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De Laval Nozzle

A de Laval nozzle is a tube that is pinched in the middle, making a carefully balanced, asymmetric hourglass shape. It is used to accelerate a hot, pressurized gas passing through it to a higher supersonic speed in the axial (thrust) direction, by converting the heat energy of the flow into kinetic energy.

Exhaust gas velocity from a de Laval nozzle increases with the square root of the temperature, and inversely with the square root of the molar mass. The heat capacity also plays a major part, increasing as the isobaric and isochoric heat capacities converge. Increasing inlet pressure or decreasing exhaust pressure also increase the velocity.

Formula

QuantityVariable[Subscript["v", "e"], "Speed"] == Sqrt[2]*Sqrt[(Quantity[1, "MolarGasConstant"]*QuantityVariable["T", "Temperature"]*QuantityVariable[Subscript["C", "p"], "HeatCapacity"]*(1 - (QuantityVariable[Subscript["P", "e"], "Pressure"]/QuantityVariable["P", "Pressure"])^((QuantityVariable[Subscript["C", "p"], "HeatCapacity"] - QuantityVariable[Subscript["C", "V"], "HeatCapacity"])/QuantityVariable[Subscript["C", "p"], "HeatCapacity"])))/(QuantityVariable["m", "MolarMass"]*(QuantityVariable[Subscript["C", "p"], "HeatCapacity"] - QuantityVariable[Subscript["C", "V"], "HeatCapacity"]))]

symbol description physical quantity
ve exhaust gas velocity "Speed"
m molar mass "MolarMass"
T temperature "Temperature"
Cp isobaric heat capacity "HeatCapacity"
CV isochoric heat capacity "HeatCapacity"
P inlet gas pressure "Pressure"
Pe exhaust gas pressure "Pressure"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["De Laval Nozzle"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ResourceObject["De Laval Nozzle"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ResourceObject["De Laval Nozzle"], {QuantityVariable[ \!\(\*SubscriptBox[\("v"\), \("e"\)]\),"Speed"] -> None, QuantityVariable[ \!\(\*SubscriptBox[\("P"\), \("e"\)]\),"Pressure"] -> Quantity[0.1`, "Megapascals"], QuantityVariable["P","Pressure"] -> Quantity[7, "Megapascals"], QuantityVariable["T","Temperature"] -> Quantity[3500, "Kelvins"]}]
Out[3]=

Source Metadata

  • Creator:
  • Date: 1888

Publisher Information