Fluids. Density of Fluids

In these revision notes for Fluids. Density of Fluids, we cover the following key points:

• What is matter?
• How many states of matter are there normally? What are their properties?
• The meaning of fluids
• What is volume? Which are the units (standard and auxiliary of volume?
• What is density? How can we calculate it?
• How to calculate the density of a mixture?

Fluids. Density of Fluids Revision Notes

All objects are made up by tiny particles called atoms. They are the 'building blocks" of matter.

Matter is described as a "physical substance in general, which occupies space and possesses rest mass, especially as distinct from energy."

Matter can exist in three stable states in nature. They are:

1. Solid state. In this state, particles are "packed" in stable positions, which they cannot leave. In solid state the potential energy that keeps the particles together, which is also known as the "binding energy" is much greater than kinetic energy of particles. As a result, atoms in solids can only vibrate around their equilibrium position but they cannot leave their actual place and find new neighbouring atoms.
2. Liquid state. In this state, particles are still very close but they are not "attached" together. Their potential energy is still a bit greater than kinetic energy but the difference between them is very narrow. As a result, particles can slide easily over each other forming horizontal layers. As a result, the surface of liquids is always flat.
3. Gaseous state. In this state, particles move freely in space as their kinetic energy is greater than the potential (binding) energy. They look like balloons flying in the sky or like bubbles flowing in water.

"Fluid" is described as "something able to flow easily". In this regard, only liquids and gases qualify to belong in this category as they can flow easily.

By definition, "Volume, V, is the amount of space an object occupies."

On the other hand, "Density is the mass of a substance in the unit of volume."

In formulae, we express the density by the letter 'ρ' (rho), the mass by 'm' and the volume by 'V'. Therefore, the equation of density becomes

Obviously, the SI unit of density is [kg/m³] as mass is measured in [kg] and volume in [m³]. However, in many cases, especially when dealing with small amounts of matter, we often use another unit to express density. It is gram per cubic centimetre, i.e. [g/cm³]. The conversion factor between these two units is as follows:

The units of volume change 1000 by 1000. Therefore, to ease calculations and conversions, an auxiliary unit of volume known as "Litre, L" is introduced. Litre is used only in fluids, i.e. to express the volume of liquids and gases. Litre is numerically equal to cubic decimetre (1 L = 1 dm³) but it offers an important advantage compared to standard SI units of volume: its multiples and sub-multiples change 10 by 10 instead of 1000 by 1000.

To calculate the density of a gas, we simply divide its mass with the volume of the whole container as gases fill up all the space of the closed container in which they are.

In most cases, materials we use in daily life are not made of pure substances but by mixing two or more substances. Therefore, we are often required to calculate the density of a mixture instead of that of a pure substance. To calculate the density of a mixture, we use the formula

Thus, for two substances (1) and (2), we can write

For three substances (1), (2) and (3), we can write

and so on.