MARTINDALE’S CALCULATORS ONLINE CENTER ENGINEERING CENTER FLUID MECHANICS – COMPUTATIONAL FLUID DYNAMICS (CFD) CENTER (Calculators, Applets, Spreadsheets, 
FLUID MECHANICS COURSE, LECTURES, ETC. WITH VIDEOS/MOVIES & AUDIO/SOUND
MARINE HYDRODYNAMICS COURSE, LECTURES, ETC .WITH VIDEOS/MOVIES & AUDIO/SOUND
LES of Turbulent Twophase Combustion Movies; LES of Turbulent Combustion Movies; LES of Cold Mixing Movies; Flames Interactions Movies; Pollutants Emission Movies; Supersonic Flows Movies; etc…” Unsteady Flow Calculations on Hybrid Grids
Jet Tumble Interaction in Piston Engine Movies; LES Computations of a Jet in Cross Flow (JICF) Movies; LES Computations of the Burner Swirl Flow Movies; Unsteady Turbulence Movies; etc…” Advanced Aerodynamics and Multiphysics
Aeroelasticity Movies; Unsteady Aerodynamics Movies; etc…” For more information see the
Freesurface Liquid Dynamics 2D Movies; Freesurface Liquid Dynamics 3D Movies; Industrial Application Movies; etc…” For more information see the
Introduction to the Study of Fluid Motion Video Lecture (Fluid Mechanics Terminology); Introduction to the Study of Fluid Motion Video Lecture (Experimental Fluid Dynamics); Fundamental Principles of Flows Video Lecture (Basic Concepts and Physical Relationships of Fluid Motion); Hunter Rouse – Fundamental Principles of Flows Video Lecture (Flow Dynamics); Fluid Motion in a Gravitational Field Video Lecture (Gravitational Waves); etc…” Examples of
Characteristics of the Laminar and Turbulent Flows Video Lecture (Boundary Layer Flows); Fundamental Principles of Flows Video Lecture (Cavitation); Effects of Fluid Compressibility (Elastic Waves); Characteristics of the Laminar and Turbulent Flows Video Lecture (Flow around an Airfoil); Fundamental Principles of Flows Video Lecture (Flow Separation); Fluid Motion in a Gravitational Field Video Lecture (Flow over Weirs); Fluid Motion in a Gravitational Field & Effects of Fluid Compressibility Video Lecture (Gravitational Waves); Fluid Motion in a Gravitational Field Video Lecture (Hydraulic Jump); Fundamental Principles of Flows Video Lecture (Propulsion); etc…” For more information see the
a particular film. Each is heavily illustrated with experimental scenes from the film…” Examples of “Illustrated Experiments in Fluid Mechanics” Video Lessons include
Cavitation Video; Channel Flow of a Compression Fluid Video; Deformation of Continuous Media Video; Eulerian Lagrangian Description Video; Flow Instabilities Video; Flow Visualization Video; Fluid Dynamics of Drag Part I, II, III, IV Videos; Fluid Quantity and Flow Video; Low Reynolds Number Flow Video; Magnetohydrodynamics Video; Pressure Fields and Fluid Acceleration Video; etc…” For more information see the
Chapter 3: Bernoulli Equation; Chapter 5: Mass, Momentum, and Energy Equations; Chapter 7: Dimensional Analysis and Modeling; etc…” Examples of “Mechanics of Fluids and Transport Processes” Course Chapter Videos include
Chapter 4 Videos
Chapter 5 Videos
Chapter 11 Videos
For more information see the
visualization project for the numerical study of stationary and nonstationary flows in two and three space dimensions which is designed for education and research…” Examples of “Virtual Album of Fluid Flow” Videos Subject Categories & Subcategories include
Channel Flow with Hills and Bumps Videos; Merger of Pipe Flows Videos; Flow around Balls Videos, Circles, Cylinders, etc. Videos; Flow around Vehicles Videos; Flow around Wings Videos; etc…” Incompressible Flow in Moving 2D Domains
Channel Flow with Moving Balls Videos; Channel Flow with Moving Flaps Videos; etc…” Incompressible NonNewtonian Flow in Fixed 2D Domains
Incompressible Flow in Fixed 3D Domains
Driven Cavity Flow Videos; etc…” Incompressible Flow in Moving 3D Domains
Numerical Laboratory
Hopper Videos; Heat exchanger Videos; etc…” For more information see

Chapter 3: Bernoulli Equation; Chapter 5: Mass, Momentum, and Energy Equations; Chapter 7: Dimensional Analysis and Modeling; etc…” Examples of “Mechanics of Fluids and Transport Processes” Course Chapter Videos include
Chapter 4 Videos
Chapter 5 Videos
Chapter 11 Videos
For more information see the
Stability of a Floating Body; Conservation of Mass, Momentum, and Energy in a Sluice Gate/Hydraulic Jump; Measurement of Velocity Profile and Head Loss/Friction Factor in Pipe Flow; Measurement of Pressure Distribution and Lift for an Airfoil; etc. For more information see the
