment of inertia, I, for that shape. Compute the displaced volume, (Vd) πΌ Compute ππ΅ = ππ β’ I is the smallest moment of inertia of a floating objects area at the surface Compute ymc = ycb + MB If ymc > ycg, the body is stable If ymc < ycg, the body is unstable