Buoyancy, Flotation and Stability

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Buoyancy, Flotation and Stability

• When a stationary body is completely
• submerged in a fluid, or floating
• (partially submerged), the resultant
• fluid force on the body is the buoyant
• force.
• A net upward force results because
• Buoyant force has a magnitude equal
• to the weight of the fluid displaced by
• body and is directed vertically upward.
• Archimedes principle (287-212 BC)

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Buoyant force passes through the centroid of the
displaced volume
Figure 2.24 (p. 70)
Buoyant force on submerged and floating bodies.
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Example 1

• A spherical buoys has a diameter of 1.5 m, weighs
  8.50 kN
• and is anchored to the seafloor with a cable.
  What is the
• tension on the cable when the buoy is completely
  immersed?

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Example 2

• Measuring specific gravity by a hydrometer

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Stability of Immersed and Floating Bodies

• Centers of buoyancy and gravity do not coincide
• A small rotation can result in either a
  restoring or overturning couple.
• Stability is important for floating bodies

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Stability of an immersed body
Stability of a completely immersed body center
of gravity above centroid.

• Stability of a completely
• immersed body center
• of gravity below entroid.

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Stability of a floating body
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Elementary Fluid Dynamics

• Newtons second law
• Bernoulli equation (most used and the most
  abused
• equation in fluid mechanics)
• Inviscid flow- flow where viscosity is assumed
  to be zero
• viscous effects are relatively small compared
  with other
• effects such as gravity and pressure
  differences.
• Net pressure force on a particle net gravity
  force in particle
• Two dimensional flow (in x-z plane)
• Steady flow (shown in Figure 3.1)

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Figure 3.1 (p. 95) (a) Flow in the x-y plane. (b)
flow in terms of streamline and normal
coordinates.
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Streamlines

• Velocity vector is tangent to the path of flow
• Lines that are tangent to the velocity vectors
  throughout
• the flow field are called streamlines
• Equation for a streamline

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Force balance on a Streamline
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Figure 3.3 (p. 97)Free-body diagram of a fluid
particle for which the important forces are those
due to pressure and gravity.
The physical interpretation is that a
change in fluid particle speed is
accomplished by the appropriate combination
of pressure gradient and particle weight along
the streamline.