What is a fluid? (Aa)
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Perfect Gas (Acd)
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Fluid statics(Cb)
Oceans at rest(Cc)
Fluid static forces(Cf)
Archimedes Principle(Cg)
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Archimedes Principle for a floating body(Ci)
Stability of a floating body(Cj)
Surface Tension(Ck)
Pressure differences due to Surface Tension(Cm)
Contact Angle(Cn)
Descriptions of Fluid Motion (Ba)
Descriptions of Fluid Motions (Baa)
Fluid Accelerations(Bab)
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Derivation of the Relation between the Time Derivatives (Bad)
Transport Thereom (Bae)
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Continuity equation in various coordinate systems (Bce)
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Streamlines, Pathlines and Streaklines (Bcg)
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Examples of streamfunctions (Bcj)
Newton's Law(Bd)
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Bernoulli's Equation (Bdg)
Energy Implications of Bernoulli's Equation (Bdh)
Momentum Theorem (Be)
Linear Momentum Theorem (Bea)
Example: Arbitrary Duct (Beb)
Example: Fire Hose Nozzle (Bec )
Example: Fire Hose with Bend (Bed)
Connection between drag and a wake (Bee)
Jet Engine (Bef)
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Angular Momentum Theorem (Beh)
Example: Pump or Turbine (Bei)
Steady one-dimensional internal flows (Bf)
Hydraulic System Analysis (Bfa)
Viscous Losses in Incompressible Fluid Flows (Bfb)
Viscous losses in pipes (Bfc)
Viscous Losses in Fittings (Bfd)
Diffusers and Nozzles (Bfe)
Incompressible Flows with External Energy Exchange (Bff)
Pumps and Turbines (Bfg)
Turbomachine Design (Bfh)
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Unsteady one-dimensional internal flows (Bn)
Introduction (Bna)
System Analysis(Bnb)
Quasistatic Stability Analysis(Bnc)
Quasistatic Stability Analyses(Bnca)
Turbomachine Surge(Bncb)
Ledinegg Instability(Bncc)
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Unsteady Bernoulli Equation(Bnd)
Unsteady Bernoulli Equation for a Pipe (Bnda)
Manometer Oscillations (Bndb)
Dynamic Instabilities(Bne)
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Cavitation Surge of Cavitating Pumps (Bneb)
Condensation Oscillations and Chugging (Bnec)
Time Domain Methods(Bnf)
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Wave Propagation in Ducts (Bnfb)
Method of Characteristics (Bnfc)
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Frequency Domain Methods(Bng)
Frequency Domain Methods (Bnga)
System with Rigid Body Vibration (Bngk)
Order of the System (Bngb)
Transfer Matrices (Bngc)
Distributed Systems (Bngd)
Combinations of Transfer Matrices (Bnge)
Properties of Transfer Matrices (Bngf)
Measurement of Transfer Matrices (Bngl)
Some Simple Transfer Matrices (Bngg)
Fluctuation Energy Flux (Bngh)
Non-Cavitating Pumps (Bngi)
Cavitating Inducers (Bngj)
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Cavitating Propeller (Bngn)
Incompressible, Inviscid, Irrotational Flow (Bg)
Potential Flow (Bga)
Methods of Solution of Laplace's Equation (Bgb)
Gravity Waves on a Liquid Surface (Bgc)
Separation of Variables (Cartesian) (Bgca)
Gravity Wave Boundary Conditions (Bgcb)
