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Dimensionless Numbers Glossary

A        

  • A - B - C - D - E - F - G - H - I - J - K - L - M - N - O - P - Q - R - S - T - U - V - W - X - Y - Z
  • Abbe Number  -  The measure of material's dispersion (variation of refractive index versus wavelength) with high values of V indicating dispersion.  It is used to classify glass and other optically transparent materials.
  • Aeration Number  -  Is used for the agitated mixing of gas and liquids.
  • Air–fuel Ratio  -  The mass ratio of air to fuel mixture present in an internal combustion engines.
  • Alfven Number  -  Describe the ratio of the flow velocity of a plasma or fluid to the Alfvén speed.  The Alfvén speed is the speed at which magnetic disturbances propagate through a magnetized plasma, and it depends on the magnetic field strength and the medium's density.
  • Algebric Difference in Grade  -  The difference in grades.
  • Annual Fuel Utilization Efficiency  -  Measure the efficiency of a gas furnace or boiler will operate over an entire heating season.
  • Archimedes Number  -  Analyzes flow as it relates to a system of density differences.  It is used when dealing with gravitational settling of particles in fluid.
  • Arrhenius Equation  -  Where the temperature dependance of the reaction rateconstant which is the rate of chemical reaction.
  • Atomic Number  -  Equal to the number of protons in an atom's nucleus. The atomic number determines which element an atom is.
  • Atwood Number  -  Describes density difference between two adjacent fluids with a common interface.

B         

  • A - B - C - D - E - F - G - H - I - J - K - L - M - N - O - P - Q - R - S - T - U - V - W - X - Y - Z
  • Bagnold Number  -  The ratio of grain collision stresses to various fluid stresses in a granular flow with interstitial Newtonian fluid.
  • Bejan Number - Fluid Mechanics  -  The pressure drop along a length of channel.
  • Bejan Number - Heat Transfer  -  The pressure drop along a channel of length.
  • Bejan Number - Mass Transfer  -  The pressure drop along a channel of length.
  • Bingham Number  -  The ratio of yield stress to visvous stress.  In fluid dynamics and rheology to characterize the flow behavior of certain types of fluids known as Bingham fluids.  Bingham fluids exhibit a yield stress, which means they require a certain amount of applied force (stress) before they start to flow.  Once this yield stress is exceeded, the fluid behaves like a viscous fluid and flows freely.
  • Biot Number  -  The ratio of internal thermal resistance of solid to fluid thermal resistance.  This is used for heat transfer between fluids and solids.
  • Blake Number  -  Is proportional to inertial force and viscous force and is used in momentum transfer and flow through beds of solids.
  • Bodenstein Number  -  Used in mass transfer and diffusion in reactors calculations in particular.
  • Bond Number  -  Describe the relationship of gravitational force to surface tension force in a fluid system.  It is commonly used to analyze the behavior of fluids or fluid interfaces, especially in situations where surface tension plays a significant role.
  • Brinkman Number  -  The heat conduction from a wall to a flowing viscous fluid, comminly used in polymer processes.
  • Brownell-Katz Number  -  The balance between the forces driving fluid flow and those resisting it, aiding in the design and analysis of processes like enhanced oil recovery or groundwater flow.  While a precise mathematical definition can vary depending on the specific application, it generally takes the form of a product or ratio involving the Capillary Number (which compares viscous forces to surface tension) and the Bond Number (which compares gravitational forces to surface tension).
  • Buckling Coefficient  -  Is an instability that leads to a failure mode.

