Density, Volume, Flow Rates Reference Page
Are You Dense? Crank Up the Volume and Go With the Flow!

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Intro to Are You Dense? Crank Up the Volume and Go With the Flow!

Density, volume, and flow rate are among the most frequently used quantities in chemical and thermal process engineering. Engineers use them to describe how much material is present, how much space it occupies, and how quickly it moves through a system.

These ideas can be expressed on either a mass basis or a mole basis, and both are important in chemical engineering. This set of videos introduces the relationships among mass density, specific volume, molar density, molar volume, mass flow rate, molar flow rate, volumetric flow rate, and fluid velocity.

The videos also connect these ideas to mixture composition through mass fractions and mole fractions, which are used constantly in material balances and process calculations.

Just The Facts

The Just the Facts video introduces the main definitions and equations for density, volume, and flow rate on both a mass basis and a mole basis.

Visuals

The Full Story

The Full Story video examines common conceptions and misconceptions about density, volume, and flow rate before developing the key definitions and relationships used in engineering calculations.

Visuals

Examples and Definitions

Definitions

Mass Density
Mass density is the mass of a substance per unit volume. It is commonly denoted by \(\rho\):

\[ \rho = \frac{m}{V} \]

Typical units include \(\mathrm{kg/m^3}\) and \(\mathrm{g/cm^3}\).

Specific Volume
Specific volume is the volume per unit mass and is the reciprocal of mass density:

\[ v = \frac{V}{m} = \frac{1}{\rho} \]

Typical units include \(\mathrm{m^3/kg}\).

Molar Density
Molar density is the number of moles per unit volume. It is either denoted by \(\rho\) or by \(C\) :

\[ \rho = C = \frac{n}{V} \]

Typical units include \(\mathrm{mol/m^3}\) and \(\mathrm{mol/L}\).

Molar Volume
Molar volume is the volume occupied per mole and is the reciprocal of molar density:

\[ \hat{V} = \frac{V}{n} = \frac{1}{\Rightarrow} \]

Typical units include \(\mathrm{m^3/mol}\) and \(\mathrm{L/mol}\).

Mass Fraction
Mass fraction is the ratio of the mass of one component to the total mass of the mixture:

\[ x_i = \frac{m_i}{\sum_j m_j} \]

It is dimensionless.

Mole Fraction
Mole fraction is the ratio of the number of moles of one component to the total number of moles in the mixture:

\[ y_i = \frac{n_i}{\sum_j n_j} \]

It is dimensionless.

Mass Flow Rate
Mass flow rate is the mass of material passing through a surface per unit time:

\[ \dot{m} = \frac{dm}{dt} \]

Typical units include \(\mathrm{kg/s}\) and \(\mathrm{g/min}\).

Molar Flow Rate
Molar flow rate is the number of moles passing through a surface per unit time:

\[ \dot{n} = \frac{dn}{dt} \]

Typical units include \(\mathrm{mol/s}\) and \(\mathrm{mol/min}\).

Volumetric Flow Rate
Volumetric flow rate is the volume of fluid passing through a surface per unit time:

\[ \dot{V} = \frac{dV}{dt} \]

Typical units include \(\mathrm{m^3/s}\) and \(\mathrm{L/min}\).

Fluid Velocity
Fluid velocity is the speed and direction of fluid motion. In one-dimensional flow calculations, the average fluid speed is often related to volumetric flow rate by

\[ \dot{V} = u A \]

where \(A\) is the cross-sectional area and \(u\) is the average velocity.

Cross-Sectional Area
Cross-sectional area is the area perpendicular to the direction of flow. It is used in relating fluid velocity to volumetric flow rate. For a circular pipe of diameter \(D\),

\[ A = \frac{\pi D^2}{4} \]