Flow Transport and Interaction Processes…” Fluid Mechanics Topics/Processes Videos;
Discharge Coefficient…”
Pipe Diameter; Pipe Relative Roughness; Pipe Length from A to B; Elevation Gain from A to B; Fluid Density; Fluid Viscosity (Dynamic)…”
Characteristic Distance (or Pipe Diameter); Fluid Density; Fluid Viscosity (Dynamic)…”
For more information see

physical phenomena and/or engineering processes. A wide range of topics and advanced problemsolving techniques are discussed…” Examples of “Advanced Fluid Dynamics of the Environment” Course Chapters & Subchapters include
Lubrication Approximation for Flow in a Thin Layer; Release from a Pile on a Horizontal Plane; Aerosols and Coagulation; etc…” High Speed Flows and Boundary Layers
Two Dimensional Laminar Jet; Karman’s Momentum Integral Approach; Unsteady Boundary Layers; etc…” Heat and Mass Transport
Selective Withdrawal of Thermally Stratified Fluid; Dispersion of Suspension in a Steady Shear Flow; etc…” Instability
Inviscid Instability Mechanism of Parallel Flows; etc…” Flow and Transport in Porous Media
Geothermal Convection in Porous Media; Geothermal Plume; etc…” Coastal Geophysical Fluid Dynamics (GFD)
Steady Onshore Wind in a Shallow Sea; Cyclonic Current Forced by a Swirling Wind; Free Waves near a Coast in a Sea of Constant Depth; Transient Motion in a TwoLayered Sea; etc…” Surface Tension
Fluid Statics; Fluid Jets; etc…” For more information see
numerical methods with applicability to essentially any problem associated with a partial diﬀerential equation (PDE) or system of PDEs independent of type, spatial dimension or form of nonlinearity….” Examples of “Computational Numberical Analysis” Course Subject Categories & Subcategories include
TimeSplitting Methods for Evolution Equations; Various Miscellaneous Topics
Systems of PDEs; Numerical Solution of BlockBanded Algebraic Systems; CellRe and Aliasing Treatments; etc…” For more information see
are written to emphasize the mathematics of the Navier–Stokes (N.–S.) equations of incompressible ﬂow and the algorithms that have been developed over the past 30 years for solving them…..” Examples of “CFD of Incompressible Flow” Course Subject Categories include
Special Numerical Diﬃculties of the Navier–Stokes Equations; Solution Algorithms for the N.–S. Equations; etc…” For more information see
frustrating and important problems in all of classical physics. It is a fact that most ﬂuid ﬂows are turbulent, and at the same time ﬂuids occur, and in many cases represent the dominant physics, on all macroscopic scales throughout the known universe—from the interior of biological cells, to circulatory and respiratory systems of living creatures, to countless technological devices…” Examples of “Introductory Lectures on Turbulence: Physics, Mathematics and Modeling” Course Lectures include
Statistical Analysis and Modeling of Turbulence
The Kolmogorov Theory of Turbulence; etc. LargeEddy Simulation and MultiScale Methods
Dynamical Systems and MultiScale Methods; etc. For more information see
in the context of naval architecture and ocean science and engineering. Transport theorem and conservation principles. NavierStokes’ equation. Dimensional analysis. Ideal and potential flows. Vorticity and Kelvin’s theorem. Hydrodynamic forces…” Examples from over “24” “Marine Hydrodynamics” Course Lectures include
NavierStokes Equation; Similarity Parameters from Governing Equations; Vortex Structures, Bernoulli Equation; Vorticity Equation; Lifting Surfaces; Vortex Induced Vibrations; Turbulent Flow; Turbulent Boundary Layers and Model Testing; Water Waves; etc…” Includes over “25”
Cavitation Video; Channel Flow of a Compression Fluid Video; Deformation of Continuous Media Video; Eulerian Lagrangian Description Video; Flow Instabilities Video; Flow Visualization Video; Fluid Dynamics of Drag Part I, II, III, IV Video; Fluid Quantity and Flow Video; Low Reynolds Number Flow Video; Magnetohydrodynamics Video; Pressure Fields and Fluid Acceleration Video; etc…” For more information see
Climate Diagnostics; Climate Change, Variability and Prediction; Oceans and Climate; Weather and Atmospheric Dynamics; etc..”
