# Solving Specific Gravity in Process Engineering

Specific gravity is a dimensionless quantity that compares the density of a substance to the density of a reference material, usually water. Specific gravity can be calculated by dividing the density of the substance by the density of the reference material.

However, if you do not have the formula or the density values, you can still estimate the specific gravity of a substance by using a simple experiment. You will need a graduated cylinder, a balance, and the substance you want to measure. Here are the steps:

1. Fill the graduated cylinder with water and record the volume of water (Vw).
2. Weigh the empty graduated cylinder and record the mass (Mc).
3. Add the substance to the graduated cylinder and record the new volume of water and substance (Vs).
4. Weigh the graduated cylinder with water and substance and record the mass (Ms).
5. Subtract the mass of the empty graduated cylinder from the mass of the cylinder with water and substance to get the mass of the substance (Ms – Mc = Msub).
6. Subtract the volume of water from the volume of water and substance to get the volume of the substance (Vs – Vw = Vsub).
7. Divide the mass of the substance by the volume of the substance to get the density of the substance (Msub / Vsub = Dsub).
8. Divide the density of the substance by the density of water at the same temperature to get the specific gravity of the substance (Dsub / Dw = SGsub).

Specific gravity (SG) is calculated using the formula:

SG =

For liquids, the reference substance is usually water at a specified temperature, commonly 4°C (39.2°F) or 20°C (68°F). For solids and gases, air is often used as the reference.

## Scenario

Let’s consider a scenario in a chemical processing plant where a solution’s specific gravity needs to be determined. The solution contains a mixture of water, ethanol, and methanol. The densities of ethanol and methanol at the given temperature are known. We need to calculate the specific gravity of this solution to ensure its quality meets the required specifications.

## Example Calculation

Given:

• Density of water = 1000 kg/m³
• Density of ethanol = 789 kg/m³
• Density of methanol = 791 kg/m³
• Volume of water = 100 L
• Volume of ethanol = 50 L
• Volume of methanol = 30 L

First, we need to find the total mass of the solution:

Mass of water = Volume of water × Density of water =

Similarly, calculate the mass of ethanol and methanol:

Mass of ethanol =

Mass of methanol =

Total mass of the solution:

Total mass = Mass of water + Mass of ethanol + Mass of methanol =

Now, calculate the volume of the solution:

Total volume = Volume of water + Volume of ethanol + Volume of methanol =

Finally, determine the density of the solution:

Density of solution =

Now, to find the specific gravity, divide the density of the solution by the density of water:

SG =