Introduction to Fluids: States of Matter and Density

Fluid Mechanics

States of Matter

Ordinary matter exists in three primary states: solids, liquids, and gases. Each state is characterized by the arrangement and energy of its constituent particles.

• Solids: Atoms or molecules are held in fixed positions by strong intermolecular forces. Although they vibrate, they do not move freely, resulting in a definite shape and volume.

• Liquids: Molecules have more energy than in solids and are not fixed in place. Intermolecular forces are weaker, allowing molecules to move past each other. Liquids have a definite volume but take the shape of their container. Liquids are not easily compressed.

• Gases: Molecules are in constant random motion and are far apart compared to their size. Intermolecular forces are very weak. Gases have neither a definite shape nor a definite volume; they expand to fill their container and are easily compressed.

Additional info: Plasma is another state of matter, consisting of ionized gases, but is not covered in this unit.

Definition of a Fluid

A fluid is any substance that can flow and thus takes the shape of its container. Both liquids and gases are classified as fluids.

• Fluids do not retain a fixed shape.

• They can be poured and will conform to the boundaries of their container.

In this unit, we focus on fluid statics—the study of fluids at rest. We assume that both the fluid and any solid objects in contact with it are stationary.

Density

Density is a fundamental property of matter, defined as the mass per unit volume. It is represented by the Greek letter \( \rho \) (rho).

• Formula:

$\rho = \frac{m}{V}$

• Where \( m \) is mass (in kilograms, kg) and \( V \) is volume (in cubic meters, m3).

• The SI unit of density is kg/m3.

• Another common unit is g/cm3. To convert: 1 g/cm3 = 1000 kg/m3.

Example: Calculating the Mass of Air in a Room

Problem: What is the mass of air in a living room with dimensions 4 m × 6 m × 2.5 m? Assume the density of air at room temperature is \( 1.2\ \mathrm{kg/m^3} \).

• Step 1: Calculate the volume of the room:

$V = \text{length} \times \text{width} \times \text{height} = 4\ \mathrm{m} \times 6\ \mathrm{m} \times 2.5\ \mathrm{m} = 60\ \mathrm{m^3}$

• Step 2: Use the density formula to find mass:

$m = \rho V = 1.2\ \mathrm{kg/m^3} \times 60\ \mathrm{m^3} = 72\ \mathrm{kg}$

• Answer: The mass of air in the room is 72 kg.