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Dean Number

The Dean number is a dimensionless group in fluid mechanics, which occurs in the study of flow in curved pipes and channels.

The Dean number is proportional to the square root of the cube of the diameter, the characteristic speed, the mass density, the reciprocal of the square root of the radius of curvature and the reciprocal of the dynamic viscosity.

Formula

QuantityVariable["De", "DeanNumber"] == (QuantityVariable["d", "Diameter"]*Sqrt[QuantityVariable["d", "Diameter"]/QuantityVariable["R", "RadiusOfCurvature"]]*QuantityVariable["v", "Speed"]*QuantityVariable["ρ", "MassDensity"])/(Sqrt[2]*QuantityVariable["η", "DynamicViscosity"])

symbol description physical quantity
De Dean number "DeanNumber"
d diameter "Diameter"
R radius of curvature "RadiusOfCurvature"
v characteristic speed "Speed"
η dynamic viscosity "DynamicViscosity"
ρ mass density "MassDensity"

Forms

Examples

Get the resource:

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

Get the formula:

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

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Dean Number"], {QuantityVariable["\[Rho]","MassDensity"] -> Quantity[1000, ("Kilograms")/("Meters")^3], QuantityVariable["v","Speed"] -> Quantity[1, ("Meters")/("Seconds")]}]
Out[3]=

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