Gravity Waves on an Infinitely Deep Ocean (Bgcc)
Gravity Waves on an Finite-Depth Ocean (Bgcd)
Standing Gravity Waves (Bgce)
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Separation of Variables in Polar Coordinates (Bgda)
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The Free Vortex (Bgdc)
Sources and Sinks (Bgdd)
Planar Rankine Half-Bodies (Bgde)
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Potential Flow around a Cylinder (Bgdh)
Cylinder with Circulation in a Uniform Stream (Bgdi)
Lift and Drag in Potential Flow (Bgdj)
Kelvin Ovals (Bgdk)
Vortex Sheets (Bgdl)
Images and Walls (Bgdm)
Point Singularities (Bgdn)
Methods of Complex Variables (Bge)
Cauchy-Riemann Equations (Bgea)
Complex Variables for Planar Potential Flows (Bgeb)
Conformal Mapping (Bgec)
Joukowski Airfoils (Bged)
Flat Plate at an Angle of Attack (Bgee)
Axisymmetric Flow (Bgf)
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Axisymmetric Flow without Swirl (Bgfb)
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General Equations of Motion (Bh)
Stress Tensor (Bha)
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Constitutive Laws (Bhc)
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Navier-Stokes Equations (Bhf)
Navier-Stokes Equations in Cylindrical Coordinates (Bhg)
Navier-Stokes Equations in Spherical Coordinates (Bhh)
Vorticity Transport Equation (Bhi)
Exact Solutions to Navier-Stokes Equations (Bi)
Introduction to Exact Solutions of Navier-Stokes Equations (Bia)
Couette and Planar Poiseuille Flow (Bib)
Poiseuille Flow (Bic)
Radial Flow (Bid)
Vortex Flow (Bie)
Rayleigh and Ekman Flow (Bif)
Laminar Round Jet (Big)
Category 2 Solutions (Bih)
Boundary Layer Flows (Bj)
Introduction to Boundary Layer Flows (Bja)
Laminar Boundary Layer Equations (Bjb)
Exact Solutions to Laminar Boundary Layer Equations (Bjc)
Blasius Solution (Bjd)
Falkner-Skan Solutions (Bje)
Thicknesses and Surface Stress (Bjf)
Development of Laminar Boundary Layers (Bjg)
Karman Momentum Integral Equation (Bjh)
Approximate Methods (Bji)
Effect of Suction (Bjj)
Turbulence (Bk)
Introduction to Turbulence(Bka)
The Development of Turbulence(Bkb)
Linear Stability Analyses(Bkc)
Stability of Parallel Flows(Bkd)
Amplification of Disturbances(Bke)
Turbulence Spectra and Scales(Bkf)
Reynolds Stresses(Bkg)
Computing Turbulent Flows(Bkn)
Turbulence Models(Bkh)
Turbulent Couette Flow(Bki)
Law of the Wall(Bkj)
Turbulent Pipe Flows(Bkl)
Rough Pipe Flows(Bkm)
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Stokes Flow (Bl)
Introduction to Stokes Flow (Bla)
Equations of Stokes Flow (Blb)
Singularities (Blc)
Slender Body Theory (Bld)
Resistive Force Theory (Ble)
Planar Flow (Blf)
Axisymmetric Flow (Blg)
Unsteady Flows (Bm)
Introduction (Bma)
Added Mass (Bmb)
Introduction (Bmba)
Added Mass Matrix (Bmbb)
Fluid Acceleration far from the Body (Bmbc)
Values of the Added Mass (Bmbd)
Added Mass for Joukowski Airfoils (Bmbe)
Additional Effects on the Added Mass (Bmbf)
Vortex Shedding (Bmc)
Compressible Flow (Bo)
Prelimaries for Compressible Flow (Boa)
One-Dimensional Isentropic Flow (Bob)
Energy Equation (Boc)
Speed of Sound (Bod)
Isentropic Duct Flows (Boe)
Choked Flow (Bof)
Effect of Friction in Duct Flows (Bog)
Shock Waves (Boh)
Rocket Engines (Boi)