C         

  • A - B - C - D - E - F - G - H - I - J - K - L - M - N - O - P - Q - R - S - T - U - V - W - X - Y - Z
  • Capillary Number  -  Representing the relative effect of viscous forces against the surface tension between a liquid/gas or liquid/liquid interface.  It is the ratio of viscous forces to surface tension forces.  It's particularly relevant when dealing with fluid flows in small-scale or capillary systems, where surface tension effects become more pronounced.  The capillary number helps determine whether the fluid behavior will be dominated by viscous effects or by surface tension effects. 
  • Carnot Efficiency  -  The theroetical maximum efficiency of any heat engine depending only on the temperatures it operates between.
  • Cauchy Number  -  The ratio of inertial force to compressibility force in a flow.  When the compressibility is important the elastic forces must be considered along with inertial forces.
  • Cavitation Number  -  Expresses the relationship between the difference of a local absolute pressure from the vapor pressure and the kinetic energy per volume.
  • Chandrasekhar Number  -  Used in magnetic convection to represent ratio of the Lorentz force to the viscosity.
  • Chezy Coefficient  -  Dependent on surface roughness and the hydraulic mean depth.
  • Coefficient of Discharge  -  See Discharge Coefficient
  • Coefficient of Friction  -  See Friction Coefficient
  • Coefficient of Kinetic Friction  -  See Kinetic Friction Coefficient
  • Cohesion Number  -  Used in partical tchnology by which the cohesivity of different powders can be compared.
  • Colburn J Factors  -  Heat transfer equation to calculate the natural convection moment of heat from vertical surfaces or horizontal cylinders of fluid (gasses or liquids) flowing past these surfaces.
  • Compound Machines Efficiency  -  A simple machine is a mechanical device that changes the direction or magnitude of a force.  A compound machine is machines connected in series.
  • Compressibility  -  Measures the change in volume under external forces for any liquid.
  • Compressibility Factor  -  Corrects for deviation from the ideal gas law to account for the real gases behavior.
  • Compression Ratio  -  The ratio of the maximum volume to the minimum volume in a cylinder.
  • Consistancy Index  -  The range of water content to the firmness of the soil.
  • Constrictivity  -  A parameter used to describe transportation processes in porous media.
  • Correction Factor  -  A numerical value used to adjust calculations or measurements to account for errors, deviations, or specific conditions that might skew results.
  • Critical Hydraulic Gradient  -  Used in fluid dynamics, specifically in open channel flow analysis.  It refers to the minimum slope or gradient required for a fluid (liquid) to flow in an open channel without any portion of the flow becoming stagnant or backflow occurring.
  • Curvature Coefficient  -  Classifies a soil as well graded or poorly graded.
  • Courant Number  -  The measure of how much information traverses a computational grid cell in a given time interval.

D         

  • A - B - C - D - E - F - G - H - I - J - K - L - M - N - O - P - Q - R - S - T - U - V - W - X - Y - Z
  • Damping Ratio  -  Describes how oscillations in a system decay after a disturbance.
  • Darcy Friction Factor  -  Helps calculate the friction losses in pipe flow and open channel flow.  This coefficient is used in the Darcy-Weisbach equation.
  • Darcy Friction Factor - Brkić  -  Equations that allow you to calculate the friction losses in pipe flow and open channel flow.
  • Darcy Friction Factor - Free Surface Flow  -  Equations that allow you to calculate the friction losses in pipe flow and open channel flow.
  • Darcy Friction Factor - Laminar Flow  -  Equations that allow you to calculate the friction losses in pipe flow and open channel flow.
  • Darcy-Weisbach Friction Factor  -  See Darcy Friction Factor
  • Darcy-Weisbach Equation  -  The most common way of expressing the pressure drop of a piped fluid.  The equation is valid for fully developed, steady state and incompressible flow.
  • Dean Number  -  Used in momentum transfer for the flow in curved pipes and channels.
  • Deborah Number  -  The ratio of fluidity of materials under specific flow conditions, primarly used in rheology
  • Degree of Saturation  -  The ratio of volume of water to the volume of voids.
  • Determination Coefficient  -  The porportion of the variation in the dependent variable that is predicated from the independent variables.
  • Discharge Coefficient  -  The ratio of actual discharge to the theoretical discharge.
  • Drag Coefficient  -  Used to quantify the amount of force or resistance an object experienced as it moves through the fluid stream.
  • Dukhin Number  -  The surface conductivity to various electrokinetic and electroacoustic effects, as well as the electrical conductivity and permittivity of fluid heterogeneous systems.

E         

  • A - B - C - D - E - F - G - H - I - J - K - L - M - N - O - P - Q - R - S - T - U - V - W - X - Y - Z
  • Eckert Number  -  Used to calculate the ratio of the kinetic energy to enthalpy.
  • Efficiency  -  Expressed in percentage and always less than 100%.
  • Ekman Number  -  In fluid dynamics it describes the ratio of various forces to Coriolis forces.
  • Elasticity Number  -  The ratio of elastic force to internal force in viscoelastic flow.
  • Elongation Percentage  -  The percentage of elongation at the fracture.
  • Emissivity  -  A measure of a material's ability to emit thermal radiation.  It is defined as the ratio of the thermal radiation emitted by a material to the thermal radiation emitted by a blackbody at the same temperature.
  • Energy Efficiency  -  Measure the efficiency with which a product uses energy to function.  It is calculated by dividing a product's BTU output by its wattage.
  • Eotvos Number  -  Measures the importance of gravitational forces compared to surface tension forces for the movement of liquid front.
  • Ericksen Number  -  The ratio of the viscous to elastic forces.
  • Euler Number  -  Used for analyzing flow where the differential pressure between two points is important.

