Characteristics of Fluids and Solids

Matter exists in four fundamental phases: solid, liquid, gas, and plasma. This chapter focuses on the first three.

• Solids have a definite shape and volume. Their particles are tightly packed in a fixed arrangement, making solids rigid and resistant to changes in shape or volume under typical conditions.

• Fluids — which include both liquids and gases — have no fixed shape and instead conform to the shape of their container. The key difference between the two: liquids have a definite volume and are essentially incompressible, while gases are compressible and expand to fill the entire volume of their container.

This distinction sets the stage for the rest of the chapter — the ability of fluids to flow and take the shape of their containers underlies pressure, buoyancy, and fluid flow.

Key Takeaways

• Solids hold a fixed shape and volume; fluids (liquids and gases) conform to their container — liquids are incompressible with a fixed volume, gases are compressible.

• Density (ρ = m/V) measures mass per volume; water's density is 1 g/cm³ = 1000 kg/m³. Specific gravity compares a substance's density to water's and is dimensionless.

• Pressure is force per unit area, measured in pascals (Pa = N/m²), and is a scalar quantity despite being derived from force.

• Atmospheric pressure is the baseline pressure from Earth's atmosphere; absolute pressure adds the fluid's own contribution (P = P_0 + ρgz); gauge pressure is measured relative to atmospheric pressure (P_gauge = P − P_atm).

Density and Specific Gravity

Density measures how much mass is packed into a given volume of a substance:

ρ = m/V

where ρ (rho) is density, m is mass, and V is volume. Density explains why some objects float and others sink — a stone sinks in water because its density is greater than water's, while a leaf floats because it's less dense.

The SI unit of density is kilograms per cubic meter (kg/m³), though grams per milliliter (g/mL) or grams per cubic centimeter (g/cm³) are also common. The density of water is a value worth memorizing for the MCAT:

• 1 g/cm³, or equivalently

• 1000 kg/m³

The weight of a fluid follows directly from its density:

F_g = ρVg

where F_g is the gravitational force (weight), ρ is fluid density, V is fluid volume, and g is the acceleration due to gravity (≈ 9.8 m/s²). This relationship is the basis for buoyancy calculations.

Specific gravity (SG) compares the density of a fluid to that of pure water at 1 atm and 4°C (water's temperature of maximum density):

SG = ρ / (1 g/cm³)

Because it's a ratio of two densities, specific gravity is dimensionless. SG < 1 means the substance is less dense than water and will float; SG > 1 means it's denser and will sink.

MCAT Callout — Worked Example: Oil Density and Specific Gravity: A sample of oil has a mass of 46 g and a volume of 50 mL. Its density is ρ = 46 g / 50 mL = 0.92 g/mL. Its specific gravity is SG = 0.92 g/mL ÷ 1 g/mL = 0.92. Since SG < 1, the oil floats on water.

Pressure

Pressure is defined as force per unit area. For a given force, the smaller the area over which it's applied, the higher the pressure.

The SI unit for pressure is the pascal (Pa), equal to one newton per square meter (N/m²) — one pascal is one newton of force spread over one square meter of area. The MCAT expects comfort converting between several common pressure units:

Despite being derived from force, pressure is a scalar quantity — it has magnitude but no direction. This might seem counterintuitive, since force itself is a vector. The reason: pressure comes from the magnitude of the normal force, not its direction. In a closed container of fluid, pressure is exerted equally in all directions at any given point, because fluid molecules move randomly and collide with the container walls (and any surface inside it) equally in every direction. This is also why pressure in a fluid is the same at all points at the same depth.

Pressure differences explain a range of everyday phenomena:

• Respiration: air flows in and out of the lungs because of pressure differences — air rushes in when lung pressure drops below atmospheric pressure, and is expelled when lung pressure rises above it.

• Weather systems: differences in atmospheric pressure create wind, and extreme differences can produce storms and tornadoes.

• Engineering: structures must be designed to withstand pressure differences from wind and water.

Absolute, Atmospheric, and Gauge Pressure

Fluid mechanics distinguishes three related but distinct pressure concepts.

Atmospheric pressure is the pressure exerted by the weight of Earth's atmosphere on everything at or near its surface. It decreases with increasing altitude, as there's less air column weighing down from above. At sea level, average atmospheric pressure is:

• 101.3 kPa

• 1 atm

• 760 mmHg

• 14.7 psi

High-altitude cities like Denver experience lower atmospheric pressure (around 0.83 atm) than low-lying areas like Death Valley (as high as 1.01 atm). Atmospheric pressure has real physiological effects — it influences the boiling point of liquids and the oxygen-binding capacity of hemoglobin in blood.