Two-dimensional Flows (Boj)
Planar Supersonic Flows for Small Turn Angles (Bok)
Prandtl-Meyer Expansion Fan (Bol)
Oblique Shock Wave (Bom)
Compressible Potential Flow (Bon)
Supersonic Potential Flow (Boo)
Prandtl-Glauert Mapping (Bop)
Open Channel Flow (Bp)
Introduction to Open Channel Flows (Bpa)
Gravity Waves Boundary Conditions (Bgcb)
Gravity Waves on an Infinitely Deep Ocean (Bgcc)
Gravity Waves on an Finite-Depth Ocean (Bgcd)
Standing Waves (Bgce)
Gravity Waves at Vertical Boundaries (Bgcf)
Finite Amplitude Waves(Bpb)
Hydraulic Jumps(Bpc)
Frictionless Flow(Bpd)
The Effect of Friction(Bpe)
The Shallow Water Wave Equations(Bpf)
Introduction to External Flows (Da)
Introduction (Daa)
Forces on Objects (Dab)
Introduction to Drag (Dba)
Relation between drag and the wake (Dbb)
Drag on a sphere or cylinder (Dbc)
Vortex generators (Dbd)
Form Drag (Dbe)
Skin Friction Drag (Dbf)
Wave Drag (Dbg)
Effects of Rotation (Dbh)
Introduction to Lift (Dca)
Magnus Effect (Dcb)
General Relation between Lift and the Circulation (Dcc)
Effects of Rotation (Dch)
The Flat Plate Airfoil (Dcd)
Planar Airfoil Performance (Dce)
Finite Span Performance (Dcf)
Aircraft Flight (Dcg)
Introduction to Propulsion (Dda)
Drag Propulsion (Ddb)
Propulsion Efficiency (Ddc)
Propeller Propulsion (Ddd)
Jet Propulsion (Dde)
Rocket Propulsion (Ddf)
Vortex Shedding(De)
Introduction to Vortex Shedding (Dea)
Animal Locomotion(Df)
Introduction to Animal Locomotion (Dfa)
High Reynolds Number Locomotion (Dfb)
Fish Locomotion (Dfd)
         Fish Swimming Videos
Bird Flight (Dfe)
Low Reynolds Number Locomotion (Dfc)
Prokaryotic Locomotion (Dff)
Flagellar Locomotion (Dfg)
         Flagella Videos
Ciliary Propulsion (Dfh)
         Cilia Videos
Internal flows and Mucus Propulsion (Dfi)
         Mucus Videos
Preparation for Experiments (Ka)
Design of Experiments (Kb)
Experimental Techniques (Kc)
Introduction (Kca)
Auto- and Cross-Correlation (Kcb)
Least Squares Fits (Kcc)
Instrumentation (Kd)
Introduction (Kda)
Flow Visualization (Kdb)
Introduction (Kdba)
Flow Tracers (Kdbb)
Particle Image Velocimetry (Kdbc)
Optical Techniques (Kdbd)
Flow Rate and Velocity (Kdc)
Introduction (Kdca)
Measurements using Bernoulli's Equation (Kdcb)
Electromagnetic Flow Meters (Kdcc)
Laser Velocimetry (Kdcd)
Acoustic Doppler Velocimetry (Kdce)
Vortex Shedding Flowmeter (Kdcf)
Pressure, Stresses and Sound     (Kdd)
Introduction (Kdda)
Manometers (Kddb)
Strain Gauges (Kddc)
Pressure Transducers (Kddd)
Acoustic Pressures (Kdde)
Forces (Kde)
Introduction (Kdea)
Force Balances (Kdeb)
Acceleration and Vibration (Kdf)
Other Fluid Measurements(Kdg)
Some Facilities (Ke)
Introduction (Kea)
Wind Tunnels (Keb)
Water Tunnels (Kec)
Towing Tanks (Ked)
Model Basins (Kee)
Introduction (Ma)
Introduction (Maa)
Turbomachines (Mab)
Turbomachine Design (Mac)
Cavitation (Mad)
Unsteady Flows (Mae)
Pumps (Mb)
Introduction (Mba)
Types of Pumps(Mbg)
Fluid Mechanics of Centrifugal and Axial Flow Pumps(Mbb)
Introduction (Mbbk)
Geometric Notation (Mbba)
Cascades (Mbbb)
Flow Notation (Mbbc)
Specific Speed (Mbbd)
Pump Geometries (Mbbe)
Energy Balance (Mbbf)
Idealized Non-cavitating Pump Performance (Mbbg)
Four-quadrant Performance (Mbbj)
Pumps in Parallel (Mbbh)
Pumps in Series (Mbbk)
Two-dimensional Performance Analysis(Mbc)
Linear Cascade Analyses(Mbcb)