F         

G         

  • A - B - C - D - E - F - G - H - I - J - K - L - M - N - O - P - Q - R - S - T - U - V - W - X - Y - Z
  • Galilei Number  -  See Galileo Number
  • Galileo Number  -  Used in fluid dynamics to describe fluid film flow over walls.  It is a ratio of forces present in the flow of viscous fluids.
  • Gas Compressibility Factor  -  A factor independent of the quantity of gas and determined by the character of the gas, the temperature, and pressure.
  • Gibbs Phase Rule  -  A fundamental principle in thermodynamics that provides a relationship between the number of phases, components, and degrees of freedom in a system at equilibrium.
  • Glide Ratio  -  Heavier-than-air flight without the use of thrust.
  • Golden Ratio (Divine Porportion, Golden Mean, Golden Section)  -  A mathematical ratio commonly found in nature and design.
  • Gortler Number  -  The secondary flows that appear in the boundary layer flow along a concave wall.
  • Graetz Number  -  Characterizes laminar flow with heat transfer in a conduit.  This number is used to determine the thermal development on the entrance to ducts.
  • Grashof Number  -  The ratio of buoyant to viscous forces.
  • Gravimetric Factor  -  The number by which the weight of a gravimetric determination has to be multiplied in order to obtain the mass of the analyte it contains.

H         

I         

  • A - B - C - D - E - F - G - H - I - J - K - L - M - N - O - P - Q - R - S - T - U - V - W - X - Y - Z
  • Iribarren Number  -  Used to model several effects of surface gravity waves on beaches and coastal surfaces.

J         

K         

  • A - B - C - D - E - F - G - H - I - J - K - L - M - N - O - P - Q - R - S - T - U - V - W - X - Y - Z
  • Karlovitz Number  -  The ratio of chemical time scale to Kolmogorov time scale.
  • Keulegan–Carpenter Number  -  Describes the relative importance of the drag forces over inertia forces for bluff objects in an oscillatory fluid flow.
  • Kinetic Friction Coefficient  -  The amount of force that resists motion at a constant velocity.
  • Knudsen Number  -  Used in fluid dynamics to determine what type of analysis should be used to model an object moving through a fluid.  It is defined as the ratio of the molecular mean free path length to a representative physical length scale.
  • Kutateladze Number  -  Is the reciprocal of Jakok Number.  Note that there is a second Kutateladze Number that is related to electric arcs.

L         

  • A - B - C - D - E - F - G - H - I - J - K - L - M - N - O - P - Q - R - S - T - U - V - W - X - Y - Z
  • Laplace Number  -  Used in the charcaterization of free surface fluid dynamics.  It is a ratio of surface tension to the momentum transport inside a fluid.
  • Lewis Number  -  The ratio of thermal diffusivity to mass diffusivity.  It is used to characterize fluid flows where there is simultaneous heat and mass transfer.
  • Lift Coefficient  -  Represents the lift generated by a lifting body to the fluid density around the body, the density of the fluid around the body, velocity of the fulid and an associated reference area.
  • Liquid Critical Pressure Ratio Factor FF  -  The ratio between pressure in vena contracta and the pressure at the maximum effective choke pressure drop across the valve.
  • Liquid Index  -  Scaling the natural moisture content of a soil sample to the liquid limit and plastic limit.
  • Liquid Limit  -  The minimum water content at which soil just begins to flow.
  • Liquid Pressure Recovery Factor  -  The ratio of pressure drop that occures between the vena contracta and the upstream pressure.
  • Lockhart-Martinelli Parameter  -  Used in two-phase flow calculations.  It expresses the liquid fraction of a flowing fluid.
  • Lorentz Factor  -  The factor by which time, length, and relativistic mass change for an object while that object is motion. 
  • Loss Coefficient  -  Measures the minor loss to the change in velocity due to friction thru pipes, fittings, and valves.
  • Love Number  -  Parameters that measure the rigidity of a planetary body and the susceptibility of its shape to change in responce to a tidal potential.
  • Lundquist Number  -  A ratio that compares the timescale of an Alfven wave crossing to the timescale of resistive diffusion.

M         

  • A - B - C - D - E - F - G - H - I - J - K - L - M - N - O - P - Q - R - S - T - U - V - W - X - Y - Z
  • Mach Number  -  The ratio of the velocity of flow to the velocity of sound.  The speed of sound in this equation is dependent on the density of the medium that the sound is traveling through.
  • Machinability Index  -  Used to compare the machinability of different materials in the various cutting process.
  • Manning's Roughness Coefficient  -  Measures the frictional resistance exerted by a channel, culvert or pipe on the flow.
  • Marangoni Number  -  Compares the rate of transport due to Marangoni flows, with a rate of transport of diffusion.
  • Margin of Safety  -  The factor of safety minus 1.
  • Margin of Safety for Failure Load  -  It represents the difference between the failure load (the maximum load at which the structure/component/system fails) and the working load limit or the maximum intended load.
  • Markstein Number  -  Characterizes the effect of local heat release of a propagating flame on variations in the surface topology along the flame and the associated local flame front curvature.
  • Mass Transfer Coefficient  -  A porportional constant to the difference in the concentrations and the rate of mass transfer.
  • Mechanical Efficiency  -  The ratio of the work output to work inpit.
  • Modulation Index  -  A parameter that quantifies the extent to which a carrier wave is modified by the modulating signal in a communication system.
  • Moisture Content  -  The quantity of water contained in a material.
  • Mole Fraction  -  The number of molecules (moles) of a solution in a mixture divided by the total number of moles present in the solution.
  • Morton Number  -  The shape of bubbles or drops moving in a surrounding fluid or continuous phase.
  • Motor Efficiency  -  The ratio of shaft power out and electric power input of a motor.
  • Motor Volumetric Efficiency  -  Measure used in the automotive industry to assess how well an internal combustion engine can draw in and expel air during the intake and exhaust strokes, respectively.