The Stress Tensor for a Fluid and the Navier Stokes Equations; Frictional boundary layers; Fundamental Theorems: Vorticity and Circulation; Geostrophy, QuasiGeostrophy; Internal Waves and Instabilities; etc…” For more information see

Normal Shock Relations Calculator; Oblique Shock Relations Calculator For more information see
Thermal/Fluid Systems; etc…” For more information see
Liquid or Gas Pipe & Pump Curve Calculator (DarcyWeisbach); Water Pipe Calculator (HazenWilliams); Water Pipe & Pump Curve Calculator (HazenWilliams)…” Venturi, Nozzle, and Orifice Flow Meters Calculators include
Orifice Calculators (Liquids)…” Open Channels & Culverts Calculators include
Circular Culvert Calculator; Trapezoidal Channel Calculator; Rectangular Channel Calculators…”
Opstream Pressure; Downstream Pressure; Pressure Drop through Orifice; Kinematic Viscosity; Dynamic Viscosity; Upstream Temperature; Gas Constant; etc…” Examples from related Calculators include
forces to viscous (heavy and gluey) forces. From a detailed analysis of the momentum conservation equation, the inertial forces are characterized by the product of the density r times the velocity V times the gradient of the velocity dV/dx…” For more information see 
visualization project for the numerical study of stationary and nonstationary flows in two and three space dimensions which is designed for education and research…” Examples of “Virtual Album of Fluid Flow” Videos Subject Categories & Subcategories include:
Channel Flow with Hills and Bumps Videos; Merger of Pipe Flows Videos; Flow around Balls Videos, Circles, Cylinders, etc. Videos; Flow around Vehicles Videos; Flow around Wings Videos; etc…” Incompressible Flow in Moving 2D Domains
Channel Flow with Moving Balls Videos; Channel Flow with Moving Flaps Videos; etc…” Incompressible NonNewtonian Flow in Fixed 2D Domains
Incompressible Flow in Fixed 3D Domains
Driven Cavity Flow Videos; etc…” Incompressible Flow in Moving 3D Domains
Numerical Laboratory
Hopper Videos; Heat exchanger Videos; etc…” For more information see
Xenon, Sulfur Hexafluoride…” Mach Number; Pa; Initital Pressure; Driven Section; K;
Xenon, Sulfur Hexafluoride…” K; Initial Temperature; Driver Section. Gas Dynamics Calculator OUTPUT values include:
MW; Specific Heat Ratio; Initial Wave Speed; Reflected Wave Speed; etc…” Gas Dynamics TIMING ISSUES Calculator INPUT Values include:
Time Between Pressure Transducers; Distance Between Trigger Transducer and Window Centerline; etc…” Gas Dynamics TIMING ISSUES Calculator OUTPUT values include:
Estimated Delay Time for Membrane; etc…” Gas Dynamics BOOST TANK Calculator INPUT Values include:
Diaphragm Rupture Pressure; etc…” Gas Dynamics BOOST TANK Calculator OUTPUT values include:
For more information see the
shock wave parameters and microscopic and macroscopic parameters…” Gas Dynamics Calculator includes Normal Shock Calculator & Flow Regime Calculator:
Normal Shock Gas Dynamics Calculator output values includes:
For more information see 
THERMAL CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS
Stainless Steel; etc…” Thickness; Temperature…” For more information see
Fluid Properties: Thermal Fluid Properties Calculator; Heat Sinks: Natural Convection for Rectangular Heat Sinks Calculator; Special Functions Calculator
complementary error functions, gamma functions, and Bessel functions of integer or fractional order, etc. Spreading Resistance Calculators
Spreading Resistance of Rectangular Disk with Edge Cooling Calculator; etc…” For more information see the
conduction in a unit square with one boundary held at a different temperature than the other three and…” Planck’s Law Calculator
power for a number of source temperatures…” Radiation View Factors Calculators include:
Coaxial Disks Calculator; Coaxial Cylinders Calculator; Parallel Rectangles Calculator…” Solution of Blasius Equation Calculator
for flow in a laminar, selfsimilar, flat plate boundary layer. The RungeKutta integration scheme and shooting algorithm…” InternalFlow Convection Correlations Calculator
a circular pipe as a function of the Reynolds (based on diameter) and Prandtl numbers…” OneDimensional Compressible Flows Calculator
(2) Normal shock functions, (3) Flow with friction (Fanno Line), and (4) Flow with heat addition (Rayleigh Line)…” For more information see
the growth and subsequent collapse of microscopic bubbles. Due to the high pressures released during the collapse of the bubbles, energy can be emitted in the form of light, hence sonoluminescence. If the energy is great enough, it is thought that fusion reactions can be initiated, or sonofusion. Sonofusion or bubble cavitation is thought to be more correctly termed acoustic inertial confinement fusion…” Sonofusion Calculators include:
Kinetics of Fusion Calculators (concentration of deuterium atoms & neutron emission intensity); Heat Production Calculators For more information see
Boiler; Charged Fibers; Charged Particles; CO2 Sequestration; Coal Ash Deposition; CRCD; Fractured Rocks; Gas Hydrates; Glass Furnaces; Indoor Air; Nano Aerosols; Particle Resuspension; Powder Dispersion; Sediment Transportration Control; etc…” For more information see the
turbulent flow situation in pipes…” For more information see
For more information see
assumes that the distance from the larger diameter to the smaller is short enough that viscous losses can be neglected, and assumes…” For more information see the
the easiest to use, the cheapest to develop and very accurate instrument for flow rate measuring in pipe systems…” For more information see
Set Angle of Attack; Start Tunnel; etc…” For more information see

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