Deviation Angle(Mbcc)
Viscous Effects in Linear Cascades(Mbcd)
Radial Cascade Analyses(Mbce)
Viscous Effects in Radial Flows(Mbcf)
Other Flow Features (Mbd)
Three-Dimensional Flow Effects (Mbdb)
Radial Equilibrium Example (Mbdc)
Discharge Flow Management (Mbdd)
Prerotation (Mbde)
Other Secondary Flows (Mbdf)
Introduction (Mbea)
Cavitation Parameters (Mbeb)
Cavitation Inception (Mbec)
Scaling of Cavitation Inception (Mbed)
Pump Performance (Mbee)
Types of Impeller Cavitation (Mbef)
Cavitation Inception Data (Mbeg)
Cavitation Bubble Dynamics (Mbew)
Cavitation Damage (Mbeh)
Mechanism of Cavitation Damage (Mbex)
Cavitation Noise (Mbei)
Cavitating Pump Performance (Mbej)
Inducer Designs (Mbem)
Inducer Performance (Mben)
Effects of Inducer Geometry (Mbep)
Analyses of Cavitation in Pumps (Mbeq)
Thermal Effect on Pump Performance (Mber)
Free Streamline Methods (Mbes)
Supercavitating Cascades (Mbet)
Partially Cavitating Cascades (Mbeu)
Cavitation Performance Correlations (Mbev)
         Inducer Cavitation Videos
         Pump Cavitation Videos
Pump Vibration (Mbf)
Frequencies of Oscillation(Mbfb)
Unsteady Flows(Mbfc)
Rotating Stall(Mbfd)
Rotating Cavitation(Mbfe)
Rotor-Stator Interaction: Flow Patterns(Mbfh)
Rotor-Stator Interaction: Forces(Mbfi)
Developed Cavity Oscillation(Mbfj)
Acoustic Resonances(Mbfk)
Blade Flutter(Mbfm)
Pogo Instabilities(Mbfn)
Turbines (Md)
Introduction (Mda)
Types of Turbines (Mdb)
Pelton Wheel (Mdc)
Impulse and Reaction Turbines (Mdd)
Basic Fluid Mechanics of Turbines (Mde)
Two-dimensional Analyses (Mdi)
Reaction Turbines (Mdj)
Propeller and Kaplan Turbines (Mdf)
Francis Turbine (Mdg)
Cavitation in Turbines (Mdh)
Fluid Couplings(Me)
Performance Analysis(Meb)
Reversible Fluid Coupling(Mec)
Rotordynamics of Fluid Machinery (Mc)
Introduction (Mca)
Notation (Mcb)
Hydrodynamic Bearings and Seals(Mcc)
Bearings at Low Reynolds Numbers(Mcd)
Annulus at High Reynolds Numbers(Mce)
Squeeze Film Dampers(Mcf)
Turbulent Annular Seals(Mcg)
Labyrinth Seals(Mch)
Blade Tip Rotordynamic Effects(Mci)
Steady Radial Forces(Mcj)
Effect of Cavitation(Mck)
Centrifugal Pumps(Mcm)
Moments and Lines of Action(Mcn)
Axial Flow Inducers(Mcp)
Propeller Cavitation(Mfe)
Propeller Cavitation Damage(Mff)
Cavitation Performance(Mfg)
Dynamic Characteristics(Mfh)
         Propeller Cavitation Videos
Flow Valves(Mg)
Hydraulic Valves (Mga)
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Introduction (Na)
Scope (Naa)
Multiphase Flow Models (Nab)
Multiphase Flow Notation (Nac)
Size Distributions (Nad)
Equations of Motion(Nb)
Averaging (Nba)
Conservation of Mass (Nbb)
Number Continuity Equation (Nbc)
Fick's Law (Nbd)
Equations of Motion (Nbe)
Disperse Phase Momentum Equation (Nbf)
On Disperse Phase Interaction(Nbg)
Equations for Conservation of Energy (Nbh)
Heat Transfer between Separated Phases (Nbi)
Interaction with turbulence (Nc)
Particle and Turbulence (Nca)
Effect on Turbulence Stability (Ncb)
On the equations of motion (Nd)
Comments (Nda)
Averaging (Ndb)
Averaging Contributions to the Mean Motion (Ndc)
Averaging in Pipe Flows (Ndd)
Modeling with the Combined Phase Equations (Nde)
Mass, Force and Energy Interaction Terms (Ndf)
Single particle motion (Ne)
Introduction (Nea)
Sphere Flow - High Reynolds Number (Neb)
Sphere Flow - Low Reynolds Number (Nec)
