Volume, Density, Flow Rate

E82 – Basic Process Variables

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Mass Density and Molar Density

The mass density, or usually just density, is a measure of the mass per volume, with SI units of kg/m³.

The molar density is a measure of the number of moles per volume, with SI units of g-mol/m³. It has the same units as concentration.

The reciprocal is the specific volume, with SI units of m³/kg.

The reciprocal is the molar volume, with SI units of m³/g-mol. F,R,&B reuse the symbols for density and specific volume for these.

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Specific Gravity

The specific gravity is the ratio of the density to a reference density.

The most common reference density is liquid water at 4°C.

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Concentration

The molar concentration or simply concentration is the number of moles per unit volume.

For an ideal gas it can be calculated as:

The mass concentration is the mass per unit volume (same units as density). It is most often used for quantities such as salinity.

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Mass, Molar, and Volumetric Flow Rates

The mass flow rate is simply the amount of mass flowing past a given location in a period of time. For open, steady-state systems, the sum of the mass flow rates in equals the sum of the mass flow rates out.

The molar flow rate is number of moles flowing past a given location in a period of time. For open, steady-state systems with no reactions, the sum of the molar flow rates in equals the sum of the molar flow rates out. For reacting systems, it is in general, not true.

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Mass, Molar, and Volumetric Flow Rates (cont.)

The volumetric flow rate is the volume of fluid flowing past a given location in a period of time. In general, for open, steady-state systems, the sum of the volumetric flow rates in is not equal to the sum of the volumetric flow rates out.

The following relationship exists among the volumetric flow rate of a fluid, the average fluid velocity, and the cross-sectional area of the flow.

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Mass, Molar, and Volumetric Flow Rates (cont.)

The relationship between the mass flow rate and the volumetric flow rate is:

For an open, steady-state system with one inlet and one outlet.

Do not forget! Volume is not a conserved quantity. Just because the mass or molar flowrate is constant, it does not follow that the volumetric flow rate is constant.

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