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Bernoulli's Equation Hydraulic Grade Line

Calculate gas and liquid pipeline hydraulic pressure or hydraulic grade line (HGL) from data points using the Bernoulli equation.

The hydraulic or piezometric pressure is calculated by

`Ph = Ps + Pz `

where :

Ps = static pressure
Pz = potential or pressure
Ph = hydraulic or piezometric pressure (HGL)

For constant diameter pipelines, the friction pressure loss can be calculated from the difference in hydraulic pressure (changes in dynamic pressure are ignored). For gas pipelines, the changes in dynamic pressure are usually small compared to the other terms.

Note : The pressure terms are calculated at the selected data point. The data point option is set to pipe inlet when the page loads. Click calculate to update the data point options to include all of the data points before you select the data point. Click calculate each time you change the position data (X) values, and before you select the data point. Data points can be entered as comma separated values (Xi, Zi, Pi) with each set on a new line, or copy and paste from a spreadsheet.

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CALCULATOR : Bernoulli Equation Liquid Pipeline Hydraulic Grade Line HGL From Data Points [FREE]   ±

Calculate the Bernoulli equation hydraulic pressure or HGL (hydraulic grade line) and pressure loss from data points for liquid and general fluid pipelines.

Enter data points as three values separated by commas (position X, elevation Z, static pressure P) with each set of data on a new line. The position data should be in ascending order from the pipeline inlet to the pipeline outlet. Static pressure is gauge pressure (change units on the setup page).

Select a data point to calculate the pressure terms at that data point (default is the pipe inlet). The hydraulic pressure equals the sum of the potential pressure and the static pressure. For liquid pipelines with constant diameter, the friction pressure loss is equal to the difference in hydraulic pressure.

Note : The data point option is set to pipe inlet when the page loads. Click calculate to update the data point options to include all of the data points, then select the data point. Click calculate each time you change the position data (X) values, and before you select the data point.

Use the Result Plot option to plot the static pressure, potential pressure and hydraulic pressure versus position. Use the Result Table option to display a table of static pressure, potential pressure, hydraulic pressure, delta hydraulic pressure and delta pressure per length versus data point.

Tool Input

  • datatype : Data Point (Click Calculate To Update)
  • Xdata : Position Data Points
  • Zdata : Elevation Data Points
  • Pdata : Static Pressure Data Points
  • ρ : Density

Tool Output

  • Ph : Hydraulic Pressure At Data Point
  • PhΔ : Pressure Loss (From Inlet)
  • PhΔ/d : Pressure Loss Per Length
  • Phi : Hydraulic Pressure At Inlet
  • Ps : Static Pressure At Data Point
  • Pz : Potential Pressure At Data Point
  • ZΔ : Delta Elevation
  • d : Distance From Pipe Inlet

CALCULATOR : Bernoulli Equation Gas Pipeline Hydraulic Grade Line HGL From Data Points [FREE]   ±

Calculate the Bernoulli equation hydraulic pressure or HGL (hydraulic grade line) and pressure loss from data points for gas pipelines.

Enter data points as three values separated by commas (position X, elevation Z, static pressure P) with each set of data on a new line. The position data should be in ascending order from the pipeline inlet to the pipeline outlet. Static pressure is gauge pressure (change units on the setup page).

Select a data point to calculate the pressure terms at that data point (default is the pipe inlet). The hydraulic pressure equals the sum of the potential pressure and the static pressure. For gas pipelines with constant diameter, the friction pressure loss is approximately equal to the difference in hydraulic pressure (changes in dynamic pressure are ignored). The pressure loss for gas pipelines can be calculated more accurately using the total pressure or EGL (energy grade line).

Note : The data point option is set to pipe inlet when the page loads. Click calculate to update the data point options to include all of the data points, then select the data point. Click calculate each time you change the position data (X) values, and before you select the data point.

Use the Result Plot option to plot the static pressure, potential pressure and hydraulic pressure versus position. Use the Result Table option to display a table of static pressure, potential pressure, hydraulic pressure, delta hydraulic pressure and delta pressure per length versus data point.

Tool Input

  • fluidtype : Fluid Type
    • SGu : User Defined Gas Specific Gravity
  • zfactype : Compressibility Factor Type
    • zu : User Defined Compressibility Factor
  • datatype : Data Point (Click Calculate To Update)
  • Xdata : Position Data Points
  • Zdata : Elevation Data Points
  • Pdata : Static Pressure Data Points
  • T : Temperature

Tool Output

  • Ph : Hydraulic Pressure At Data Point
  • PhΔ : Pressure Loss (From Inlet)
  • PhΔ/d : Pressure Loss Per Length
  • Phi : Hydraulic Pressure At Inlet
  • Ps : Static Pressure At Data Point
  • Pz : Potential Pressure At Data Point
  • SG : Gas Specific Gravity
  • ZΔ : Delta Elevation
  • d : Distance From Pipe Inlet
  • z : Gas Compressibility Factor
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 Gas Density And Compressibility Factor [FREE]   ±

Calculate Bernoulli equation gas density and compressibility factor from the fluid pressure, temperature and critical point constants for selected gases.

The compressibility factor can be calculated from either the Peng Robinson, Soave, Redlich Kwong, or van der Waals equation of state (EOS). The compressibility factor calculation is valid for gas phase only. Use the Result Plot option to plot compressibility factor versus pressure and temperature, compressibility factor versus pressure and equation of state type, or compressibility factor versus temperature and equation of state type.

Tool Input

  • fluidtype : Fluid Type
    • SGu : User Defined Gas Specific Gravity
    • ωu : User Defined Acentric Factor
    • Pcu : User Defined Critical Pressure
    • Tcu : User Defined Critical Temperature
  • eostype : Equation Of State
    • Zu : User Defined Compressibility Factor
  • P : Fluid Pressure
  • T : Fluid Temperature

Tool Output

  • ρ : Fluid Density
  • ω : Accentric Factor
  • Pc : Critical Point Pressure
  • Pr : Reduced Pressure
  • SG : Gas Specific Gravity Relative To Air
  • Tc : Critical Point Temperature
  • Tr : Reduced Temperature
  • Vm : Molar Volume
  • Z : Compressibility Factor
  • cvg : Convergence Check
  • mw : Fluid Molar Mass
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
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