Proved that shows that the fuel quantity (Q) is directly proportional to both the measured volume (𝑉𝑚 ) and the Density-Volume Correction Factor (DVCF), and inversely proportional to the density ( 𝜌 )

 The relationship between fuel quantity and the Density-Volume Correction Factor (DVCF) lies in the adjustment of the measured volume of fuel to its volume at standard conditions, considering its density. This correction ensures accurate measurement and accounting for the actual mass of the fuel.

Here's how fuel quantity ($𝑄$) and DVCF ($𝐷𝑉𝐶𝐹$) are related:

1. Measured Volume (${𝑉}_{𝑚}$): This is the volume of fuel measured directly from the storage tank or container. It's typically measured in liters, gallons, or other volume units.

2. Corrected Volume ($𝑉$): This is the volume of the fuel adjusted to its volume at standard conditions using the DVCF. It accounts for the expansion or contraction of the fuel due to temperature and pressure variations.

3. Density ($𝜌$): This is the mass per unit volume of the fuel, typically measured in kg/m³, lb/ft³, or similar units.

4. Fuel Quantity ($𝑄$): This is the actual mass of the fuel, typically measured in kg, lb, or other mass units.

The relationship can be summarized as follows:

$𝑉={𝑉}_{𝑚}\times 𝐷𝑉𝐶𝐹$

$𝑄=𝜌\times 𝑉$

Therefore,

$𝑄=𝜌\times {𝑉}_{𝑚}\times 𝐷𝑉𝐶𝐹$

This equation shows that the fuel quantity ($𝑄$) is directly proportional to both the measured volume (${𝑉}_{𝑚}$) and the Density-Volume Correction Factor ($𝐷𝑉𝐶𝐹$), and inversely proportional to the density ($𝜌$). It highlights how adjusting the measured volume with the DVCF and considering the density allows for accurate determination of the fuel quantity.