Density with Specific Gravity in Process Engineering

Density is a property of matter that tells us how much mass is contained in a given volume of a substance. For example, a block of iron has more mass than a block of wood of the same size, so the iron has a higher density. Density is measured in units of mass per unit volume, such as kilograms per cubic meter or pounds per cubic inch.

Specific gravity is a relative measure that compares the density of a substance to the density of a reference substance, usually water at a specified temperature. Water has a density of about 1,000 kilograms per cubic meter or 62.4 pounds per cubic foot at 4°C (39.2°F), which is its highest density. Specific gravity is a pure number or dimensionless, meaning it has no units. It tells us how many times the substance is heavier or lighter than water.

For example, the specific gravity of gold is 19.3, which means that gold is 19.3 times denser than water. The specific gravity of air is 0.0012, which means that air is 0.0012 times denser than water, or 833 times lighter than water.

Understanding Density

Density is defined as the mass per unit volume of a substance. Mathematically, it is expressed as:

Density = $\frac{Mass}{Volume}$

Specific Gravity

Specific gravity (SG) is a dimensionless ratio comparing the density of a substance to the density of a reference substance, typically water at 4°C. It is calculated as:

Specific Gravity (SG) = $\frac{Density\, of\, Substance}{Density\, of\, Water\, at\, 4°C}$

Example

Let’s consider a scenario in a chemical processing plant where a process engineer needs to determine the specific gravity of a liquid mixture. The mixture consists of two components: Component A and Component B. The density of Component A is 800 kg/m³, while the density of Component B is 1200 kg/m³. The engineer needs to calculate the specific gravity of the mixture.

Calculation:

Calculate the mass fraction (W_i) of each component in the mixture. Assuming equal volumes of Component A and Component B.
Determine the mass of each component (m_i) using the density and volume (V_i) of the components.
Calculate the total mass (m_total) of the mixture.
Determine the total volume (V_total) of the mixture.
Calculate the density of the mixture (?_mixture).
Calculate the specific gravity of the mixture (SG_mixture).

Results:

Given the densities of Component A and Component B, let’s assume V_A = V_B = 1 m³ for simplicity.

m_A = 800 kg/m³ × 1 m³ = 800 kg

m_B = 1200 kg/m³ × 1 m³ = 1200 kg

m_total = 800 kg + 1200 kg = 2000 kg

V_total = 1 m³ + 1 m³ = 2 m³

?_mixture = $\frac{2000 kg}{2 m³}$ = 1000 kg/m³

SG_mixture = $\frac{1000 kg/m³}{1000 kg/m³}$ = 1

Therefore, the specific gravity of the mixture is 1, indicating that its density is the same as water at 4°C.