N         

O         

P         

  • A - B - C - D - E - F - G - H - I - J - K - L - M - N - O - P - Q - R - S - T - U - V - W - X - Y - Z
  • Péclet Number  -  Defined as a ratio of heat transport by convection to heat transport by conduction.
  • Pi  -  Archimedes' constant number that never ends and never repeats. The ratio of the circumference of a circle to the diameter.
  • Pigging Efficiency  -  Expressed in percentage and always less than 100%.
  • Pipeline Parameter  -  Proportional to maximum water hammer pressure rise and static pressure.
  • Piping Geometry Factor  -  The pressure and velocity changes caused by fittings such as bends, expanders, reducers, tees, and Y's if directly conected to the valve.
  • Pitting Resistance Equivalent Number (PREN)  -  A way to measure the pitting corrosion resistance of various types of stainless steel in a chlorine based environment.
  • Plastic Index  -  The range of water content over which the soil remains in the plastic state.
  • Plastic Limit   -  The water content at which the soil changes from semi-solid state to solid state.
  • Poisson's Ratio  -  The elastic ratio between lateral strain and longitudinal strain.
  • Porosity  -  The ratio between the pore volume of a substance and its total volume.  Porosity of a measure of a rocks capacity to store fluids.
  • Power Number  -  Represents the proportional drag force and inertial force. It is used in momentum transfer and power consumption by fans, mixers and pump impellers at a specified rotational speed.
  • Prandtl Number  -  In fluid dynamics is used to calculate force by the ratio of momentum diffusivity (kinematic viscosity) and thermal diffusivities.
  • Pressure Coefficient  -  The relative pressures throughout a flow field in fluid dynamics.
  • Pump Efficiency  -  The ratio of total horsepower output to shaft horsepower input of the pump or power output to power input.
  • Pump Static Efficiency  -  Efficiency under steady state or static conditions when pumping a fluid.  It is a measure of how effectively the pump converts input power into hydraulic energy in the fluid.
  • Pump Volumetric Efficiency  -  Specifically refers to this concept in the context of positive displacement pumps, such as those used in hydraulic systems or certain types of compressors.

Q         

R         

S         

T         

  • A - B - C - D - E - F - G - H - I - J - K - L - M - N - O - P - Q - R - S - T - U - V - W - X - Y - Z
  • Tayor Number  -  The quantity that characterizes the importance of centrifugal forces due to the rotation of a fluid about an axis, relative to viscous forces.
  • Thermal Efficiency  -  The fraction of heat that is converted to work or desired output divided by required input.
  • Tortuosity  -  The dispersion of fluid flow in porous media.
  • Turbine Static Efficiency  -  Is efficiency under steady state or static conditions when converting fluid energy into mechanical or electrical energy.
  • Turbulent Prandtl Number  -  The ratio between the momentum eddy diffusivity and the heat transfer eddy diffusivity.

U         

V         

  • A - B - C - D - E - F - G - H - I - J - K - L - M - N - O - P - Q - R - S - T - U - V - W - X - Y - Z
  • Vadasz Number  -  Governs the effect of porosity on flow in a porous media.
  • Valve Coefficient  -  See Flow Coefficient
  • Valve Flow Coefficient Cv / Kv  -  See Flow Coefficient
  • Valve Flow Coefficient for Liquid  -
  • Viscosity Index  -  A measure used to describe how the viscosity of a lubricant, typically an oil, changes with temperature.  It’s an important property in the field of tribology (the study of friction, wear, and lubrication) because it indicates how well a lubricant maintains its thickness (viscosity) across a range of temperatures.
  • Void Ratio  -  The ratio of the volume of voids to the volume of solids.
  • Volumetric Efficiency  -  The more air inside the combustion chamber, the more fuel that can be burned and the higher the output engine torque and power.
  • Von Karman Constant  -  The logarithmic law describing the distribution of the longitudinal velocity in the wall-normal direction of a turbulent fluid flow near a boundary with a no-slip condition.

W         

X

Y

Z

 

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