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Chapter 8: Fluid Mechanics

Chapter 8: Fluid Mechanics. Learning Goal. To define a fluid. To distinguish a gas from a liquid. States of Matter. Solids – definite volume, definite shape Liquids – definite volume, indefinite shape Gases – indefinite volume, indefinite shape

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Chapter 8: Fluid Mechanics

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  1. Chapter 8:Fluid Mechanics

  2. Learning Goal • To define a fluid. • To distinguish a gas from a liquid

  3. States of Matter • Solids – definite volume, definite shape • Liquids – definite volume, indefinite shape • Gases – indefinite volume, indefinite shape • (Also plasma and Bose-Einstein condensates but we don’t need to worry about those.)

  4. What state of matter is glass? • Solid • Liquid • Gas

  5. What state of matter is honey? • Solid • Liquid • Gas

  6. The Nature of Fluids Fluids: • Liquids and Gases comprise the category of what we call fluids. • Fluids exhibit certain characteristics that solids do not – they flow when subjected to shear stress

  7. Properties of static fluids

  8. Learning Goal • To use density to describe a fluid. • To apply buoyant force to explain why some objects float or sink in a fluid.

  9. Static Fluid Properties • Density () = mass / volume • Viscosity = internal resistance to flow Note: Atmospheric pressure and temperature influence a fluid’s density and viscosity

  10. Density The density of an object is represented by: Density = mass / volume While this formula is familiar to us, we will use it in subsequent derivations.

  11. Specific Gravity • In order to have a constant comparison, we use specific gravity instead of density sometimes. • Since water has a density of 1 g/mL or 1 x 103 kg/m3, we eliminate the units and call the number specific gravity. • Ex. For iron which has a density of 7.86 g/mL, the specific gravity is 7.86 (or 7.86 as dense as water).

  12. Which is more dense, a pound of feathers or a pound of bricks? • A pound of bricks • A pound of feathers • They are the same

  13. Common Density Misconceptions • Let’s expel some common misconceptions about density. • Refer to your worksheet for the following Turning Point questions about whether the object will float or sink.

  14. A. (Refer to worksheet) • Sink • Float

  15. B. (Refer to worksheet) • Sink • Float

  16. C. (Refer to worksheet) • Sink • Float

  17. D. (Refer to worksheet) • Sink • Float

  18. E. (Refer to worksheet) • Sink • Float

  19. F. (Refer to worksheet) • Sink • Float

  20. G. (Refer to worksheet) • Sink • Float

  21. H. (Refer to worksheet) • Sink • Float

  22. I. (Refer to worksheet) • Sink • Float

  23. J. (Refer to worksheet) • Sink • Float

  24. Buoyancy • The upward force present when an object floats in a fluid, or feels lighter, is the buoyant force on the object. • The weight of an object immersed in a fluid is the apparent weight of the object (versus the actual weight). • Apparent weight = FG - FB

  25. Buoyant Force • FB = Fg (displaced fluid) = mfg • Magnitude of = weight of of buoyant force fluid displaced

  26. Apparent Weight • The apparent weight of an object is the net weight between the force of gravity and the buoyant force. Fnet = FB – Fg

  27. The apparent weight of an object in a fluid, FB – Fg , could also be called what? • Net Force • Tensional Force • Buoyant Force • Actual Weight

  28. If an object is sinking to the bottom of a glass of water, the buoyant force must be? • Equal to the Net Force • Less than Fg • More than Fg • Equal to Fg

  29. If an object is sinking to the bottom of a glass of water, the buoyant force must be? • Equal to the Net Force • Less than Fg • More than Fg • Equal to Fg

  30. What must be true for the buoyant force to be greater than gravitational force? • Object is floating continuously upward • Object is floating at the top of the fluid • Object is sinking

  31. Floating Objects • By Newton’s third law, if an object is floating, and there is a force downward due to acceleration of gravity, there must be an equal buoyant force upward to bring about equilibrium • Fb = Fw = mog

  32. Archimedes’ Principle • Displaced volume of a fluid is the increase in volume of a fluid due to the insertion of an object. • Archimedes’ Principle states that any object completely or partially submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced.

  33. If a rock is completely submerged in a fluid, what must be true? • The volume of the displaced fluid = the volume of the rock • The weight of the rock = weight of the fluid that was displaced. • Both 1 and 2 • None of the above

  34. If a raft is floating and is partially submerged in a fluid, what must be true? • The volume of the displaced fluid = the volume of the raft • The weight of the raft = weight of the fluid that was displaced. • Both 1 and 2 • None of the above

  35. Archimedes Principle example • A bargain hunter purchases a “gold” crown at a garage sale. 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 6.86N. Is the crown made of pure gold?

  36. Pressure in Fluids • Pressure occurs within fluids due to the constant motion of their molecules.

  37. Common Pressure Units • For example, standard atmospheric pressure is: • 14.7 psi (pounds per square inch) • 1.01 x 105 Pa (Pascal) = N/m2 • 760 mmHg (millimeters mercury) • 1 atm (atmosphere)

  38. Pressure cont. • Pressure is a measure of force per given area. • P = F / A • Karate Chop demo

  39. Bed of Nails

  40. Pascal’s Principle

  41. Pascal’s Principle • Because force is inversely proportional to area, one can vary the cross-sectional area to provide more force. • Eg. Hydraulic brakes, car jacks, clogging of arteries

  42. In order to use a lesser force to accomplish a difficult task, you should apply the force on the hydraulic cylinder with • Smaller radius • Larger radius • Doesn’t matter

  43. Ex. 2 • A car weighing 12000 N sits on a hydraulic press piston with an area of 0.90 m2. Compressed air exerts a force on a second piston, which has an area of 0.20m2. How large must this force be to support the car?

  44. Pressure as a function of depth

  45. Which hole will have the water shoot out the furthest? • Top hole • Middle Hole • Bottom Hole • All will be equal

  46. Absolute and Gauge Pressure • Absolute pressure = Atmospheric + Gauge Pressure Pressure • Atmospheric pressure is the pressure due to the gases in the atmosphere (always present) • Gauge pressure is the pressure due to a fluid (not counting atmospheric pressure) • Absolute pressure is the total pressure

  47. Ex. 3 • Calculate the absolute pressure at an ocean depth of 1,000m. Assume that the density of water is 1,025 kg/m3 and that Po= 1.01 x 105Pa. What is the gauge pressure as well?

  48. Laminar versus Turbulent Flow Laminar flow: • Low velocity relative to fluid medium • Streamline path Turbulent flow: • High velocity relative to fluid medium • Irregular Flow (Eddy currents)

  49. 15-6

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