Learning Outcomes

Upon completing this lesson, you will be able to:

• Differentiate between the phases of matter and define density and specific gravity.
• Define pressure and calculate the pressure at a certain depth within a fluid.
• Distinguish between atmospheric, absolute, and gauge pressure.
• State Pascal's Principle and apply it to hydraulic systems.

Topics Covered

• Phases of Matter, Density, and Specific Gravity
• Pressure in Fluids
• Pascal's Principle

I. Phases of Matter, Density, and Specific Gravity

A. Phases of Matter

Matter typically exists in three phases: solid, liquid, and gas. A fluid is a substance that can flow and take the shape of its container. Both liquids and gases are considered fluids.

• Solids: Have a definite shape and volume.
• Liquids: Have a definite volume but no definite shape.
• Gases: Have neither a definite shape nor a definite volume; they expand to fill their container.

A fourth phase of matter can be distinguished, the plasma phase, which occurs only at very high temperatures and consists of ionized atoms (electrons separated from the nuclei).

B. Density $(\rho)$

Density is a fundamental property of a substance that describes how much mass is packed into a given volume.

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

• $m$ is the mass.

• $V$ is the volume.

• The SI unit for density is kilograms per cubic meter $(kg/m^3)$.

• The density of water is approximately $1000 , kg/m^3$.

We will sometimes use the concept of density to write the mass of an object as:

$$ m=\rho V $$

and the weight of an object as

$$ mg = \rho Vg $$

The Table specifies temperature and atmospheric pressure because they affect the density of substances (although the effect is slight for liquids and solids). Note that air is roughly 1000 times less dense than water.

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Example 1

What is the mass of a solid iron wrecking ball of radius 18 cm?

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C. Specific Gravity (SG)

Specific Gravity is the ratio of the density of a substance to the density of a reference substance, usually water at $4^\circ C$, and it is a dimensionless quantity.

$$ SG = \frac{\rho_{\text{substance}}}{\rho_{\text{water}}} $$

Density of water: $\rho_{\text{water}}=1000 \text{ kg/m}^3$

An object with an SG less than $1$ will float in water, while an object with an SG greater than $1$ will sink.