AERODYNAMICS FOR ENGINEERING STUDENTS
FLUID MECHANICS IN CHEMICAL ENGINEERING GENERAL CONCEPTS OF A FLUID STRESSES, PRESSURE, VELOCITY, AND THE BASIC LAWS PHYSICAL PROPERTIES—DENSITY, VISCOSITY, AND SURFACE TENSION UNITS AND SYSTEMS OF UNITS EXAMPLE 1 1—UNITS CONVERSION EXAMPLE 1 2—MASS OF AIR IN A ROOM HYDROSTATICS EXAMPLE 1 3—PRESSURE IN AN OIL STORAGE TANK EXAMPLE 1 4—MULTIPLE FLUID HYDROSTATICS EXAMPLE 1 5—PRESSURE VARIATIONS IN A GAS EXAMPLE 1 6—HYDROSTATIC FORCE ON A CURVED SURFACE EXAMPLE 1 7—APPLICATION OF ARCHIMEDES’ LAW PRESSURE CHANGE CAUSED BY ROTATION EXAMPLE 1 8—OVER?OW FROM A SPINNING CONTAINER PROBLEMS FOR CHAPTER GENERAL CONSERVATION LAWS MASS BALANCES EXAMPLE 2 1—MASS BALANCE FOR TANK EVACUATION ENERGY BALANCES EXAMPLE 2 2—PUMPING N-PENTANE BERNOULLI’S EQUATION APPLICATIONS OF BERNOULLI’S EQUATION EXAMPLE 2 3—TANK FILLING MOMENTUM BALANCES EXAMPLE 2 4—IMPINGING JET OF WATER EXAMPLE 2 5—VELOCITY OF WAVE ON WATER EXAMPLE 2 6—FLOW MEASUREMENT BY A ROTAMETER PRESSURE, VELOCITY, AND FLOW RATE MEASUREMENT INTRODUCTION LAMINAR FLOW EXAMPLE 3 1—POLYMER FLOW IN A PIPELINE MODELS FOR SHEAR STRESS PIPING AND PUMPING PROBLEMS EXAMPLE 3 2—UNLOADING OIL FROM A TANKER SPECI?ED FLOW RATE AND DIAMETER EXAMPLE 3 3—UNLOADING OIL FROM A TANKER SPECI?ED DIAMETER AND PRESSURE DROP EXAMPLE 3 4—UNLOADING OIL FROM A TANKER SPECI?ED FLOW RATE AND PRESSURE DROP EXAMPLE 3 5—UNLOADING OIL FROM A TANKER MISCELLANEOUS ADDITIONAL CALCULATIONS FLOW IN NONCIRCULAR DUCTS EXAMPLE 3 6—FLOW IN AN IRRIGATION DITCH COMPRESSIBLE GAS FLOW IN PIPELINES COMPRESSIBLE FLOW IN NOZZLES COMPLEX PIPING SYSTEMS EXAMPLE 3 7—SOLUTION OF A PIPING/PUMPING PROBLEM PUMPS AND COMPRESSORS EXAMPLE 4 1—PUMPS IN SERIES AND PARALLEL DRAG FORCE ON SOLID PARTICLES IN FLUIDS EXAMPLE 4 2—MANUFACTURE OF LEAD SHOT FLOW THROUGH PACKED BEDS EXAMPLE 4 3—PRESSURE DROP IN A PACKED-BED REACTOR FILTRATION FLUIDIZATION DYNAMICS OF A BUBBLE-CAP DISTILLATION COLUMN CYCLONE SEPARATORS SEDIMENTATION DIMENSIONAL ANALYSIS EXAMPLE 4 4—THICKNESS OF THE LAMINAR SUBLAYER INTRODUCTION TO VECTOR ANALYSIS VECTOR OPERATIONS EXAMPLE 5 1—THE GRADIENT OF A SCALAR EXAMPLE 5 2—THE DIVERGENCE OF A VECTOR EXAMPLE 5 3—AN ALTERNATIVE TO THE DI?ERENTIAL ELEMENT EXAMPLE 5 4—THE CURL OF A VECTOR EXAMPLE 5 5—THE LAPLACIAN OF A SCALAR OTHER COORDINATE SYSTEMS THE CONVECTIVE DERIVATIVE DI?ERENTIAL MASS BALANCE EXAMPLE 5 6—PHYSICAL INTERPRETATION OF THE NET RATE OF MASS OUT?OW EXAMPLE 5 7—ALTERNATIVE DERIVATION OF THE CONTINUITY EQUATION DI?ERENTIAL MOMENTUM BALANCES NEWTONIAN STRESS COMPONENTS IN CARTESIAN COORDINATES EXAMPLE 5 8—CONSTANT-VISCOSITY MOMENTUM BALANCES IN TERMS OF VELOCITY GRADIENTS EXAMPLE 5 9—VECTOR FORM OF VARIABLE-VISCOSITY MOMENTUM