Lecture Slides: Lecture Fluid Mechanics

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The lecture slides of lecture Fluid Mechanics of the Modelling Course of Industrial Design of the TU Delft

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Lecture Slides: Lecture Fluid Mechanics

  1. 1. P-L-2 Fluid Mechanics Basic principles and concepts The Modelling Team Department of Design Engineering Faculty of Industrial Design Engineering Delft University of Technology Challenge the future 1
  2. 2. Aim Aim To develop a basic understanding of the properties of fluids; To show how fluids behave in a real environment To demonstrate that those simple behaviours might be modelled so as to provide useful data for designs To communicate with experts in their professional languages Challenge the future 2
  3. 3. Contents What is fluid? Basic properties of fluid Conservation of Mass Conservation of Energy Flow resistances Challenge the future 3
  4. 4. What is fluid? The Modelling Team Department of Design Engineering Faculty of Industrial Design Engineering Delft University of Technology Challenge the future 4
  5. 5. Fluid Fluid Gas Liquid Differences Ref. http://en.wikipedia.org/wiki/Fluid, Courtesy of http://eggfuel.ie/, http://allsizewallpapers.blogspot.com/2009/03/blue-water-widescreen-wallpaper.html Challenge the future 5
  6. 6. Fluid Fluid Gas Liquid Compressible Not compressible Ref. http://en.wikipedia.org/wiki/Fluid, Courtesy of http://eggfuel.ie/, http://allsizewallpapers.blogspot.com/2009/03/blue-water-widescreen-wallpaper.html Challenge the future 6
  7. 7. States of Matter Solid liquid Gas Challenge the future 7
  8. 8. Why is gas compressible? Liquid Shape of the container Fixed volume Free surface Distances between molecules in gas are much larger than liquid & Solid Solid Gas Holds shape Shape of the container Fixed volume Volume of the container Challenge the future 8
  9. 9. Basic properties of fluids Challenge the future 9
  10. 10. Density m  V water= 998 kg/m3(20°C) How about 4°C? air= 1.2 kg/m3(20°C) Ref. http://en.wikipedia.org/wiki/Properties_of_water, http://en.wikipedia.org/wiki/Density_of_air Challenge the future 10
  11. 11. Pressure F p A 1 pa (pascal) = 1 N/m2( named after Blaise Pascal) 1 bar = 100,000 pa ; 1 atm = 101,325 pa Courtesy of http://en.wikipedia.org/wiki/Blaise_Pascal Challenge the future 11
  12. 12. Case study: Pressure on the bottom of a tank Weight of the Water Area of the bottom Mass m  Density  Volume  ρ  bottom area  height   Ah Pressure Differential mg Agh p   gh form: dp   gdh A A h p h The basic Challenge the future 12
  13. 13. Viscosity – An example Water Measures “how thick” the fluid is Different types of fluid: Different viscosity Honey It is varying, for example, when honey is heated. Ref. http://en.wikipedia.org/wiki/Viscosity Challenge the future 13
  14. 14. Viscosity   u y u y Ref. http://en.wikipedia.org/wiki/Viscosity Challenge the future 14
  15. 15. Viscosity – examples Liquid (25°C) Viscosity (Pa*s) Water 8.94e-4 Blood(37°C) 3e-3 to 4e-3 Air 17.4e-6 Olive oil 0.081 Ketchup 50-100 Molten chocolate* 45-130 Honey 2-10 Oil (light) 1.1 Oil (heavy) 6.6 Gasoline 0.006 Ref. http://en.wikipedia.org/wiki/Viscosity Challenge the future 15
  16. 16. Ideal Gas Challenge the future 16
  17. 17. Physics behind – Boyle’s Law Boyle’s law PV1  PV2 1 2 Ref. http://www.antonine-education.co.uk/New_items/STA/Gas%20Laws/Gas_Laws.htm Courtesy of http://youareaflyonmywall.blogspot.com/2010/04/surviving-and-thriving-in-disaster.html Challenge the future 17
  18. 18. Case study: The bike pump The bike pump Question: How many full strokes are needed to pump a flat tyre to 2 bar (relative pressure) using a bike pump? We choose: 1. the pump has a cylindrical shape; The length is about 50 cm and the inner diameter is 30 mm; 2. the temperature of the pump, air and the tyre are constant during the process; the atmosphere pressure is 1 bar; 3. the tyre is torus-shaped, the volume of the tyre is 2.2 Liter. Challenge the future 18
