notes on fluid mechanics.pdf - NOTES ON FLUID MECHANICS...

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NOTES ON FLUID MECHANICS Peter E. Clark Department of Chemical Engineering November 12, 2008 1
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Contents 1 Introduction 5 1.1 Review . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.1.1 Density . . . . . . . . . . . . . . . . . . . . . 6 1.1.2 Specific Gravity . . . . . . . . . . . . . . . . . 6 1.1.3 Specific Weight . . . . . . . . . . . . . . . . . 6 1.2 Newtonian Fluids . . . . . . . . . . . . . . . . . . . . 7 1.2.1 Shear Stress . . . . . . . . . . . . . . . . . . . 7 1.2.2 Shear Rate . . . . . . . . . . . . . . . . . . . . 7 1.2.3 Viscosity . . . . . . . . . . . . . . . . . . . . 8 1.3 Non-Newtonian Fluids . . . . . . . . . . . . . . . . . 9 1.3.1 Power Law Fluids . . . . . . . . . . . . . . . . 9 1.3.2 Bingham Plastic . . . . . . . . . . . . . . . . . 10 1.3.3 Herschel-Bulkley Fluids . . . . . . . . . . . . 11 1.3.4 Dilatant Fluids . . . . . . . . . . . . . . . . . 11 1.3.5 Time Dependent Fluids . . . . . . . . . . . . . 11 1.4 Kinematic Viscosity . . . . . . . . . . . . . . . . . . . 12 1.5 Surface Tension . . . . . . . . . . . . . . . . . . . . . 12 1.6 Pressure . . . . . . . . . . . . . . . . . . . . . . . . . 13 2 Fluid Statics 15 2.1 Basic Equation of Fluid Statics . . . . . . . . . . . . . 16 2.2 Pressure - Depth Relationships . . . . . . . . . . . . . 16 2.2.1 Constant Density Fluids . . . . . . . . . . . . 16 2.2.2 Variable Density Fluids . . . . . . . . . . . . . 17 2.3 Pressure Forces . . . . . . . . . . . . . . . . . . . . . 18 2.4 Buoyancy . . . . . . . . . . . . . . . . . . . . . . . . 19 2.5 Pressure Measurement . . . . . . . . . . . . . . . . . 20 2.5.1 Manometers . . . . . . . . . . . . . . . . . . . 20 2
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Contents 2.5.2 Bourdon Tube . . . . . . . . . . . . . . . . . . 23 2.5.3 Pressure Transducers . . . . . . . . . . . . . . 24 2.6 Accelerated Rigid-Body Motion . . . . . . . . . . . . 24 3 Balance Equations 27 3.0.1 Equation of Continuity . . . . . . . . . . . . . 28 3.1 Control Volume . . . . . . . . . . . . . . . . . . . . . 29 3.2 Fluid Velocity in a Confined Region . . . . . . . . . . 30 3.2.1 Flow Regimes . . . . . . . . . . . . . . . . . . 31 3.2.2 Plug or Creeping Flow . . . . . . . . . . . . . 32 3.2.3 Laminar Flow . . . . . . . . . . . . . . . . . . 33 3.2.4 Turbulent Flow . . . . . . . . . . . . . . . . . 33 3.3 Unsteady-State Mass Balances . . . . . . . . . . . . . 33 3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . 35 4 The First Law of Thermodynamics 37 4.1 Energy Transfer . . . . . . . . . . . . . . . . . . . . . 37 4.2 Energy Balance . . . . . . . . . . . . . . . . . . . . . 38 4.2.1 Sign Conventions . . . . . . . . . . . . . . . . 39 4.2.2 Potential Energy . . . . . . . . . . . . . . . . 39 4.2.3 Kinetic Energy . . . . . . . . . . . . . . . . . 40 4.3 Internal Energy . . . . . . . . . . . . . . . . . . . . . 40 4.4 Work . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . 41 5 Bernoulli Equation 43 5.1 Applying the Bernoulli Equation . . . . . . . . . . . . 44 5.2 Bernoulli Equation With Friction . . . . . . . . . . . . 47 5.3 Gas Flows . . . . . . . . . . . . . . . . . . . . . . . . 48 5.4 Non-Flow Work . . . . . . . . . . . . . . . . . . . . . 50 5.5 Flow Measurement . . . . . . . . . . . . . . . . . . . 50 5.5.1 Pitot Tube . . . . . . . . . . . . . . . . . . . . 51 5.5.2 Static Pitot Tube . . . . . . . . . . . . . . . . 52 5.5.3 Venturi Meter . . . . . . . . . . . . . . . . . . 53 5.5.4 Orifice Meter . . . . . . . . . . . . . . . . . . 54 5.5.5 Rotameters . . . . . . . . . . . . . . . . . . . 55 5.6 Unsteady Flows . . . . . . . . . . . . . . . . . . . . . 56 5.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . 60 3
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Contents 6 Fluid Friction in Steady One-Dimensional Flow 61 7 Momentum Balance 63 7.1 Newton’s Laws . . . . . . . . . . . . . . . . . . . . . 63 7.2 Control Volumes . . . . . . . . . . . . . . . . . . . . 63 7.3 Forces on a Control Volume . . . . . . . . . . . . . . . 65 7.4 Steady Flow . . . . . . . . . . . . . . . . . . . . . . . 66 7.5 Rotational Motion and Angular Momentum . . . . . . 73 7.5.1 Review . . . . . . . . . . . . . . . . . . . . . 73 4
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1 Introduction Outline 1. Review a) Density b) Specific gravity c) Specific weight 2. Newtonian Fluids a) Stress b) Strain c) Strain rate or shear rate d) Viscosity 3. Non-Newtonian Fluids a) Pseudoplastic b) Bingham Plastic c) Yield pseudoplastic or Herschel-Bulkly Fluid d) Dilatant e) Time dependent i. Rheopetic ii. Thixotropic 4. Kinematic Viscosity 5. Surface Tension 5
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1. Introduction 6. Pressure 7. Computer Problems 1.1 Review There are a few concepts that need to be reviewed to aid in understanding the text. 1.1.1 Density ρ = mass volume Units : kg m 3 ; g cm 3 : lb m ft 3 (1.1) Density is an extremely important property of matter. The density of a material can be considered continuous except at the molecular level. Density can also be thought of as the constant that relates mass to volume. This makes it easy to convert between the two. 1.1.2 Specific Gravity SG = ρ ρ re f Where ρ re f = 1000 kg m 3 ;1 g cm 3 ;62 . 4 lb m ft 3 ;8 . 33 lb m gal (1.2) Specific gravity is used instead of density to tabulate data for different materials. Using the specific gravity, the density in any set of units may be found by picking the reference density in the desired units.
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