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Reading Materials: Chapter 6

Reading Materials: Chapter 6 . Fluid Flow. LECTURES 16-18. What is a Fluid. Material that continually deforms under a shear stress Divided into two groups Liquid Gases. GASES.

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Reading Materials: Chapter 6

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  1. Reading Materials: Chapter 6 Fluid Flow LECTURES 16-18 CHEM ENG 1007

  2. What is a Fluid • Material that continually deforms under a shear stress • Divided into two groups • Liquid • Gases CHEM ENG 1007

  3. GASES Characterized as loosely-associated molecules which are normally not close together and which travel through space for long distances before colliding with each other. The velocity of their travel depends on the temperature of the gas. Characteristic of gases: Readily compressible Expand quickly and fill a container To convert from volume to mass/mole use PV=nRT CHEM ENG 1007

  4. LIQUIDS Characterized by molecules which are very close together and which are in collision with each other very frequently as they move around each other. The velocity of that motion and the rate of that collision depend on the temperature of the liquid. Characteristic of liquids: Slightly compressible Takes shape of container sides and bottom To convert from volume to mass/mole use Density = mass/volume CHEM ENG 1007

  5. Fluid-Like Systems Solids present in fluids • Slurries • fine particles suspended in liquid • Solids in a fluidized bed • particles moving with the fluid in a tall reactor. CHEM ENG 1007

  6. Density Flow rate Pressure Viscosity Surface tension Others Thermal conductivity Electrical conductivity Boiling point Freezing point Heat capacity Enthalpy Variables associated with fluids CHEM ENG 1007

  7. Flow Rate Rate at which a material is transported through a process line. • Mass flow rate: • Molar flow rate: • Volume flow rate: where: CHEM ENG 1007

  8. Pressure The pressure of the fluid is defined as the total force (exerted on the boundary by the fluid molecules) divided by the surface area of the boundary it is acting upon. CHEM ENG 1007

  9. Puzzle A woman’s high heels sink into the soft ground, but the larger shoes of the much bigger man do not. Pressure = force/area CHEM ENG 1007

  10. Pressure We express pressure in two ways: absolute and gauge pressures • Gauge Pressure: fluid pressure that is measured relative to the atmospheric pressure. • Absolute Pressure: the total magnitude of force exerted per unit area In process calculations: • Pabs = Pgauge + Patmosphere • Pabs = 0 in complete vacuum • Letter “a” or “g” is added to designate absolute or gauge, thus psia or psig CHEM ENG 1007

  11. Standard Atmospheric Pressure At sea level, 0oC and 45o latitude: Patm = 1 atm = 101,325 Pa = 14.7 psi = 1.01325 bars = 760 mmHg = 10.333 m H2O = 33. 9 ft H2O CHEM ENG 1007

  12. Standard Atmospheric Pressure How much does the atmosphere heigh? Answer: the same as 76 cm of mercury. How? Torricelli filled a tube with mercury and inverted it into an open container of mercury. Air pressure acting on the mercury in the dish can support a column of mercury 76 cm in height. CHEM ENG 1007

  13. Example 7.1 A man pumps his automobile tire until the tire gauge reads 34.0 psi. If the atmosphere in his community is 14.2 psia, what is the absolute pressure of the air in the tire? Solution: Pg = 34.0 psig Patm = 14.2 psia Pabs = 34.0 + 14.2 = 48.2 psia CHEM ENG 1007

  14. Hydrostatic Pressure It is the pressure (P) of the fluid at the base of the column. That is the force (F) exerted on the base divided by the base area (A). F thus equals the force on the top surface plus the weight of the fluid in the column. P = P0+ gh h = height of a hypothetical column of the fluid A pressure may also be expressed as a head of a particular fluid (Ph) Ph = P0 + h CHEM ENG 1007

  15. Example 7.2 For the tank depicted in Fig. 7.2, if the NaOH solution is 8 ft high, what is the pressure at the bottom of the tank? Assume that the density of the NaOH solution is the same as that of water. Perform the calculation in metric units. Solution: P1 = 0 Pa (gauge), so P2 = 23,896 Pa (gauge) or P2 = 23,896 + 101,325 = 125,221 Pa (absolute) CHEM ENG 1007

  16. Quick Quiz 1 What is the pressure 30.0 m below the surface of a lake? Assume the atmospheric pressure (the pressure at the surface) is 10.4 m H2O? Express your answer in atm. Solution: Ph = P0 + h = 10.4 + 30.0 = 40.4 m H2O CHEM ENG 1007

  17. Figure 3.4-3 (p. 57) of Felder and RousseauBourdon gauge. It is used to measured fluid pressure from nearly perfect vacuums to about 7000 atm. Fluid Pressure Measurement A hollow tube closed at one end and bent into a C configuration. The open end of the tube is exposed to the fluid whose pressure is to be measured. As the pressure increases, the tube tends to straighten, causing a pointer attached to the tube to rotate. CHEM ENG 1007

  18. Figure 3.4-4 (p. 58)Manometers. It is used for more accurate measurements of pressure (below about 3 atm) Fluid Pressure Measurement Gauge pressure Pressure difference Absolute pressure CHEM ENG 1007

  19. Figure 3.4-5 (p. 58)Differential Manometer variables. Fluid Pressure Measurement If  is gas then  may be neglected CHEM ENG 1007

  20. Illustration 1 A manometer reading gives 100 mmHg, calculate the absolute pressure. Solution: Measured gauge pressure: Pabs = 13,328 + 101,325 = 114,653 Pa = 115 kPa CHEM ENG 1007