  19. 19. Physics behind – Charles’ Law Ref. http://en.wikipedia.org/wiki/Charles's_law Challenge the future 19
  20. 20. Physics behind – Charles’ Law The Microwave Popcorn V1 V2  T1 T2 What is the unit of temperature? Ref. http://en.wikipedia.org/wiki/Charles's_law Challenge the future 20
  21. 21. Physics behind – When Boyle meets Charles Ref. http://en.wikipedia.org/wiki/Combined_gas_law Challenge the future 21
  22. 22. Physics behind – When Boyle meets Charles PV1  PV2 1 2 V1 V2  T1 T2 PV1 PV2 1  2 T1 T2 Ref. http://library.thinkquest.org/12596/combined.html http://en.wikipedia.org/wiki/Combined_gas_law Challenge the future 22
  23. 23. Flow rate Challenge the future 23
  24. 24. Liquid moves due to pressure differences Ref. http://www.freshgasflow.com/physics/flow/flow.html Challenge the future 24
  25. 25. Flow rate  m q Mass of liquid passing a given area Time Volume of liquid passing a given area Time  m  q Mass flow rate  Density  Volumetric flow rate kg s kg m3 kg   m3 s s Ref. http://www.freshgasflow.com/physics/flow/flow.html Challenge the future 25
  26. 26. Basic laws of fluid mechanics Challenge the future 26
  27. 27. Conservation of Mass  m1  m1   m1  m 2  0  A1v1t   A2 v2t  0 A1v1  A2 v2  0 Ref. http://www.grc.nasa.gov/WWW/K-12/airplane/mass.html Challenge the future 27
  28. 28. Case study: Garden spray Water Inlet: Diameter 0.012m Outlet: Diameter:0.004m The inlet water speed is 0.8m/s How about the outlet speed?  Inlet  Outlet Courtesy of www.gardena.com Challenge the future 28
  29. 29. Case study: Garden spray Cause Effect Water in Water out WaterOut  Waterin  0   mout  min  0,  Aout vout   Ain vin  0 2 2  Rout vout   Rin vin  0 vout 2 Rin  vin 2  7.2m / s Rout Challenge the future 29
  30. 30. Conservation of energy pa   gh a 2 va pb    gh 2  b v b2   Constant 2 For inviscid, adiabatic flow with no additional sources or sinks of energy, the higher the speed, the lower the pressure Ref. http://en.wikipedia.org/wiki/Bernoulli's_principle Challenge the future 30
  31. 31. Conservation of energy Ref. http://www.freshgasflow.com/physics/flow/flow.html Challenge the future 31
  32. 32. Conservation of energy pa   gh a 2 va pb    gh  2 b v b2   Constant 2 Ref. http://en.wikipedia.org/wiki/Bernoulli's_principle Challenge the future 32
  33. 33. Conservation of energy F  m dv  0 dt p  A  ( p  dp )  A  m  g   A  dp    A  dL  g  dh dv  m  0 dL dt dh dv    A  dL   0 dL dt  dp    g  dh    dL  dp dh F  0  pb   0  g  dh  v  dv  0  p dv dL  dL dt b b dp a   p  A  g  hb    b a  g  dh   g  (hb  h a b a v  dv  0 )  v 2 b  v 2 2 a  0 v b2 p v2  b  g  h b  b  Constant 2 2  Challenge the future 33
  34. 34. Case study: Torricelli's law Ref. http://en.wikipedia.org/wiki/Torricelli's_law Challenge the future 34
  35. 35. Case study: Torricelli's law 2 2 va pb vb  gha    ghb   2  2 pa pa va db ha pa  pb pb hb  0 if d a  db , va can be neglected vb  2 gha Ref. http://en.wikipedia.org/wiki/Torricelli's_law Challenge the future 35
  36. 36. Case study: Garden spray - pressure Water Inlet: Diameter 0.012m Outlet: Diameter:0.003m The inlet water pressure is 1.3bar How about the outlet speed?  Inlet  Outlet Courtesy of www.gardena.com Challenge the future 36
  37. 37. Case study: Garden spray Cause Effect Cause Effect Energy in Energy out Water in Water out 2 2   mout  min  0  vout 2 Rin  vin 2 Rout vin  0.87, vout  7.79 Challenge the future 37
  38. 38. Product – Venturi Masks The venturi mask is a medical device to deliver a known oxygen concentration to patients on controlled oxygen therapy. The color of the device reflects the delivered oxygen concentration, for example: blue = 24%; yellow = 28%; white = 31%; Green = 35%; pink = 40%; orange = 50%. oxygen therapy. Ref. http://en.wikipedia.org/wiki/Venturi_mask, http://www.flexicare.com/us/products/oxygen--aerosol-therapy/fixed-concentration/ventimask.aspx, http://boundtree.co.uk/index.php?route=product/product&product_id=1807 Challenge the future 38
