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Bernoulli's Energy Equation

Bernoulli's energy equation derives from Bernoulli's principle, which states that an increase in the speed of a fluid across a surface will result in a decrease of the force exerted (pressure) on that surface, or a decrease in the fluid's potential energy vectored toward that surface.

Bernoulli's energy equation states that the sum of the pressure divided by the fluid density, the kinetic energy divided by the mass and the potential energy due to gravity divded by mass remains constant.

Formula

QuantityVariable[Subscript["P", "1"], "Pressure"]/QuantityVariable["ρ", "MassDensity"] + QuantityVariable[Subscript["v", "1"], "Speed"]^2/2 + Quantity[1, "StandardAccelerationOfGravity"]*QuantityVariable[Subscript["z", "1"], "Height"] == QuantityVariable[Subscript["P", "2"], "Pressure"]/QuantityVariable["ρ", "MassDensity"] + QuantityVariable[Subscript["v", "2"], "Speed"]^2/2 + Quantity[1, "StandardAccelerationOfGravity"]*QuantityVariable[Subscript["z", "2"], "Height"]

symbol description physical quantity
ρ fluid density "MassDensity"
P1 pressure "Pressure"
v1 speed "Speed"
z1 vertical displacement "Height"
P2 downstream pressure "Pressure"
v2 downstream speed "Speed"
z2 downstream vertical displacement "Height"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Bernoulli's Energy Equation"]
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Get the formula:

In[2]:=
FormulaData[ResourceObject["Bernoulli's Energy Equation"]]
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Use some values:

In[3]:=
FormulaData[ ResourceObject["Bernoulli's Energy Equation"], {QuantityVariable[ \!\(\*SubscriptBox[\("z"\), \("2"\)]\),"Height"] -> Quantity[1, "Meters"], QuantityVariable[ \!\(\*SubscriptBox[\("z"\), \("1"\)]\),"Height"] -> Quantity[1, "Meters"], QuantityVariable[ \!\(\*SubscriptBox[\("v"\), \("2"\)]\),"Speed"] -> Quantity[1.25`, ("Meters")/("Seconds")], QuantityVariable[ \!\(\*SubscriptBox[\("v"\), \("1"\)]\),"Speed"] -> Quantity[5, ("Meters")/("Seconds")], QuantityVariable[ \!\(\*SubscriptBox[\("P"\), \("1"\)]\),"Pressure"] -> Quantity[300, "Kilopascals"]}]
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Source Metadata

  • Creator:
  • Date: 1738

Publisher Information