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Pipeng Free Online Software : Prandtl Tube Calculators
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Pipeng : Bernoulli Prandtl Tube - Pitot Static Tube Calculation Module

Prandtl Tube Calculators

Description : Bernoulli Prandtl or Pitot-Static tube calculators.

Discussion : Pitot-Static tubes or Prandtl tubes are commonly used to measure fluid velocity. For liquids (incompressible flow) the velocity is calculated from the difference between the static pressure and the Pitot tube pressure (the impact pressure). For compressible flow the Mach number can be calculated from the ratio of the Pitot tube pressure to the static pressure. Prandtl tubes are commonly used on aircaraft to measure the the Mach number and air speed. The air speed is obtained by multiplying the Mach number by the speed of sound. The speed of sound can be calculated from the air temperature.

Figures :

Calculator Tools In This Module:

CALC : Flow : Bernoulli 041 : Prandtl Tube Velocity From Pressure : Incompressible Flow : Calculator
CALC : Flow : Bernoulli 042 : Prandtl Tube Pressure From Velocity : Incompressible Flow : Calculator
CALC : Flow : Bernoulli 043 : Prandtl Tube Velocity From Pressure : Subsonic And Supersonic Compressible Air Flow : Calculator
CALC : Flow : Bernoulli 044 : Prandtl Tube Pressure From Velocity : Subsonic And Supersonic Compressible Air Flow : Calculator
CALC : Flow : Bernoulli 045 : Prandtl Tube Velocity From Pressure : Subsonic And Supersonic Compressible Gas Flow : Calculator
CALC : Flow : Bernoulli 046 : Prandtl Tube Pressure From Velocity : Subsonic And Supersonic Compressible Gas Flow : Calculator
CALC : Flow : Numbers 022 : Velocity From Mach Number : Air Ideal Gas Or User Defined Speed Of Sound : Calculator


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Module List

CALC : Flow : Bernoulli 041 : Prandtl Tube Velocity From Pressure : Incompressible Flow : Calculator

Description : Calculate the fluid velocity from the pressure difference across a Pitot-Static or Prandtl tube, for incompressible flow.

Discussion : Prandtl tubes or Pitot-Static tubes are commonly used to measure the velocity of liquid flow in tubes. The fluid velocity can be calculated from the difference between the static pressure and the pitot pressure (the sum of static and impact pressure).

Figures :

Input Variables :

  • ρ = Fluid Density
  • Pp = External Fluid Pitot Tube Pressure
  • Ps = External Fluid Static Pressure

Output Variables :

  • V = Fluid Velocity

Calculation :

V = √( 2 ( Pp - Ps ) / ρ )

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CALC : Flow : Bernoulli 042 : Prandtl Tube Pressure From Velocity : Incompressible Flow : Calculator

Description : Calculate the pressure difference across a Pitot-Static or Prandtl tube from the fluid velocity, for incompressible flow.

Discussion : The difference between the static air pressure and the pitot pressure (the sum of static and impact pressure) can be calculated from the fluid velocity.

Figures :

Input Variables :

  • ρ = Fluid Density
  • Ps = External Fluid Static Pressure
  • V = Fluid Velocity

Output Variables :

  • Pp = External Fluid Pitot Tube Pressure

Calculation :

Pp = 0.5 V 2 ρ + Ps

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CALC : Flow : Bernoulli 043 : Prandtl Tube Velocity From Pressure : Subsonic And Supersonic Compressible Air Flow : Calculator

Description : Calculate the fluid velocity from the Prandtl tube pressure ratio, for compressible air flow.

Discussion : The Prandtl tube pressure ratio can be used to calculate the Mach number of the flow in low pressure air. The tool is valid for a typical range of atmospheric conditions. For abnormal conditions use the ideal gas tool. The speed of sound can be calculated from the air temperature or user defined.

Options :

  • Speed of Sound : calculated for air or user defined

Input Variables :

  • A = Speed Of Sound Type
  • Pp = Fluid Pitot Tube Pressure
  • Ps = Fluid Static Pressure
  • T = Fluid Absolute Temperature
  • ad = Defined Sound Velocity

Output Variables :

  • Ma = Fluid Dimensionless Mach Number
  • Mk = Fluid Dimensionless Check Mach Number
  • PoS = Prandtl Tube Pressure Ratio
  • PoSs = Prandtl Tube Sonic Pressure Ratio
  • V = Fluid Velocity
  • a = Sound Velocity

Calculation :

PoS = Pp / Ps
PoSs = ( 6 / 5 ) 7 / 2
If PoS <= PoSs
  Ma = √( 5 ( PoS 2 / 7 - 1 ) )
  Mk = Ma
Otherwise
 list( Ma ) = MachAir( PoS )
  Mk = PoS ( 7 Ma 2 - 1 ) 2.5 / ( 166.9216 Ma 6 )
End of If Block
 If A = 1 : Air
  a = 20.047 √( T )
 Otherwise If A = 2 : User Defined
  a = ad
 End of If Block
V = Ma a

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CALC : Flow : Bernoulli 044 : Prandtl Tube Pressure From Velocity : Subsonic And Supersonic Compressible Air Flow : Calculator

Description : Calculate the Pradtl tube Pitot pressure from the fluid velocity, for compressible air flow.

Discussion : The Prandtl tube Pitot pressure can be calculated from the Mach number. The sound velocity can be calculated or user defined.