Molecular Effects (Ned)
Unsteady Particle Motions (Nee)
Effect of Concentration on Added Mass (Nef)
Unsteady Potential Flow (Neg)
Unsteady Stokes Flow (Neh)
Particle Equation of Motion (Nei)
Magnitude of Relative Motion (Nej)
Effect of Concentration on Particle Motion (Nek)
Effect of Concentration on Particle Drag (Nel)
Bubble or droplet translation (Nf)
Introduction (Nfa)
Dimensional Analysis of Deformation due to Translation (Nfb)
Bubble Shapes and Terminal Velocities (Nfc)
Marangoni Effects (Nfd)
Bjerknes Forces (Nfe)
Growing Bubbles (Nff)
Bubble growth and collapse (Ng)
Introduction (Nga)
Rayleigh-Plesset Equation (Ngb)
Bubble Contents (Ngc)
In the Absence of Thermal Effects (Ngd)
Stability of Vapor/Gas Bubbles (Nge)
Thermal Effects on Growth (Ngf)
Thermally Controlled Growth (Ngg)
Cavitation and Boiling (Ngh)
Bubble Growth by Mass Diffusion (Ngi)
Bubble Natural Frequencies (Ngj)
Nonlinear Effects (Ngk)
Rectified Mass Diffusion (Ngl)
Cavitation (Nh)
Introduction (Nha)
Cavitation Inception (Nhb)
Cavitation Bubble Collapse (Nhc)
Shape during Bubble Collapse (Nhd)
Cavitation Damage (Nhe)
Cavitating Bubble Shapes (Nhf)
Cavitation Noise (Nhg)
Cavitation Luminescence (Nhh)
Cavitation Chemistry (Nhi)
Vapor Explosions (Nhj)
         Bubble Dynamics Videos
Cavitating Flows (Nt)
Introduction (Nta)
Traveling Bubble Cavitation (Ntb)
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Experimental Observations (Ntd)
Large Scale Cavitation Structures (Nte)
Vortex Cavitation (Ntf)
Cloud Cavitation (Ntg)
Attached or Sheet Cavitation (Nth)
Cavitating Foils (Nti)
Cavity Closure (Ntj)
         Cavitating Flow Videos
Free Streamline Flows (Nu)
Introduction (Nua)
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Wall Effects and Choked Flows (Nud)
Steady Planar Flows (Nue)
Some Nonlinear Results (Nuf)
Linearized Methods (Nug)
Flat Plate Hydrofoil (Nuh)
Cavitating Cascades (Nui)
Three Dimensional Flows (Nuj)
Numerical Methods (Nuk)
Unsteady Flows (Nul)
Boiling and Condensation (Ni)
Introduction (Nia)
Pool Boiling on Horizontal Surface (Nib)
Nucleate Boiling on Horizontal Surface (Nic)
Film Boiling on Horizontal Surface (Nid)
Leidenfrost Effect (Nie)
Boiling on Vertical Surface (Nif)
Film Boiling on Vertical Surface (Nig)
Condensation (Nih)
Film Condensation (Nii)
Flow patterns (Nj)
Multiphase Flow Patterns (Nja)
Examples of Flow Regime Maps (Njb)
Slurry Flow Regimes (Njc)
Vertical Pipe Flow (Njd)
Flow Pattern Classifications (Nje)
Disperse Phase Separation and Dispersion (Njf)
Example: Horizontal Pipe Flow (Njg)
Particle Size and Particle Fission (Njh)
Examples of Flow-determined Bubble Size (Nji)
Bubbly or Mist Flow Limits (Njj)
Other Bubbly Flow Limits (Njk)
Other Particle Size Effects (Njl)
Stability of Disperse Mixtures (Njm)
Inhomogeneity Instability of Vertical Flows (Njn)
Kelvin-Helmholtz Instability (Njo)
Stratified Flow Instability (Njp)
Annular Flow Instability (Njq)
      Two-Component Flow Videos
      Three-Component Flow Videos
Energy conversion (Nk)
Introduction (Nka)
Disperse Horizontal Flow Friction (Nkb)
Homogeneous Flow Friction (Nkc)
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Vertical Flow Friction (Nke)
Two Component Separated Flow Friction (Nkf)
Friction with Phase Change (Nkg)
Multiphase Flow in Pumps (Nkh)
