Fluid Mechanics

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Fluid Mechanics

  1. 1. MECHANICS OF FLUIDS
  2. 2. FLUIDS Anything that can flow Liquid and Gases Fluid DynamicsFluid Static - Study of fluids in motion - study of fluids at rest
  3. 3. Density - ratio of mass of a substance to its volume V m =ρ ρ = density m = mass V = volume Unit: kg/m3
  4. 4. Density When the can is squeezed, the density increases. What will happen to its density?
  5. 5. Density
  6. 6. Pressure - force per unit area A F P = P = pressure F = force A = area Unit: N/m2 or Pa
  7. 7. Pressure
  8. 8. Pressure
  9. 9. Pressure It is the same any particular depth in liquid contained in vessels of different sizes or shape. 12 Pa 12 Pa 12 Pa
  10. 10. 1. Pascal’s Principle The pressure applied at any given point on a confined fluid is transmitted undiminished throughout the fluid. Application
  11. 11. 1. Pascal’s Principle The pressure applied at any given point on a confined fluid is transmitted undiminished throughout the fluid. Application This is much better!
  12. 12. 1. Pascal’s Principle The pressure applied at any given point on a confined fluid is transmitted undiminished throughout the fluid. 2 2 1 1 21 A F A F PP = =
  13. 13. 1. Pascal’s Principle F1 = 2500 N F2 = ? W = 10000 N A1 = 2 m2 A2 = 8 m2 2 2 1 1 21 A F A F PP = =
  14. 14. 2. Bernoulli’s Principle - As the velocity of the fluid increases, its pressure decreases
  15. 15. Buoyancy The fluid always go from high pressure area to low pressure area What will happen if the train passes on your side? Lower velocity Higher pressure Higher velocity Lower pressure
  16. 16. Buoyancy - upward force when object is submerge in fluid Buoyant force
  17. 17. 3. Archimedes’ Principle A body partly or entire submerged in a fluid is buoyed up by a force equal in magnitude to the weight of the displaced fluid. BF = Wair - Wwater BF = Wfluid displaced
  18. 18. Problems 1. An 80 kg metal cylinder 2m long and with each end of area 25 cm2 stands vertically on one end. What pressure does the cylinder exert on the floor? 2. A piston of cross-sectional area "a" is used in a hydraulic press to exert a small force of magnitude "f" on the enclosed liquid. A connecting pipe leads to a larger piston of cross- sectional area A. If the piston diameters are 3.80 cm and 53.0 cm, what force magnitude on the small piston will balance a 20.0 kN force on the large piston?
  19. 19. Problems 3. What is the maximum weight a solid, square, pinewood raft measuring 4.0 m on a side and 0.30 m thick support and still float in water? How much weight can we add in the raft so that it can still float? ρwood = 420 kg/m3 4. A solid aluminum cylinder, ρ = 2700 kg/m3 weighs 0.067 kg in air and 0.045 kg in turpentine. Determine the density of the turpentine.

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