Ch. 9 Fluid Mechanics

1. Ch. 9Fluid Mechanics pgs. 317 - 342

2. Fluids • A non solid state of matter • Have the ability to flow • Atoms or molecules are free to move past each other • Can alter their shape

3. Fluids • Liquids have a definite volume • Gases do not have a definite volume

4. Mass Density () • When describing fluids, the mass density is the mass per unit volume of a substance • Units are kg/m3 • Mass density is often just called density • Should remember this from Chemistry

5. Mass Density () • Volume (V) has units of m3

6. Mass Density • Liquids are almost incompressible, so their densities change very little with pressure • Gases are compressible and can have densities over a wide range of values

7. Buoyant Force (FB) • Fluids exert an upward force on objects that are partially or completely submerged in it • Keeps objects afloat • Acts in the opposite direction of the force of gravity • Which means floating is a type of equilibrium An upward force counteracts the force of gravity for these objects. This upward force is called the bouyant force.

8. Floating Objects • The density of an object determines the depth of submersion • For an object to float, the object’s density can never be greater than the density of the fluid • Objects can still sink if the buoyant force is not enough to keep it afloat

9. Floating Objects • Buoyant force = Weight of floating object • When an object floats in a fluid, the net force is zero • If the object’s density is less than the fluid density, the net force is positive (upward) and the object floats.

10. Floating Objects • When an object floats in a fluid, the net force is zero • If the object’s density is less than the fluid density, the net force is positive (upward) and the object floats.

11. Submerged Objects • Apparent Weight • Objects submerged in a fluid have a net force on them that is smaller than their weight. • Whether an object floats or sinks depends on the net force

12. Archimedes’ Principle • Any object completely or partially submerged in a fluid experiences an upward buoyant force equal in magnitude to the weight of the fluid displaced by the object.

13. Archimedes’ Principle • The apparent weight of a submerged object depends on density. • When submerged, the volumes are equal. • The net force is the apparent weight of the object • Fnet = Fg (object) – FB

14. Archimedes’ Principle • Archimedes’ Principle is applied to the net force (remember that m = ρV), so • Fnet = Fg – FB • Fnet = mog – mfg • Fnet = (ρoVo – ρfVf)g

15. Archimedes’ Principle • If the object floats on the surface, we know for a fact Fbuoy = mg! The volume of displaced water equals the volume of the submerged portion of the ship.

16. Submerged Objects • The apparent weight of a submerged object depends on density • When submerged, the volumes are equal. Using Archimedes’ Principle: • Fnet = ρoVog – ρfVfg • Fnet = ρog – ρfg

17. Buoyant Force • Buoyancy can be changed by changing average density • A fish can adjust its average density by inflating or deflating an organ called a swim bladder • The ballast tank of a submarine works in the same way as the swim bladder of a fish

18. Buoyant Force • If the object and fluid densities are the same, the object floats suspended underwater. • If the object’s density is greater than the fluid density, the net force is negative (downward) and the object sinks

19. A bargain hunter purchases a “gold” crown at a flea market. After she gets home, she hangs the crown from a scale and finds its weight to be 7.84 N. She then weighs the crown while it is immersed in water, and the scale reads 6.86 N. Is the crown made of pure gold? (Density of fresh water is 1x103 kg/m3 and density of gold is 19.3 x 103 kg/m3)