Homogeneous Flows(Nl)
Introduction (Nla)
Sonic Speed (Nlb)
Sonic Speed at Higher Frequencies (Nlc)
Sonic Speed with Phase Change (Nld)
Barotropic Relations (Nle)
Nozzle Flows (Nlf)
Vapor/Liquid Nozzle Flow (Nlg)
Condensation Shocks (Nlh)
Flows with bubble dynamics(Nm)
Introduction (Nma)
Basic Equations (Nmb)
Acoustics of Bubbly Mixtures (Nmc)
Comparison with Experiments (Nmd)
Normal Shock Waves in Bubbly Flows (Nme)
Shock Waves Structure (Nmf)
Oblique Shock Waves (Nmg)
Spherical Bubble Cloud Modes (Nmh)
Spherical Bubble Cloud Response (Nmi)
Flows with gas dynamics (Nn)
Introduction (Nna)
Equations for a Dusty Gas (Nnb)
Homogeneous Flow with Gas Dynamics (Nnc)
Velocity and Temperature Relaxation (Nnd)
Normal Shock Wave (Nne)
Acoustic Damping (Nnf)
Linear Stability of Laminar Flow (Nng)
Flow over a Wavy Wall (Nnh)
Small Slip Perturbation (Nni)
Sprays (No)
Introduction (Noa)
Ocean Spray (Nob)
Spray Formation by Bubbling (Noc)
Spray Formation by Wind Shear (Nod)
Spray Formation by Initially Laminar Jets (Noe)
Spray Formation by Turbulent Jets (Nof)
Single Droplet Mechanics (Nog)
Single Droplet Combustion (Noh)
Spray Combustion (Noi)
Granular flows (Np)
Introduction (Npa)
Particle Interaction Models (Npb)
Computer Simulations (Npc)
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Soil Liquefaction (Npu)
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Flow Regime Rheologies (Npe)
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Slow Granular Flow (Npg)
Mohr-Coulomb Models (Nph)
Hopper Flows (Npi)
Rapid Granular Flow (Npj)
Examples of Rapid Flow Equations (Npk)
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Rapid Flow Simulations (Npm)
Chute Flows (Npq)
Heat Transfer (Npr)
Effect of Interstitial Fluid (Npn)
Particle Collisions (Npo)
Classes of Interstitial Fluid Effects (Npp)
      Shear Flow Simulation Videos
      Chute Flow Simulation Videos
      Mixture Flow Simulation Videos
      Force Chain Videos
      Wave Propagation Videos
      Vibration Effects Videos
      Booming Dunes Videos
Drift flux models (Nq)
Introduction (Nqa)
Drift Flux Method (Nqb)
Vertical Pipe Flow (Nqc)
Fluidized Bed (Nqd)
Pool Boiling Crisis (Nqe)
Corrections for Pipe Flows (Nqf)
System instablities (Nr)
Introduction (Nra)
System Structure (Nrb)
Quasistatic Stability (Nrc)
Turbomachine Surge (Nrd)
Ledinegg Instability (Nre)
Geyser Instability (Nrf)
Concentration Waves (Nrg)
Dynamic Instabilities (Nrh)
Cavitation Surge in Pumps (Nri)
Chugging and Condensation Oscillations (Nrj)
Unsteady Internal Flow Methods (Nrk)
Transfer Functions (Nrl)
Uniform Homogeneous Flow (Nrm)
Non-Cavitating Pumps (Nrp)
Cavitating Inducers (Nrq)
Bubbly Flow Model for Cavitating Inducers (Nrt)
Cavitating Turbine (Nrr)
Cavitating Propeller (Nrs)
Kinematic waves(Ns)
Introduction (Nsa)
Kinematic Wave Analysis (Nsb)
Kinematic Wave Speed at Flooding (Nsc)
Kinematic Waves in Steady Flows (Nsd)
Kinematic Shock Waves (Nse)
Kinematic Shock Stability (Nsf)
Compressibility and Phase Change Effects (Nsg)
Batch Sedimentation (Nsh)
Dynamics of Cavitating Pumps (Nsi)
Two-dimensional Shocks (Nsj)
Numerical Methods (Oa)
Boundary Integral Methods (Ob)
Finite Difference Methods (Oc)
Finite Differences Example (Od)
Finite Element Methods (Oe)

Last updated 6/10/06.
Christopher E. Brennen