  21. How does pressure relate to flow? In the absence of other forces, fluids tend to flow from regions of high pressure to regions where the pressure is lower. Therefore, pressure differences provide a driving force for fluid flow. Example: when a tire is punctured, air flows out of the high pressure tire to the atmosphere, which is a low pressure. CHEM ENG 1007

  22. Viscosity (m) Characterises its resistance to flow • A measure of “stickiness” of a fluid • A “frictional force” Low viscosity fluid High viscosity fluid Less energy required for mixing More energy required for mixing CHEM ENG 1007

  23. Viscosity (m) • Measurement - “Shear stress/shear rate” • Units • SI: kg/(m.s) = N.s/m2 = Pa.s • cgs: cp (centipoise) • 1 cP = 10-2 poise = 10-3Pa.s = 1 mPa.s CHEM ENG 1007

  24. Viscosity of various fluids CHEM ENG 1007

  25. Viscosity of various fluids • Substance (25°C) Viscosity (Pa.s) • Water 1 x 10-3 • Mercury 1.5 x 10-3 • Air 1.8 x 10-5 • Castor oil 0.99 CHEM ENG 1007

  26. Kinematic viscosity The property viscosity may also be combined with the fluid’s density to give the property kinematic viscosity CHEM ENG 1007

  27. Types of viscous fluids CHEM ENG 1007

  28. Types of viscous fluids • Newtonian fluid • e.g. water, air, other gases. • 2-4 Non-Newtonian fluids • Bingham-plastic. • e.g. toothpaste, margarine, soap • Pseudo-plastic (shear thinning) • e.g. mayonnaise, polymer melts, paints. • Dilatant (shear thickening) • e.g. wet beach sand, starch in water CHEM ENG 1007

  29. Shear stress Viscosity Examples Water Glycerine Alcohol Air Shear rate Shear rate Newtonian fluids Question: How would you determine the viscosity from a plot of shear stress against shear rate? With Newtonian fluids, shear stress increases proportionately with the shear rate CHEM ENG 1007

  30. Pseudoplastic Viscosity Shear rate Other types of Non-Newtonian fluids Dilatant Viscosity Shear rate Viscosity changes with power input CHEM ENG 1007

  31. Other types of Non-Newtonian fluids Thixotropic Rheopetic Viscosity Viscosity Time Time Viscosity changes with time at constant shear rate CHEM ENG 1007

  32. Non-Newtonian fluids can have more than one property Non-Newtonian fluids Example: • Damp gypsum • Pseudoplastic, Thixotropic and Viscoelastic • Cream • Dilatant, Rheopectic and not Viscoelastic Viscoelastic: Fluid returns to original viscosity after power input ceases CHEM ENG 1007

  33. Ideal / Inviscid Fluid Hypothetical fluid which is incompressible and has zero viscosity. CHEM ENG 1007

  34. Fluid Flow Principles • Flow patterns vary with: • velocity • geometry of surface, and • fluid properties such as viscosity, density. Classic experiment by Osborne Reynolds (1883) observed two types of fluid flow: • Laminar flow – low flow rates • Turbulent flow – higher flow rates CHEM ENG 1007

  35. Reynolds’ experiment (i) Low flow rates: fluid moves in parallel layers. (ii) High flow rates: cross currents (eddies) develop CHEM ENG 1007

  36. Reynolds Number Reynolds’ key variables Arrange into single “dimensionless group”: CHEM ENG 1007

  37. Reynolds Number For pipe flow: Re < 2,100 - laminar flow 2,100 < Re < 10,000 - transition region Re > 10,000 - turbulent flow Pipe-flow systems with the same Re are said to be dynamically similar. CHEM ENG 1007

  38. Illustration 2 Fluid flow through a pipe Water at 25oC flows through a pipe of internal diameter 0.1 m at a velocity 0.2 m/s. • Is the flow laminar flow or turbulent? • What is the effect of reducing the velocity by a factor of 10? CHEM ENG 1007

  39. Solution CHEM ENG 1007

  40. (i) Laminar Flow Velocity Profiles: Laminar Flow • Velocity profile is parabolic with the maximum velocity occurring in the centre of the pipe (r = 0) CHEM ENG 1007

  41. Velocity Profiles: Laminar Flow L R r (i) Velocities of a fluid in laminar flow through a circular pipe CHEM ENG 1007

  42. Velocity Profiles: Laminar Flow • Volumetric flow rate: • Mean velocity: CHEM ENG 1007

  43. Velocity Profiles: Turbulent Flow • Difficult to mathematically model due to its complex and rapidly changing flow patterns. • Experimental measurements show for time-averaged velocity and mean velocity (ii) Turbulent Flow CHEM ENG 1007

  44. Velocity Profiles: Plug Flow • Common assumption for highly turbulent flow is that velocity does not vary over cross-section: (iii) Plug Flow CHEM ENG 1007

  45. Mass Conservation in Fluid Flow Consider steady-state, one-dimensional fluid through pipe CHEM ENG 1007

  46. Mass Conservation in Fluid Flow Is v2 in (a) less than v2 in (b)? No, they are both the same. CHEM ENG 1007

  47. Fluid Friction • Frictional force cause pressure drop during fluid flow through a constant diameter horizontal pipe. • Consider flow situation in pipe below. CHEM ENG 1007

  48. Fluid Friction Momentum balance: f = friction factor; L = length of pipe; D = diameter of pipe; CHEM ENG 1007

  49. Fluid Friction CHEM ENG 1007

  50. Example 7.7 • What value of the friction per mass of fluid (ef) is necessary to cause a decrease in pressure equal to • 10 psi (answer in Btu/lbm)? CHEM ENG 1007

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