Fuel Calculation Formulas

Volume and mass calculation formulas used in fuel metering systems.

• Indicated Volume (Raw Volume)

  The volume read directly by the meter with no temperature or density correction applied.

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  $$IV = \frac{\text{Input Pulses}}{K\text{-Factor}}$$

  Variables

  $IV$

  Indicated Volume — uncorrected meter reading

  $K$

  Meter K-Factor — volume units per pulse

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• Gross Volume

  The physical volume measured by the meter at actual conditions, without temperature correction.

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  $$GV = \frac{MF \times \text{Input Pulses}}{K\text{-Factor}}$$

  Variables

  $MF$

  Meter Factor — calibration correction coefficient

  $K$

  Meter K-Factor

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• Net Volume / GST Volume

  The volume of the fluid referenced to the standard temperature of +15 °C (Gross Standard Temperature Volume).

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  $$\displaystyle GST = \frac{CTL \times MF \times \text{Input Pulses}}{K\text{-Factor}}$$

  Variables

  $CTL$

  Correction for Temperature on Liquid

  $MF$

  Meter Factor

  $K$

  Meter K-Factor

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• Mass Volume (MASS)

  The true mass of the fuel based on its density. Mass is constant regardless of temperature-driven volume changes.

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  • $MASS = \text{Gross Volume} \times \text{Observed Density}$
  • $MASS = \text{GST} \times \text{Reference Density}$

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• Correction for Temperature on Steel of a Prover (CTSP)

  Corrects for the expansion or contraction of the prover's steel body due to temperature changes.

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  $$CTSP = 1 + [CCE \times (T_p - T_{ref})]$$

  Variables

  $CCE$

  Coefficient of cubic expansion for steel (mild steel: 0.0000186)

  $Tp$

  Measured temperature of the prover body

  $Tref$

  Reference temperature at which the prover was calibrated

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• Volume Correction Factor (VCF / CTL)

  Corrects measured volume to standard conditions by compensating for thermal expansion or contraction of the liquid.

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  $$VCF = \frac{1}{1 + \beta \times (T_{obs} - T_{std})}$$

  Variables

  $β$

  Volumetric thermal expansion coefficient of the liquid (β)

  $Tobs$

  Observed (actual) temperature at measurement

  $Tstd$

  Standard reference temperature (typically +15 °C)

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• Combined Correction Factor (CCF)

  Combines CTSP and CTLP into a single correction value applied to prover-based calibration.

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  $$CCF = CTSP \times CTL_P$$

  Variables

  $CTSP$

  Correction for Temperature on Steel of the Prover

  $CTLP$

  Correction for Temperature on Liquid in the Prover

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• Corrected Meter Volume (CMF)

  The meter's registered volume after applying temperature correction factors to reach standard conditions.

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  $$CMF = VCF \times IV$$

  Variables

  $VCF$

  Volume Correction Factor

  $IV$

  Indicated (uncorrected) Volume

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• Meter Factor

  A calibration coefficient that corrects the difference between the volume measured by the flow meter and the true prover volume.

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  $$\displaystyle MF = \frac{\text{Corrected Prover Volume}}{\text{Corrected Meter Volume}}$$

  Variables

  $CPV$

  Corrected Prover Volume

  $CMV$

  Corrected Meter Volume

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