  39. 39. Product – Venturi Masks Ref. http://en.wikipedia.org/wiki/Venturi_mask, http://www.flexicare.com/us/products/oxygen--aerosol-therapy/fixedconcentration/ventimask.aspx, http://boundtree.co.uk/index.php?route=product/product&product_id=1807 Challenge the future 39
  40. 40. Resistances Challenge the future 40
  41. 41. Bullet train Courtesy of http://bajansunonline.com/japans-new-bullet-train-debuts/ Challenge the future 41
  42. 42. Laminar vs Turbulent flow 1. Laminar flow occurs in smooth tubes and at LOW flow rates. 1. Turbulent flow flows in rough tubes and at higher flow rates. 2. Laminar is streamlined and there is no turbulence. The flow occurs in parallel layers, with minimal disruption between these layers. 2. The flow is not streamlined. There is a lot of swirling (eddies) of the fluid. 3. The flow is not greatest at the centre. Thus, as shown in red, the "velocity profile" of turbulent flow is more flat than that caused by laminar flow. 3. Laminar is greatest at the centre and diminishes towards the periphery. This makes the laminar flow describe a bullet shaped "velocity profile”. Ref http://www.freshgasflow.com/physics/flow/flow.html Challenge the future 42
  43. 43. Reynolds number In fluid mechanics, the Reynolds number (Re) is a dimensionless number that gives a measure of the ratio of inertial forces to viscous forces. mean velocity of the object relative to the fluid density of the fluid characteristic linear dimension dynamic viscosity of the fluid Ref: http://en.wikipedia.org/wiki/Reynolds_number Challenge the future 43
  44. 44. The meaning of Reynolds number The inertia force = Laminar • when Re < 2300 The viscous forces Transient • when 2300 < Re < 4000 Turbulent • when Re > 4000 Challenge the future 44
  45. 45. Laminar flow resistances of a level tube - Hagen–Poiseuille equation r L Ref. http://en.wikipedia.org/wiki/Hagen–Poiseuille_equation Challenge the future 45
  46. 46. Orifice resistances A discount from the ideal speed (Torricelli's law) Named: Discharge coefficient Ref. http://en.wikipedia.org/wiki/Torricelli's_law Challenge the future 46
  47. 47. Orifice resistances vb  2 gha pa db ha va vb  cd 2 gha pb  mb   Ab vb   Ab cd 2 gha  m   g h 1 2    C d 2  A2  p R Ref. http://en.wikipedia.org/wiki/Torricelli's_law Challenge the future 47
  48. 48. Case study – Garden rain water barrels Water in barrel Cylinder: Bottom area 0.2m2 Water height: 0.5m Orifice radius:0.02m Discharge coefficient of the orifice: 0.6 How long will the water stream last?  Earth  Orifice Courtesy of http://mymontys.com/wordpress/?m=201008 Challenge the future 48
  49. 49. Case study – Garden rain water barrels Cause Cause Cause Cause Gravity & Orifice Pressure Orifice Water lost in the barrel Effect Water level drops in the barrel Effect Effect Effect Water go out of orifice Slows the speed Water out from the orifice  m1    dh(t ) Abarrel dt  m2   Cd Aorifice 2 gh(t )    m1  m2 dh(t ) Abarrel   Cd Aorifice 2 gh(t ) dt Challenge the future 49
  50. 50. Case study – Garden rain water barrels MFR in relation of time R = 0.02m Bottom area A = 0.2m2 H = 0.5m Pa=1bar V Pb=1bar Challenge the future 50
  51. 51. Case study – Garden rain water barrels MFR in relation of time R = 0.02m Bottom area A = 0.2m2 H = 0.5m Pa=1bar V Pb=1bar Challenge the future 51
  52. 52. Industrial design applications Challenge the future 52
  53. 53. Applications Fluid mechanics Courtesy of http://www.ferrocompany.com/product-2884-BRT2.html http://brokenjpg.net/?tag=water-guns http://www.halebathrooms.co.uk/escale-wash-basin-cabinet-3220-p.asp http://suriptotitl.wordpress.com/2012/06/02/mixer/ http://www.connox.com/categories/cooking/tea/fruit-basket-teapot.html http://lakeannalife.com/outfitters.htm Challenge the future 53
  54. 54. Thank you The Modelling Team Department of Design Engineering Faculty of Industrial Design Engineering Delft University of Technology Challenge the future 54

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