Richardson Number Calculator

This calculator computes Richardson Number, which is a dimensionless number used in fluid dynamics to quantify the relative importance of buoyancy forces to inertial forces within a fluid flow. This calculator uses the relationship between Richardson Number, Grashof Number and Reynolds Number which is valid in the context of thermal convection.
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CalculationInputs﻿﻿Gr
:4.00​
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﻿﻿Re
:4.00​
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Output﻿﻿Ri
:0.25​
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Ri=GrRe2Ri=\dfrac{Gr}{Re^2}Ri=Re2Gr​
Where:
﻿﻿Gr
 is Grashof Number (dimensionless), which is the ratio of buoyancy forces to friction forces in a fluid flow. It's used to determine whether a flow is laminar or turbulent in natural convection.
﻿﻿Re
 is Reynolds Number (dimensionless), which is the ratio of inertial forces to friction forces in a fluid flow. It's used to determine whether a flow is laminar or turbulent in forced convection.
﻿﻿Ri
 is Richardson Number (dimensionless), which is the ratio of buoyancy forces to inertial forces in a fluid flow. It's used to determine whether natural convection effects or forced convection effects dominate in a fluid flow.
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ExplanationRichardson Number is named after Lewis Fry Richardson, a British mathematician and physicist who made significant contributions to meteorology and fluid dynamics.
In the context of thermal convection, which is the transfer of heat from one place to another due to the movement of fluid, the Richardson number represents the importance of natural convection relative to forced convection.
Natural convection is where the fluid flow causing heat transfer in a fluid is driven by buoyancy rather then an external source. Buoyancy occurs solely by a density difference due to a temperature gradient. An example of natural convection is the cycling movement of boiling water in a pot, in which warm water at the bottom of the pot expands, rises to the top of the pot, cools down, and falls within the same pot. 
Forced convection is where the fluid flow causing heat transfer in a fluid is driven by an external source. An example of forced convection is spinning a spoon in a cup of hot water.
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Natural convection, forced convection and their corresponding Richardson number
Typically:
﻿﻿Ri>>1
 means natural convection effects in fluid flow dominate
﻿﻿Ri<<1
 means forced convection effects in fluid flow dominate
﻿﻿Ri≈1
 means forced and natural convection effects are comparable
The significance of the Richardson number includes investigating turbidity and density currents in lakes, reservoirs and oceans.
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Related ResourcesBernoulli Mass Flow Rate Calculator
Froude Number Calculator: Open Channel Flow
Péclet Number Calculator 
Reynolds Number Calculator
Reynolds Number Calculator (for motion of a viscous fluid)
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