# Solid and Liquid Density

### Upon studying this section, you should be familiar with the following:

• The interrelations between density, mass, volume, and specific gravity for a liquid or solid,
• Putting it another way, know the two interrelations that can get you to the density of a solid or liquid (ρ(SG) and ρ(m,V)).

Explanation:

There is a relationship between the density of a solid or liquid to its specific gravity and the density of a reference state. There is also a relationship between the density of a solid or liquid with its mass and volume.

Density from Specific Gravity:

Specific Gravity (SG) is a ratio of densties, the density (ρ) of a specific substance and of a reference and is therefore unitless.

SGi = ρi / ρref

because water is usually the reference, you get

SGi = ρi / ρH2O, or ρi = SGi * ρH2O

and when 1 g/mL is the density of water, which is usually an acceptable approximation at moderate temperatures and pressures, so you will usually use the following equation to calculate the density of substance knowing its specific gravity:

ρi = SGi * 1 g/mL

If the problem statement gives the density of water to be anything other that 1 g/mL (for example, .98 g/mL), use that density in place of 1 g/mL in the above equation (ρi = SGi * .98 g/mL).

Density from Mass and Volume:

The relationship for the density of a solid or liquid given its mass and volume is the following:

density = mass / volume, or ρ = m / V

Example 1:

The specific gravity of gasoline is approximately 0.70. Determine the mass (kg) of 50.0 liters of gasoline.

| See Solution

Example 2:

Calculate densities in lbm/ft3 of the following substances:

1. a liquid with density of 995 kg/m3.
2. a solid with a specific gravity of 5.7.
Goto | Check Answer | See Solution

Example 3:

Calculate the density of mercury in lbm/ft3 from a tabulated specific gravity, and calculate the volume in ft3 occupied by 215 kg of mercury. Goto | Check Answer | See Solution

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