Specific Gravity Formula

Specific gravity is one of the properties of any fluid. The specific gravity is having much application even in our everyday life. In order to understand fluid dynamics, we must understand what is the specific gravity and the specific gravity formula as a priority. The specific gravity often is even referred to as the relative density and it is a dimensionless entity. The density of the object majorly determines this factor. In this topic, we will discuss what is specific gravity, what is specific gravity formula and a small derivation of specific gravity formula along with solved examples.

Specific Gravity of Liquid

The specific gravity of liquid refers to the ratio of the density of an object or the fluid and the reference material, usually, water is considered as reference material for fluids and air for gases. Furthermore, the specific gravity of a liquid or an object can tell us if the object will sink or float in reference material. Besides, the reference material for liquids is water that always has a density of either 1 gram per cubic centimetre or 1000 kg/m³ and the specific gravity of water is always one.

In general, we can say the specific gravity defines whether an object will sink or float in water. Anyways, there are many other factors that determine whether an object will float or sink, such as density, specific weight, etc. The specific gravity of the object is always denoted by the letter S.

Application of Specific Gravity

The main application of specific gravity is that it lets us decide whether the given object is denser than the water or not. If the specific gravity of the object is less than the specific gravity of water i.e., S ＜ 1 then the object will float on the water. At the same time if the specific gravity of the object is found to be greater than the specific gravity of water i.e., S > 1 then the object will sink in the water. For example, we can think of a plastic ball floating on water. 

If we know the specific gravity of any material then we can easily determine the density of the material. Let us have a look at the specific gravities of a few familiar objects:

• The specific gravity of water = 1

• The specific gravity of mercury = 13 . 6

• The specific gravity of aluminium = 2.72

• Specific gravity of gold = 19.3

What Is Specific Gravity Formula?

Let us have a look at the specific gravity of liquid derivation to understand what is specific gravity formula. According to the definition of specific gravity, we can formulate the same mathematically as follows:

⇒ S = \[\frac{\rho_{object}}{\rho_{water}}\]

Where,

\[\rho\]\[_{object}\] - The density of the object or the material under consideration

\[\rho\]\[_{water}\] - The density of the water (or the reference material depending upon the material used)

Since both the numerator and the denominator have the same units (i.e., both are densities), hence they cancel out each other, thus the specific gravity is a dimensionless physical quantity. From the specific gravity formula, it is clear that the specific gravity is directly proportional to the density of the materials. In order to calculate the specific gravity, we must first know how to calculate the density of the materials.

The density of the materials can be calculated by using the formula:

⇒ \[\rho\] = \[\frac{mass}{volume}\] = \[\frac{m}{v}\] Kg/m\[^{3}\]

We know that the mass of an object can be in grams, kilograms, and pounds, irrespective of the unit of measurement the density of the object can be determined. At the same time, the density directly relates to the mass of the object. So, we can also rewrite the specific gravity by dividing the mass of an object with the mass of the water without violating the laws of physics. Thus, the specific gravity formula in terms of mass is given by:

⇒ S = \[\frac{\text{mass of the object}}{\text{mass of the water}}\] 

And from the theories of physics, we have seen that the mass of the object is also directly related to density. Also, from Newton’s law, we know that the mass is measured in Newtons. Hence, we can also calculate the specific gravity of an object with the help of the weight of the object and water, and it is given by the formula:

⇒ S = \[\frac{\text{Weight of the object}}{\text{Weight of the water}}\] 

One of the important points to note down here is that in all these formulas of specific gravity all the units are the same and they cancel each other out.

Solved Examples:

1. A liquid has a mass of 45 grams and the volume of the water (reference material) is 5 ml. Then calculate the specific gravity of the object? Also, specify whether the object will sink or float in the water? 

(Note: Consider the density of the water is 1 gm/ml) 

Sol:

Given,

The mass of the object = m = 45 grams

The volume of the water = V = 5 ml

The density of water = \[\rho\]\[_{water}\] = 1gm/ml

We are asked to determine the specific gravity of the given object. Before we start calculating the specific gravity, we must determine the density of the given object.

Thus, the density of the given object is given by:

⇒ \[\rho\]\[_{object}\] = \[\frac{mass}{volume}\] = \[\frac{45}{5}\] = 9 gm/ml…..(1)

Therefore, the specific gravity formula is given by:

⇒ S = \[\frac{\rho_{object}}{\rho_{water}}\] …..(2)

Where,

\[\rho\]\[_{object}\] - The density of the object or the material under consideration

\[\rho\]\[_{water}\] - The density of the water 

Substituting all the values in equation (2) and simplify. We get:

⇒ S = \[\frac{9}{1}\] = 9

Thus, the specific gravity of a given object is 9. Since the specific gravity of the object is more than 1 i.e., S > 1, the object will sink in the water.

2. A liquid has a mass of 10 grams and the volume of the water (reference material) is 12 ml. Then calculate the specific gravity of the object? Also, specify whether the object will sink or float in the water? 

(Note: Consider the density of the water is 1 gm/ml) 

Sol:

Given,

The mass of the object = m = 10 grams

The volume of the water = V = 12 ml

The density of water = \[\rho\]\[_{water}\] = 1gm/ml 

We are asked to determine the specific gravity of the given object. Before we start calculating the specific gravity, we must determine the density of the given object.

Thus, the density of the given object is given by:

⇒ \[\rho\]\[_{object}\] = \[\frac{mass}{volume}\] = \[\frac{10}{12}\] = 0.8 gm/ml …..(1)

Therefore, the specific gravity formula is given by:

⇒ S = \[\frac{\rho_{object}}{\rho_{water}}\] …..(2)

Where,

\[\rho\]\[_{object}\] - The density of the object or the material under consideration

\[\rho\]\[_{water}\]  - The density of the water 

Substituting all the values in equation (2) and simplify. We get:

⇒ S = \[\frac{0.8}{1}\] 

Thus, the specific gravity of given object is 0.8. Since the specific gravity of the object is less than 1 i.e., S < 1, the object will float in the water.