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Chapter 9

Chapter 9. Fluids. Objectives for Today. Hydrostatic Pressure; P = r gh Buoyancy; Archimedes’ Principle F buoyancy = r g(Volume displaced) Pascal’s Equation P=F/A = f/a Continuity Equation A 1 V 1 =A 2 V 2 Bernoulli’s Equation P +1/2 r v 2 + r gh = constant. Density.

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Chapter 9

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  1. Chapter 9 Fluids

  2. Objectives for Today • Hydrostatic Pressure; P = rgh • Buoyancy; Archimedes’ Principle • Fbuoyancy = rg(Volume displaced) • Pascal’s Equation • P=F/A = f/a • Continuity Equation • A1V1=A2V2 • Bernoulli’s Equation • P +1/2 rv2 + rgh = constant

  3. Density • The density of a substance of uniform composition is defined as its mass per unit volume: • Units are kg/m3 (SI) or g/cm3 (cgs) • 1 g/cm3 = 1000 kg/m3

  4. Pressure • The force exerted by a fluid on a submerged object at any point if perpendicular to the surface of the object

  5. Variation of Pressure with Depth • If a fluid is at rest in a container, all portions of the fluid must be in static equilibrium • All points at the same depth must be at the same pressure • Otherwise, the fluid would not be in equilibrium (Think weather)

  6. Pressure and Depth • Examine the darker region, assumed to be a fluid • It has a cross-sectional area A • Extends to a depth h below the surface • Three external forces act on the region

  7. Pressure and Depth equation • Po is normal atmospheric pressure • = 101.3 kPa • = 14.7 lb/in2 • The pressure does not depend upon the shape of the container

  8. Pressure Units • One atmosphere (1 atm) = • 760 mm of mercury • 101.3 kPa • 14.7 lb/in2

  9. Pressure Calculation • Hoover Dam • Average Head • 158.5 meters of water • Max Pressure; • ??? Worksheet #1

  10. Pressure Calculation • P = Po + rgh • h=158.4 meters • r = 1000 kg/m3 • Pressure: • Po + rgh = 101.3KPa + 1000 x 9.8 x 158.5 Pa • = 101.3 KPa + 1,553,300 Pa • = 1655 KPa

  11. Why Black and White?

  12. Power turbines

  13. Downstream

  14. Video Clip

  15. Archimedes' Principle • Any object completely or partially submerged in a fluid is buoyed up by a force whose magnitude is equal to the weight of the fluid displaced by the object.

  16. Buoyant Force • The upward force is called the buoyant force • The physical cause of the buoyant force is the pressure difference between the top and the bottom of the object

  17. Archimedes’ Principle:Totally Submerged Object • The upward buoyant force is B=ρfluidVobjg • The downward gravitational force is w=mg=ρobjVobjg • The net force is B-w=(ρfluid-ρobj)gVobj

  18. Totally Submerged Object • The object is less dense than the fluid • The object experiences a net upward force

  19. Totally Submerged Object • The object is more dense than the fluid • The net force is downward • The object accelerates downward

  20. Archimedes’ Principle:Floating Object • Fbuoyancy = rg(Volume displaced) • The object is in static equilibrium. • The upward buoyant force is balanced by the downward force of gravity. • Volume of the fluid displaced corresponds to the volume of the object beneath the fluid level.

  21. Buoyancy in action Worksheet #2 Ship displacement 810 million N! 332 meters long How many cubic meters are displaced?

  22. Got milk? • Ship weighs 810 x 106 N = B • Density of water = 1000 kg/m3 • Volume of water displaced is • B=(810 x 106 )=Vdisp x (1000 x 9.8) • Vdisp = 82600 cubic meters or • 22 million gallons! B=rfluidgVdisp Vdisp=Wship/rwaterg

  23. Pascal’s Principle • A change in pressure applied to an enclosed fluid is transmitted undimished to every point of the fluid and to the walls of the container.

  24. Pascal’s Principle • The hydraulic press is an important application of Pascal’s Principle • Also used in hydraulic brakes, forklifts, car lifts, etc.

  25. Application Worksheet #3a

  26. Fluids in Motion:Streamline Flow • Streamline flow • every particle that passes a particular point moves exactly along the smooth path followed by particles that passed the point earlier • also called laminar flow • Streamline is the path • different streamlines cannot cross each other • the streamline at any point coincides with the direction of fluid velocity at that point

  27. Characteristics of an Ideal Fluid • The fluid is nonviscous • There is no internal friction between adjacent layers • The fluid is incompressible • Its density is constant • The fluid is steady • Its velocity, density and pressure do not change in time • The fluid moves without turbulence • No eddy currents are present

  28. Equation of Continuity • A1v1 = A2v2 • The product of the cross-sectional area of a pipe and the fluid speed is a constant • Speed is high where the pipe is narrow and speed is low where the pipe has a large diameter • Av is called the flow rate – what are its units?

  29. Application Worksheet #3b

  30. Bernoulli’s Equation Let’s take a minute to show how much you already know about this equation! Do a dimensional analysis -

  31. Bernoulli’s Equation What do the second and third terms look like? What happens we multiply by Volume?

  32. Conservation of energy • States that the sum of the pressure, the kinetic energy per unit volume, and the potential energy per unit volume has the same value at all points along a streamline.

  33. Application Worksheet #4

  34. Applications of Bernoulli’s Principle: Venturi Meter • Shows fluid flowing through a horizontal constricted pipe • Speed changes as diameter changes • Can be used to measure the speed of the fluid flow • Swiftly moving fluids exert less pressure than do slowly moving fluids

  35. Prairie Dogs • Build burrows with two openings • One is even with ground, the other built up, why?

  36. Breeze Prairie Dogs • He wants his family to have fresh air. • Apply Bernoulli’s Eq’n to a breeze over both holes.

  37. Breeze Prairie Dogs • How will the pressures over each hole compare? • What will this do the air in the tunnel?

  38. Questions? • Hydrostatic Pressure; P = rgh • Buoyancy; Archimedes’ Principle • Fbuoyancy = rg(Volume displaced) • Pascal; F/A=f/a • Continuity Equation • A1V1=A2V2 • Bernoulli’s Equation • P + 1/2 rv2 +rgh = constant

  39. Greek or Geek?

  40. Greek or Geek?

  41. Greek or Geek?

  42. Greek or Geek?

  43. Greek or Geek?

  44. Video Clip

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