Options :

  • Speed of Sound : calculated for air or user defined

Input Variables :

  • A = Speed Of Sound Type
  • Ps = Fluid Static Pressure
  • T = Fluid Absolute Temperature
  • V = Fluid Velocity
  • ad = Defined Sound Velocity

Output Variables :

  • Ma = Fluid Dimensionless Mach Number
  • PoS = Prandtl Tube Pressure Ratio
  • Pp = Fluid Pitot Tube Pressure
  • a = Sound Velocity

Calculation :

 If A = 1 : Air
  a = 20.047 √( T )
 Otherwise If A = 2 : User Defined
  a = ad
 End of If Block
Ma = V / a
If Ma <= 1
  PoS = ( 1 + Ma 2 / 5 ) 7 / 2
Otherwise
  PoS = ( 166.9216 Ma 7 ) / ( 7 Ma 2 - 1 ) 2.5
End of If Block
Pp = PoS Ps

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CALC : Flow : Bernoulli 045 : Prandtl Tube Velocity From Pressure : Subsonic And Supersonic Compressible Gas Flow : Calculator

Description : Calculate the fluid velocity from the Prandtl tube pressure ratio for compressible flow in an ideal gas.

Discussion : The Prandtl tube pressure ratio can be used to calculate the Mach number of the flow under ideal gas conditions. The speed of sound can be calculated from the air temperature or user defined.

Options :

  • Speed of Sound : calculated for ideal gas or user defined

Input Variables :

  • γ = Gas Specific Heat Ratio
  • A = Speed Of Sound Type
  • Pp = Fluid Pitot Tube Pressure
  • Ps = Fluid Static Pressure
  • T = Fluid Absolute Temperature
  • ad = Defined Sound Velocity
  • mw = Fluid Mole Weight or Molar Mass

Output Variables :

  • Ma = Fluid Dimensionless Mach Number
  • Mk = Fluid Dimensionless Check Mach Number
  • PoS = Prandtl Tube Pressure Ratio
  • PoSs = Prandtl Tube Sonic Pressure Ratio
  • V = Fluid Velocity
  • a = Sound Velocity

Calculation :

PoS = Pp / Ps
PoSs = ( ( γ + 1 ) / 2 ) γ / ( γ - 1 )
If PoS <= PoSs
  Ma = √( 2 / ( γ - 1 )( PoS( γ - 1 ) / γ - 1 ) )
  Mk = Ma
Otherwise
 list( Ma ) = MachGas( PoS , γ )
  Mk = √( PoS( γ - 1 ) / γ ( ( 2 γ ) / ( γ + 1 ) Ma 2 - ( γ - 1 ) / ( γ + 1 ) ) 1 / γ 2 / ( γ + 1 ) )
End of If Block
 If A = 1 : Ideal Gas
  a = √( ( 8314.47 γ T ) / mw )
 Otherwise If A = 2 : User Defined
  a = ad
 End of If Block
V = Ma a

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CALC : Flow : Bernoulli 046 : Prandtl Tube Pressure From Velocity : Subsonic And Supersonic Compressible Gas Flow : Calculator

Description : Calculate the Pradtl tube Pitot pressure from the fluid velocity, for compressible ideal gas flow.

Discussion : The Prandtl tube Pitot pressure can be calculated from the Mach number. The sound velocity can be calculated or user defined.

Options :

  • Speed of Sound : calculated for ideal gas or user defined

Input Variables :

  • γ = Gas Specific Heat Ratio
  • A = Speed Of Sound Type
  • Ps = Fluid Static Pressure
  • T = Fluid Absolute Temperature
  • V = Fluid Velocity
  • ad = Defined Sound Velocity
  • mw = Fluid Mole Weight or Molar Mass

Output Variables :

  • Ma = Fluid Dimensionless Mach Number
  • PoS = Prandtl Tube Pressure Ratio
  • Pp = Fluid Pitot Tube Pressure
  • a = Sound Velocity

Calculation :

 If A = 1 : Ideal Gas
  a = √( ( 8314.47 γ T ) / mw )
 Otherwise If A = 2 : User Defined
  a = ad
 End of If Block
Ma = V / a
If Ma <= 1
  PoS = ( 1 + Ma 2 ( γ - 1 ) / 2 ) γ / ( γ - 1 )
Otherwise
  PoS = ( ( ( γ + 1 ) / 2 Ma 2 ) γ / ( γ - 1 ) ) / ( ( 2 γ ) / ( γ + 1 ) Ma 2 - ( γ - 1 ) / ( γ + 1 ) ) 1 / ( γ - 1 )
End of If Block
Pp = PoS Ps

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CALC : Flow : Numbers 022 : Velocity From Mach Number : Air Ideal Gas Or User Defined Speed Of Sound : Calculator

Description : Calculate the velocity from Mach number.

Discussion : The speed of sound is either calculated for air, calculated for an ideal gas or is user defined.

Options :

  • Speed of sound calculation : air, ideal gas or user defined

Input Variables :

  • γ = Gas Specific Heat Ratio
  • A = Speed Of Sound Type
  • Ma = Fluid Dimensionless Mach Number
  • T = Fluid Absolute Temperature
  • ad = Defined Sound Velocity
  • mw = Fluid Mole Weight or Molar Mass

Output Variables :

  • V = Fluid Velocity
  • a = Sound Velocity

Calculation :

 If A = 1 : Air
  a = 20.047 √( T )
 Otherwise If A = 2 : Ideal Gas
  a = √( ( 8314.47 γ T ) / mw )
 Otherwise If A = 3 : User Defined
  a = ad
 End of If Block
V = Ma a

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