1. 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 ( BC)

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

3. 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?

4. Example 2
Measuring specific gravity by a hydrometer

5. 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

6. 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.

7. Stability of a floating body

8. Elementary Fluid Dynamics
• Newton’s 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)

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

10. 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:

11. Force balance on a Streamline

13. 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.