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Bagnold Number

The Bagnold number is the ratio of grain collision stresses to viscous fluid stresses in a granular flow with interstitial Newtonian fluid.

The Bagnold number equals the square of the diameter of the solids multiplied by the strain rate, the volume faction of the solids and the density of the solids, and divided by the dynamic viscosity of the liquid and the volume faction of the liquid.

Formula

QuantityVariable["Ba", "BagnoldNumber"] == (QuantityVariable["D", "Diameter"]^2*QuantityVariable[OverDot["ε"], "StrainRate"]*QuantityVariable[Subscript["V", "s"], "Unitless"]*QuantityVariable[Subscript["ρ", "s"], "MassDensity"])/(QuantityVariable["η", "DynamicViscosity"]*(1 - QuantityVariable[Subscript["V", "s"], "Unitless"]))

symbol description physical quantity
Ba Bagnold number "BagnoldNumber"
D solids diameter "Diameter"
η dynamic viscosity "DynamicViscosity"
ε̇ strain rate "StrainRate"
Vs solids volume fraction "Unitless"
ρs solids density "MassDensity"

Forms

Examples

Get the resource:

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

Get the formula:

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

Use some values:

In[3]:=
FormulaData[ResourceObject["Bagnold Number"], {QuantityVariable[ \!\(\*SubscriptBox[\("\[Rho]"\), \("s"\)]\),"MassDensity"] -> Quantity[3, ("Grams")/("Centimeters")^3]}]
Out[3]=

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