BALANCE SOLUTION OF THE EQUATIONS OF MOTION IN RECTANGULAR COORDINATES EXAMPLE 6 1—FLOW BETWEEN PARALLEL PLATES ALTERNATIVE SOLUTION USING A SHELL BALANCE EXAMPLE 6 2—SHELL BALANCE FOR FLOW BETWEEN PARALLEL PLATES EXAMPLE 6 3—FILM FLOW ON A MOVING SUBSTRATE EXAMPLE 6 4—TRANSIENT VISCOUS DI?USION OF MOMENTUM (COMSOL) POISEUILLE AND COUETTE FLOWS IN POLYMER PROCESSING EXAMPLE 6 5—THE SINGLE-SCREW EXTRUDER EXAMPLE 6 6—FLOW PATTERNS IN A SCREW EXTRUDER (COMSOL) SOLUTION OF THE EQUATIONS OF MOTION IN CYLINDRICAL COORDINATES EXAMPLE 6 7—FLOW THROUGH AN ANNULAR DIE EXAMPLE 6 8—SPINNING A POLYMERIC FIBER SOLUTION OF THE EQUATIONS OF MOTION IN SPHERICAL COORDINATES EXAMPLE 6 9—ANALYSIS OF A CONE-AND-PLATE RHEOMETER ROTATIONAL AND IRROTATIONAL FLOWS EXAMPLE 7 1—FORCED AND FREE VORTICES STEADY TWO-DIMENSIONAL IRROTATIONAL FLOW PHYSICAL INTERPRETATION OF THE STREAM FUNCTION EXAMPLES OF PLANAR IRROTATIONAL FLOW EXAMPLE 7 2—STAGNATION FLOW EXAMPLE 7 3—COMBINATION OF A UNIFORM STREAM AND A LINE SINK (C) EXAMPLE 7 4—FLOW PATTERNS IN A LAKE (COMSOL) AXIALLY SYMMETRIC IRROTATIONAL FLOW UNIFORM STREAMS AND POINT SOURCES DOUBLETS AND FLOW PAST A SPHERE SINGLE-PHASE FLOW IN A POROUS MEDIUM EXAMPLE 7 5—UNDERGROUND FLOW OF WATER TWO-PHASE FLOW IN POROUS MEDIA WAVE MOTION IN DEEP WATER SIMPLI?ED TREATMENT OF LAMINAR FLOW PAST A FLAT PLATE EXAMPLE 8 1—FLOW IN AN AIR INTAKE (C) SIMPLI?CATION OF THE EQUATIONS OF MOTION BLASIUS SOLUTION FOR BOUNDARY-LAYER FLOW TURBULENT BOUNDARY LAYERS EXAMPLE 8 2—LAMINAR AND TURBULENT BOUNDARY LAYERS COMPARED DIMENSIONAL ANALYSIS OF THE BOUNDARY-LAYER PROBLEM BOUNDARY-LAYER SEPARATION EXAMPLE 8 3—BOUNDARY-LAYER FLOW BETWEEN PARALLEL PLATES (COMSOL) EXAMPLE 8 4—ENTRANCE REGION FOR LAMINAR FLOW BETWEEN FLAT PLATES THE LUBRICATION APPROXIMATION EXAMPLE 8 5—FLOW IN A LUBRICATED BEARING (COMSOL) POLYMER PROCESSING BY CALENDERING EXAMPLE 8 6—PRESSURE DISTRIBUTION IN A CALENDERED SHEET THIN FILMS AND SURFACE TENSION EXAMPLE 9 1—NUMERICAL ILLUSTRATION OF A REYNOLDS STRESS TERM PHYSICAL INTERPRETATION OF THE REYNOLDS STRESSES MIXING-LENGTH THEORY DETERMINATION OF EDDY KINEMATIC VISCOSITY AND MIXING LENGTH VELOCITY PRO?LES BASED ON MIXING-LENGTH THEORY EXAMPLE 9 2—INVESTIGATION OF THE VON K´ARM´AN HYPOTHESIS THE UNIVERSAL VELOCITY PRO?LE FOR SMOOTH PIPES FRICTION FACTOR IN TERMS OF REYNOLDS NUMBER FOR SMOOTH PIPES EXAMPLE 9 3—EXPRESSION FOR THE MEAN VELOCITY THICKNESS OF THE LAMINAR SUBLAYER VELOCITY PRO?LES AND FRICTION FACTOR FOR ROUGH PIPE BLASIUS-TYPE LAW AND THE POWER-LAW VELOCITY PRO?LE A CORRELATION FOR THE REYNOLDS STRESSES COMPUTATION OF TURBULENCE BY THE K–? METHOD EXAMPLE 9 4—FLOW THROUGH AN ORI?CE PLATE (COMSOL) EXAMPLE 9 5—TURBULENT FLOW IN AN OBSTRUCTED