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Chapter 9

Chapter 9. Fluids and Buoyant Force. Fluids Substances which flow and change shape in the process. Both liquids and gases are fluids. Density  (Greek letter rho) Density  =m/V. Archimedes’ Principle.

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Chapter 9

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  1. Chapter 9 Fluids and Buoyant Force

  2. FluidsSubstances which flow and change shape in the process. • Both liquids and gases are fluids. • Density  (Greek letter rho) • Density =m/V

  3. 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 • FB (Buoyant force) =Fg (displaced fluid) = mfg

  4. Float or Sink? • Whether an object floats or sinks depends on the net force acting on it. This net force is the objects’ apparent weight • Fnet = FB –Fg(object) • If mo = mass of the submerged object then • Fnet = mfg – mog and since m = V • Then Fnet = (fVf –oVo)

  5. Table 9.1 page 319 • Densities for common objects. • For a floating object FB = Fg(object) = Mog Where FB is the buoyant force

  6. Floating Objects When an object floats in a fluid the net force is equal to zero. • Fnet = 0 = (fVf –oVo) • Or (f/o) = (Vo/Vf) • The ratio of the total volume of a floating object Vo to the submerged volume of the object Vf is equal to the ratio of the two densities. The displaced fluid can never be greater than the volume of the object itself.

  7. Floating Objects • The relationship between the weight of a submerged object and the buoyant force is • (Fg(object)/FB) = (o/f) • Because the volume of the object and the volume of the displaced fluid are equal. • See Example 9A

  8. Fluid Pressure and Temperature • Pressure = Force/Area • P = F/A • Pascal’s Principle: Pressure applied to a fluid in a closed container is transmitted equally to every point of the fluid and to the walls of the container.

  9. Fluid Pressure and Temperature • A small force F1 applied to a small piston of area A1 causes a pressure increase in a fluid. This pressure increase is transmitted to a larger piston of area A2 and the fluid exerts a force F2 on this piston. • Pincrease =(F1/A1) = (F2/A2)

  10. Fluid Pressure and Temperature • Therefore F2 = (A2/A1) • The force on the large piston is equal to the force applied to the small piston times the ratio of the area of the large piston to the area of the small piston. • See Example 9B

  11. Fluid Pressure and Temperature • Pressure varies with depth in a fluid. • Consider the submarine, the column of water above it exerts a pressure. The column has a volume equal to Area times height Ah. • The mass of the water is: • m = V = Ah

  12. Fluid Pressure and Temperature • The pressure at this depth due to the weight of the water is: • P = (mg/A) = (Vg/A) = (Ahg/A) • or P = hg • Therefore the absolute pressure is • P = Po - pgh Where Po is the atmospheric pressure,  equals density, g equals force do to gravity, and h equals depth.

  13. Fluid Pressure and Temperature • Therefore the Buoyant Force arises from the difference in fluid pressure between the top and the bottom of a submerged object.

  14. Fluids in Motion • A11 = A2 2 • Where A equals areas in region one and two, and  equals ( velocity) in each region.

  15. Fluids in Motion • Bernoulli’s Principle: the pressure of a fluid decreases as the fluids velocity increases. • P + (1/2)2 + gh = Constant Pressure + Kinetic Energy + Gravitational PE • If a fluid is static the kinetic energy is zero because of no velocity. • In a horizontal pipe the gravitational potential energy term equals zero.

  16. Properties of Gases • PV = NkBT • Where P equals pressure, V equals volume, N equals the number of gas particles, kB equals Boltzmanns Constant, and T equals the absolute temperature

  17. Properties of Gases • This is another form of an equation familiar to most of you: • The Ideal Gas Law • PV = nRT • In the Ideal Gas Law as T approaches 0 K the volume of an Ideal Gas approaches zero

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