Fluid Mechanics


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Fluid Mechanics

  1. 1. MET 306 Fluid Mechanics Lecture # 111/5/2012
  2. 2. ObjectiveDetermine Unit and DimensionsIdentify the key fluid properties used in the analysis of fluid behaviorCalculate common fluid properties given appropriate informationExplain effects of fluid compressibilityUse the concept of viscosity and surface tension11/5/2012
  3. 3. Unit and DimensionsA dimensions is used to measured the physical quantity with out numerical value.A unit is the way to assign a number to dimension  L= length is dimension  m= unit used for lengthTwo system of the fundamental dimension 1. FLT 2. MLT11/5/2012
  4. 4. Unit and Dimensions11/5/2012
  5. 5. Unit and DimensionsExample: m L 1 Velocity : LT s T Most of the fluid problem required the basic fundamental dimension witch (MLT) 2 Force : F ma MLT The equation of the velocity for uniformly acceleration body V Vo at Where: Vo is the initial velocity a is the acceleration11/5/2012 t is the time
  6. 6. Unit and DimensionsDimensionally homogeneousAll theoretically derived equation are dimensionally homogeneous that is thedimensions of the lift side of the equation must be the same as those on the right side. V Vo at 1 1 2 LT LT LT T 1 1 1 LT LT LT 1 1 LT 2 LT The equation of the velocity for uniformly acceleration body is dimensionally homogeneous and the 2 is a constant number11/5/2012
  7. 7. Unit and DimensionsDimensionally homogeneous Check whether this equation is dimensionally homogeneous or NOT 1-Equation of a freely falling body 2 d 16 . 1t Where d= distance t= time 2-Volume rate flow equation Where Q 0 . 61 A 2 gh Q= Flow rate A= Area g= gravity h= height11/5/2012
  8. 8. Systems of UnitsInternational System (SI)British gravitational system(BG)11/5/2012
  9. 9. Measures of Fluid Mass and Weight Density  The density of the fluid designated by Greek symbol (ρ)  Defined as a mass per unit volume  Used to characterize the mass of fluid  BG= slugs/ ft3 and SI= kg/m3 Specific Weight  The specific weight of the fluid designated by Greek symbol (γ)  Defined as weight per unit volume  Used to characterize the weight of the system  BG= lb/ ft3 and SI= N/m3 Specific Gravity  The specific gravity of the fluid designated by SG  Defined as a ratio of the density of the fluid to the density of the water  The density of the water @ 4oC is BG=1.94 slugs/ft3 and SI=1000 kg/m3 11/5/2012
  10. 10. Measures of Fluid Mass and WeightSpecific Gravity (Example) Calculate the density of the mercury in two system BG and SI by knowing the SGmercury @ 4oC is 13.5511/5/2012
  11. 11. Ideal Gas Law Gas are highly compressible in comparison to liquid, So from the Ideal gas law change in the temperature or the pressure of the gases can directly change the density. p R T Where p is the absolute pressure, ρ is the density, T is the absolute temperature and R is gas constant  R=R/m  R is universal gas constant 8314.3J/kg mole K  m is the molar mass11/5/2012
  12. 12. Ideal Gas LawExample The absolute pressure and temperature of a gas in large chamber are found to be 500 kPa and 60oC respectively. Find the density if the air has m =28.9711/5/2012s
  13. 13. Viscosity Dynamic viscosity BG and SI du Slug/ft s Kg/ms dy See Figure 1.1 SI Kinematic Viscosity v m2/s11/5/2012
  14. 14. Viscosity11/5/2012
  15. 15. Viscosity Example Determine the value of the Reynolds number using SI system for fluid with viscosity of 0.38 N.s/m2 and specific gravity of 0.91 flow into pipe with diameter of 25 mm with velocity of 2.6 m/s.11/5/2012
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  18. 18. Surface Tension At interface between a liquid and the gas forces develop in the liquid surface which case the surface to behave as “skin” or “membrane”11/5/2012
  19. 19. Surface Tension(σ) The pressure inside the drop can be calculated using free body diagram . The force developed around the edge due to the surface tension is 2πRσ this force must be balance by the pressure difference 2 2 R p R11/5/2012
  20. 20. Surface Tension(σ) 2 R 2 ϴ R h 2 R cos 2 R h h11/5/2012
  21. 21. Surface Tension(σ)Example What diameter of clean glass tubing is required to rise water at 20oC in tube to 1mm. Where σ of water is 0.0728 N/m and the θ =0.11/5/2012