U-DUCT (COMSOL) ANALOGIES BETWEEN MOMENTUM AND HEAT TRANSFER EXAMPLE 9 6—EVALUATION OF THE MOMENTUM/HEAT- TRANSFER ANALOGIES TURBULENT JETS RISE OF BUBBLES IN UNCON?NED LIQUIDS EXAMPLE 10 1—RISE VELOCITY OF SINGLE BUBBLES PRESSURE DROP AND VOID FRACTION IN HORIZONTAL PIPES EXAMPLE 10 2—TWO-PHASE FLOW IN A HORIZONTAL PIPE TWO-PHASE FLOW IN VERTICAL PIPES EXAMPLE 10 3—LIMITS OF BUBBLE FLOW EXAMPLE 10 4—PERFORMANCE OF A GAS-LIFT PUMP EXAMPLE 10 5—TWO-PHASE FLOW IN A VERTICAL PIPE FLOODING INTRODUCTION TO FLUIDIZATION BUBBLE MECHANICS BUBBLES IN AGGREGATIVELY FLUIDIZED BEDS EXAMPLE 10 6—FLUIDIZED BED WITH REACTION (C) CLASSI?CATION OF NON-NEWTONIAN FLUIDS CONSTITUTIVE EQUATIONS FOR INELASTIC VISCOUS FLUIDS EXAMPLE 11 1—PIPE FLOW OF A POWER-LAW FLUID EXAMPLE 11 2—PIPE FLOW OF A BINGHAM PLASTIC EXAMPLE 11 3—NON-NEWTONIAN FLOW IN A DIE (COMSOL) CONSTITUTIVE EQUATIONS FOR VISCOELASTIC FLUIDS RESPONSE TO OSCILLATORY SHEAR CHARACTERIZATION OF THE RHEOLOGICAL PROPERTIES OF FLUIDS EXAMPLE 11 4—PROOF OF THE RABINOWITSCH EQUATION EXAMPLE 11 5—WORKING EQUATION FOR A COAXIAL- CYLINDER RHEOMETER: NEWTONIAN FLUID PHYSICS OF MICROSCALE FLUID MECHANICS PRESSURE-DRIVEN FLOW THROUGH MICROSCALE TUBES EXAMPLE 12 1—CALCULATION OF REYNOLDS NUMBERS MIXING, TRANSPORT, AND DISPERSION SPECIES, ENERGY, AND CHARGE TRANSPORT THE ELECTRICAL DOUBLE LAYER AND ELECTROKINETIC PHENOMENA EXAMPLE 12 2—RELATIVE MAGNITUDES OF ELECTROOSMOTIC AND PRESSURE-DRIVEN FLOWS EXAMPLE 12 3—ELECTROOSMOTIC FLOW AROUND A PARTICLE EXAMPLE 12 4—ELECTROOSMOSIS IN A MICROCHANNEL (COMSOL) EXAMPLE 12 5—ELECTROOSMOTIC SWITCHING IN A BRANCHED MICROCHANNEL (COMSOL) MEASURING THE ZETA POTENTIAL EXAMPLE 12 6—MAGNITUDE OF TYPICAL STREAMING POTENTIALS ELECTROVISCOSITY PARTICLE AND MACROMOLECULE MOTION IN MICRO?UIDIC CHANNELS EXAMPLE 12 7—GRAVITATIONAL AND MAGNETIC SETTLING OF ASSAY BEADS INTRODUCTION AND MOTIVATION NUMERICAL METHODS LEARNING CFD BY USING ANSYS FLUENT PRACTICAL CFD EXAMPLES EXAMPLE 13 1—FLUENT: DEVELOPING FLOW IN A PIPE ENTRANCE REGION EXAMPLE 13 2—FLUENT: PIPE FLOW THROUGH A SUDDEN EXPANSION EXAMPLE 13 3—FLUENT: A TWO-DIMENSIONAL MIXING JUNCTION EXAMPLE 13 4—FLUENT: FLOW OVER A CYLINDER REFERENCES FOR CHAPTER COMSOL MULTIPHYSICS—AN OVERVIEW THE STEPS FOR SOLVING PROBLEMS IN COMSOL HOW TO RUN COMSOL EXAMPLE 14 1—FLOW IN A POROUS MEDIUM WITH AN IMPERVIOUS HOLE (COMSOL) EXAMPLE 14 2—DRAWING A COMPLEX SHAPE (COMSOL) VARIABLES, CONSTANTS, EXPRESSIONS, AND UNITS BOUNDARY CONDITIONS VARIABLES USED BY COMSOL WALL FUNCTIONS IN TURBULENT-FLOW PROBLEMS STREAMLINE PLOTTING IN COMSOL SPECIAL COMSOL FEATURES USED IN THE EXAMPLES DRAWING TOOLS FLUID MECHANICS PROBLEMS SOLVABLE BY COMSOL CONCLUSION—PROBLEMS AND LEARNING TOOLS