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3.  STABILITY OF FLOATING BODY

4. 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)

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

6. 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?

7.  Measuring specific gravity by a hydrometer

8. 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

9. Stability of a completely immersed body – center of gravity below entroid. Stability of a completely immersed body – center of gravity above centroid.

11. 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)

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

13. 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:

16. 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.