Dimensionless Numbers

dimensionless numbers banner 3Dimensionless numbers, abbreviated as DN, are nondimensional quantity of dimension one and can not be measured on a scale of physical units.  All quantities of dimension one are said to have the SI coherent derived unit "one" with the symbol "1".  It is a pure number, thus always having a dimension of 1.  The number does not change even if the number system you are working in does.  Dimensionless numbers or quantities are used in many disiplines such as chemistry, economics, engineering, mathematics, and physics.

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Dimensionless numbers Glossary


  • 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.
  • 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 rate constant 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.


  • Bagnold number  -  The ratio of grain collision stresses to various fluid stresses in a granular flow with interstitial Newtonian fluid.


  • Carnot efficiency  -  The theroetical maximum efficiency of any heat engine depending only on the temperatures it operates between.
  • 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.
  • Compression ratio  -  The ratio of the maximum volume to the minimum volume in a cylinder.
  • Courant number  -  The measure of how much information traverses a computational grid cell in a given time interval.


  • Drag coefficient  -  Used to quantify the amount of force or resistance an object experienced as it moves through the fluid stream.



  • Factor of safety  -  The ability of a system's structural capacity to be usable beyond it's expected or acrual loads.

  • Fan efficiency  -  The ratio of input and output power.


  • Glide ratio  -  Heavier-than-air flight without the use of thrust.


  • Hagen number  -  Used in forced flow calculations.  The equation is similar to the Grashof Number but for forced flow rather than natural convection.

  • Hartmann number  -  The ratio of electromagnetic force to the viscous.

  • Heat capacity ratio  -  See specific heat ratio
  • Hedstrom number  -  A dimensionless quantity used in fluid dynamics.

  • Hydraulic gradient  -  The change in height (pressure) to length between any two points.

  • Hydraulic efficiency  -  Is the ratio of hydrodynamic energy in the form of fluid to the amount of mechanical energy delivered to the rotor.


  • Injury frequency rate  -  The number of injuries based on the number of hours worked on an annual basis.
  • Injury severity rate  -  How critical or serious the injuries and illnesses sustained in a period of time by using the number of lost days per accident.



  • 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.


  • 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.
  • Lost time injury frequency rate  -  The number of lost time injuries that have occured within a given accounting period, relative to the total number of hours worked in that period.
  • Lost workday incident rate  -  The total number of working days lost within a workplace due to occupational injury or illness.


  • 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.
  • Margin of safety  -  The ratio of the system's structural capacity to the requirements or how much excess capacity.

  • Margin of safety for a failure load  -  The ratio of the system's structural capacity to the requirements or how much excess capacity.
  • Morton number  -  The shape of bubbles or drops moving in a surrounding fluid or continuous phase.

  • Motor efficiency  -  The ratio of shaft power power out and electric power input of a motor.


  • Nusselt number  -  Describes the ratio of convective heat transfer to conductive heat across a boundary.


  • Ohnesorge number  -  Relates the viscous force to inertial forces and surface tension forces.

  • Overall efficiency  -  Measures the ratio of the output of actual power to the input of actual power.  It determines the amount of energy lost overall.


  • 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.
  • 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.
  • Prandtl number  -  In fluid dynamics is used to calculate force by the ratio of momentum diffusivity (kinematic viscosity) and thermal diffusivities.
  • Pressure gradient  -  Describing which direction and at what rate the pressure changes the most at a specific location.
  • Pump efficiency  -  The ratio of total horsepower output to shaft horsepower input of the pump or power output to power input.




  • Safety factor  -  See factor of safety
  • Schmidt number  -  Used in analyzing fluid flows where there is an interface between two different fluids. 

  • Shape factor  -  Used in structural it is the strength of the shape no matter the scale for a given load, bending, torsion, or twisting.

  • Sherwood number  -  The ratio between convective mass transfer and diffusive mass transfer.

  • Skin friction coefficient  -  The ratio of shear stress and dynamic pressure of a free stream.
  • Sommerfield number  -  Used extensively in hydrodynamic lubrication analysis.

  • Specific gravity  -  The density or ratio of any substance to another substance.
  • Strouhal number  -  Used to describe oscillating flow.  It is used in fluid dynamics and is the ratio of inertial forces due to the unsteadiness of the flow or acceleration of inertial forces due to the changes in velocity between points in a flow field.


  • 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.
  • Total case incident rate  -  The number of work-related injuries per 100 full-time workers during a one year period.


  • Ursell number  -  Indicates the nonlinearity of long surface gravity waves on a fluid layer.


  • 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.


  • Water content  -  The ratio of weight of soil to the weight of water or the quantity of water contained in a material.
  • Weber number  -  Used in fluid mechanics is often useful in analysing fluid flows where there is an interface between two different fluids, especially for multiphase flows with strongly curved surfaces.
  • Womersley number  -  The pulsatile flow frequency in relation to viscous effects.





Display #
Abbe Number
Aeration Number
Archimedes Number
Arrhenius Number
Atomic Number
Atwood Number
Bagnold Number
Bejan Number - Fluid Mechanics
Bejan Number - Heat Transfer
Bejan Number - Mass Transfer
Bingham Number
Biot Number
Blake Number
Bodenstein Number
Bond Number
Buckling Coefficient
Capillary Number
Carnot Efficiency
Cauchy Number
Cavitation Number
Compound Machines Efficiency
Courant Number
Damping Ratio
Darcy Friction Factor
Darcy-Weisbach Equation

Tags: Equations for Safety Equations for Pipeline Pigging