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First Euler Number Using Pressure Difference

The Euler number is a dimensionless number used in fluid flow calculations. It expresses the relationship between a local pressure drop caused by a restriction and the kinetic energy per volume of the flow, and is used to characterize energy losses in the flow, where a perfect frictionless flow corresponds to an Euler number of 0.

The Euler number equals the pressure difference divided by the characteristic speed squared and the mass density.

Formula

QuantityVariable[Subscript["Eu", "1"], "EulerNumber1"] == QuantityVariable["Δ​P", "Pressure"]/(QuantityVariable["v", "Speed"]^2*QuantityVariable["ρ", "MassDensity"])

symbol description physical quantity
Eu1 first Euler number "EulerNumber1"
v characteristic speed "Speed"
Δ​P pressure difference "Pressure"
ρ mass density "MassDensity"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["First Euler Number Using Pressure Difference"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ ResourceObject["First Euler Number Using Pressure Difference"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "First Euler Number Using Pressure Difference"], {QuantityVariable[ "v","Speed"] -> Quantity[1, ("Meters")/("Seconds")], QuantityVariable[ \!\(\*SubscriptBox[\("Eu"\), \("1"\)]\),"EulerNumber1"] -> 1}]
Out[3]=

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