Procedures for Computing Forces

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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,
β„Žπ‘
𝐿𝑐 = π‘ π‘–π‘›πœƒ
5. Calculate total area A
6. Calculate Resultant Force,
𝐹𝑅 = π›Ύβ„Žπ‘ 𝐴
7. Calculate Ic
𝐡𝐻 3
𝐼𝑐 = 12
8. Calculate the location of the center of pressure
𝐿𝑝 = 𝐿𝑐 +
9. If desired, calculate hp
𝐿𝑐
𝐿𝑐𝐴
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:
𝛴𝐹𝑦 = 0
4. Solve for the desired force, weight, volume or specific weight
Notes:
a) The buoyant force is calculated from 𝐹𝑏 = 𝛾𝑓𝑉𝑑
b) The weight of an object is calculated from 𝑀 = 𝛾𝑉
c) An object with an average specific weight less than that of the fluid will tend to float
because 𝑀 < 𝐹𝑏 with the object submerged
d) An object with an average specific weight greater than that of the fluid will tend to sink
because 𝑀 > 𝐹𝑏 with the object submerged
e) Neutral buoyancy occurs with a body stays in a given position when it is submerged
because 𝑀 = 𝐹𝑏
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)
𝐼
Compute 𝑀𝐡 = 𝑉𝑑
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
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