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Grashof Number

The Grashof number is a dimensionless number in fluid dynamics and heat transfer that approximates the ratio of the buoyancy to viscous force acting on a fluid.

The Grashof number equals the product of the characteristic length cubed, the coefficient of thermal expansion, the temperature difference and the acceleration of gravity divided by the kinematic viscosity squared.

Formula

QuantityVariable["Gr", "GrashofNumberHeatTransfer"] == (Quantity[1, "StandardAccelerationOfGravity"]*QuantityVariable["l", "Length"]^3*QuantityVariable["α", "ThermalExpansionCoefficient"]*QuantityVariable["Δ​T", "TemperatureDifference"])/QuantityVariable["ν", "KinematicViscosity"]^2

symbol description physical quantity
Gr Grashof number for heat transfer "GrashofNumberHeatTransfer"
l characteristic length "Length"
α coefficient of thermal expansion "ThermalExpansionCoefficient"
Δ​T temperature difference "TemperatureDifference"
ν kinematic viscosity "KinematicViscosity"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Grashof Number"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ResourceObject["Grashof Number"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Grashof Number"], {QuantityVariable[ "\[CapitalDelta]\[InvisibleSpace]T","TemperatureDifference"] -> Quantity[1, "KelvinsDifference"], QuantityVariable["\[Alpha]","ThermalExpansionCoefficient"] -> Quantity[1, 1/("KelvinsDifference")], QuantityVariable["\[Nu]","KinematicViscosity"] -> Quantity[1, ("Meters")^2/("Seconds")]}]
Out[3]=

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