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Bernoulli's Equation Prandtl Tube

Calculate fluid velocity from the pressure difference across a Pitot-Static or Prandtl tube using the Bernoulli equation.

Prandtl tubes or Pitot-Static tubes are used to measure the fluid static pressure, and the fluid stagnation pressure (the sum of the static pressure and the dynamic pressure). The fluid velocity can be calculated from the dynamic pressure. The dynamic pressure is equal to the stagnation pressure minus the static pressure.

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CALCULATOR : Bernoulli Equation Liquid Prandtl Tube Velocity From Pressure [FREE]   ±

Calculate the Bernoulli equation liquid velocity from the pressure difference across a Pitot-Static or Prandtl tube.

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

Tool Input

  • Pp : Pitot Tube Pressure
  • Ps : Static Pressure
  • ρ : Fluid Density

Tool Output

  • V : Fluid Velocity
CALCULATOR : Bernoulli Equation Fresh Water Density From Temperature [FREE]   ±

Calculate Bernoulli equation fresh water density from temperature at atmospheric pressure (IAPWS R7-97 steam table).

The calculation is valid from the freezing point (0 C) to the boiling point (100 C). Use the Result Plot option to plot density versus temperature.

Reference : IAPWS R7-97 Industrial Formulation for thermodynamic Properties of Water and Steam

Tool Input

  • T : Temperature

Tool Output

  • ρ : Density
CALCULATOR : Bernoulli Equation Salt Water Density From Temperature And Salinity [FREE]   ±

Calculate Bernoulli equation salt water density from temperature and practical salinity at atmospheric pressure (TEOS-10 seawater).

Practical salinity = parts per thousand of dissolved solids (mainly salt). The absolute salinity is taken as 35.16504 / 35 times the practical salinity. The absolute salinity anomaly δSA is ignored. Use the Result Plot option to plot density versus temperature.

Reference : TEOS-10 Thermodynamic Equation Of Seawater (2010)

Tool Input

  • T : Seawater Temperature

Tool Output

  • ρ : Seawater Density
CALCULATOR : Bernoulli Equation Liquid Density And Specific Gravity [FREE]   ±

Calculate Bernoulli equation liquid density and specific gravity, degrees Baume, degrees Twaddell, and degrees API.

For liquids lighter than or equal to water the density can be defined as degrees API, or degrees Baume (Be-). For liquids heavier than water the density can be defined by degrees Baume (Be+), or degrees Twaddell.

Tool Input

  • sgtype : Density Type
    • SGu : User Defined Specific Gravity
    • Be+u : User Defined Degrees Baume SG > 1
    • Be-u : User Defined Degrees Baume SG <= 1
    • Twu : User Defined Degrees Twaddell SG > 1
    • APIu : User Defined Degrees API SG <= 1
    • ρu : User Defined Liquid Density

Tool Output

  • ρ : Fluid Density
  • API : Degrees API SG ≤ 1
  • Be+ : Degrees Baume SG > 1
  • Be- : Degrees Baume SG ≤ 1
  • SG : Specific Gravity
  • Tw : Degrees Twaddell SG > 1
CALCULATOR : Bernoulli Equation Gas Prandtl Tube Mach Number From Pressure [FREE]   ±

Calculate the Bernoulli equation gas velocity from the pressure difference across a Pitot-Static or Prandtl tube.

For subsonic and supersonic flow the Mach number can be calculated from the upstream or flowing pressure. The speed of sound and velocity can be calculated from either the upstream temperature, or the stagnation temperature measured at the tip of the Pitot tube.

For supersonic flow a normal shock wave forms in front of the Pitot tube. The Mach number and velocity can also be calculated from the downstream pressure and temperature. The downstream pressure and temperature option should not be used for subsonic flow.

The flow is assumed to be adiabatic for an ideal gas. The flow is isentropic for subsonic conditions, and non isentropic for supersonic conditions. The shock wave is non isentropic.

Tool Input

  • fluidtype : Fluid Type
    • γu : User Defined Specific Heat Ratio
    • SGu : User Defined Gas Specific Gravity
  • zfactype : Factor Type
    • Zu : User Defined Compressibility Factor
  • temptype : Measured Temperature Type
    • Tou : User Defined Stagnation Temperature
    • Tdu : User Defined Downstream Temperature
  • flowtype : Subsonic Or Supersonic Flow
  • Po : Pitot Tube Downstream Stagnation Pressure
  • Pd : Pitot Tube Downstream Static Pressure

Tool Output

  • γ : Specific Heat Ratio
  • ρd : Downstream Density
  • ρu : Upstream Density
  • Cd : Downstream Speed Of Sound
  • Cu : Upstream Speed Of Sound
  • Md : Downstream Mach Number
  • Mu : Upstream Mach Number
  • Pu : Upstream Pressure
  • Rg : Specific Gas Constant
  • SG : Gas Specific Gravity
  • Td : Downstream Temperature
  • To : Stagnation Temperature
  • Tu : Upstream Temperature
  • Vd : Downstream Velocity
  • Vu : Upstream Velocity
  • Z : Compressibility Factor
  • mmg : Gas Molar Mass

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