Absolute pressure (sometimes called hydrostatic pressure for fluids) is the total pressure on an object submerged in a fluid — the atmospheric/surface pressure plus the pressure from the fluid's own weight:

P = P_0 + ρgz

where P is absolute pressure, P_0 is the ambient or surface pressure (often, but not always, atmospheric pressure), ρ is fluid density, g is gravitational acceleration (≈ 9.8 m/s²), and z is depth below the surface. P_0 is not automatically atmospheric pressure — in open-air, everyday situations it usually is (1 atm), but in other fluid systems the surface pressure can be higher or lower.

Gauge pressure is the pressure measured relative to atmospheric pressure — the form most commonly encountered in everyday instruments:

P_gauge = P − P_atm

A tire gauge, for instance, reads gauge pressure: a reading of zero means the tire's internal pressure equals atmospheric pressure, not that the tire is empty. When P_0 = P_atm, the absolute-pressure formula simplifies to P_gauge = ρgz — common for open systems like a swimming pool or an open tank, where gauge pressure depends only on fluid density, gravity, and depth. Gauge pressure can be positive (system pressure above atmospheric) or negative (a vacuum, below atmospheric).

MCAT Callout — Absolute vs. Atmospheric vs. Gauge Pressure: Atmospheric pressure is the baseline pressure from Earth's atmosphere. Absolute pressure includes both atmospheric pressure and the pressure from the fluid itself. Gauge pressure is measured relative to atmospheric pressure — which is why a tire reading zero gauge pressure isn't actually flat, it's simply at atmospheric pressure.

Common MCAT Mistakes

• Reading gauge pressure as absolute pressure. A tire gauge reading of zero doesn't mean zero pressure inside the tire — it means the tire's internal pressure equals atmospheric pressure. Absolute pressure is always gauge pressure plus atmospheric pressure.

• Treating pressure as a vector. Because pressure is derived from force, it's tempting to assign it a direction. Pressure is a scalar — at any point in a fluid, it acts equally in all directions.

• Confusing density with specific gravity. Density has units (kg/m³ or g/cm³); specific gravity is a unitless ratio comparing a substance's density to water's. A substance can have a specific gravity of 0.92 without ever stating a unit.

• Assuming atmospheric pressure never changes. Atmospheric pressure drops with altitude — a diver's absolute pressure calculation and a mountain climber's boiling-point calculation both depend on knowing the local atmospheric (or surface) pressure, not always assuming standard sea-level 1 atm.

MCAT-Style Concept Check

Question: A diver is swimming at a depth of 10 m below the surface of a lake, where the water density is 1000 kg/m³. Atmospheric pressure at the surface is 1.0 × 10⁵ Pa, and g = 10 m/s². What is the absolute pressure experienced by the diver?

• A) 1.0 × 10⁵ Pa

• B) 1.5 × 10⁵ Pa

• C) 2.0 × 10⁵ Pa

• D) 3.0 × 10⁵ Pa

Answer: C

Explanation: Absolute pressure is P = P_0 + ρgz. Plugging in: P = 1.0 × 10⁵ Pa + (1000 kg/m³)(10 m/s²)(10 m) = 1.0 × 10⁵ Pa + 1.0 × 10⁵ Pa = 2.0 × 10⁵ Pa. The fluid's own weight contributes an additional 1.0 × 10⁵ Pa on top of the atmospheric baseline, so the total absolute pressure is 2.0 × 10⁵ Pa — answer C.

FAQ

What's the difference between a solid and a fluid?

A solid has a fixed shape and volume because its particles are locked in a rigid arrangement. A fluid — either a liquid or a gas — has no fixed shape and conforms to its container. Liquids keep a fixed volume and resist compression, while gases are compressible and expand to fill whatever space they're in.

What is specific gravity, and why is it dimensionless?

Specific gravity is the ratio of a substance's density to the density of pure water (1 g/cm³ at 1 atm and 4°C). Because it's density divided by density, the units cancel, leaving a plain number with no unit. An SG below 1 means the substance floats on water; an SG above 1 means it sinks.

Why is pressure a scalar, not a vector, quantity?

Pressure is force per unit area, and force is a vector — but pressure only depends on the magnitude of that force, not its direction. In a fluid, pressure pushes equally in every direction at a given point, which is why it's treated as a scalar rather than a vector.

What's the difference between absolute, atmospheric, and gauge pressure?

Atmospheric pressure is the baseline pressure from the weight of Earth's atmosphere (1 atm at sea level). Absolute pressure is the total pressure at a point in a fluid — atmospheric pressure plus the pressure added by the fluid's own weight (P = P_0 + ρgz). Gauge pressure is measured relative to atmospheric pressure (P_gauge = P − P_atm), which is why a tire gauge reading zero means the tire is at atmospheric pressure, not empty.