AP Physics 1 · Unit 8: Fluids ·  Lesson 8.2

Deep Dive: Pressure

🔬 Deep Dive
This is your textbook for this topic. Take your time. Read it more than once.
8.2.A.18.2.A.2Math

Defining Pressure

Pressure is the magnitude of the perpendicular force component exerted per unit area, over a given surface:

P = F⊥ / A

That word "perpendicular" is doing real work. If a force pushes at an angle against a surface, only the component pushing straight into the surface contributes to pressure — the component sliding along the surface doesn't count.

surface, area AF (applied)F⊥F∥ (ignored)Only F⊥ contributes to pressure: P = F⊥ / A. F∥ doesn't count.
🔑Pressure is a scalar quantity — magnitude only, no direction. This is genuinely different from force, which is a vector. A pressure of 50,000 Pa doesn't "point" anywhere; it's just a number.
ExampleWorked Example — Calculating Pressure from Force and Area

A 720 N crate rests on a square base 0.60 m on each side. Find the pressure the crate exerts on the floor.

8.2.A.3Concept

Incompressible Fluids Under Pressure

This connects straight back to Lesson 8.1's ideal fluid model: the volume and density of a given amount of an incompressible fluid stay constant, no matter how much pressure is exerted on it.

💡Squeeze a balloon full of air (compressible), and its volume shrinks. Squeeze a sealed container completely full of water (essentially incompressible), and the water's volume barely changes at all — this is exactly why hydraulic systems, which rely on incompressible fluid to transmit force reliably, work the way they do.
8.2.B.1Concept

Where Fluid Pressure Actually Comes From

A solid block resting on a table exerts pressure through one clean, well-defined force. A fluid is messier — and more interesting. The pressure a fluid exerts on a surface is the net result of countless individual particle collisions against that surface, all happening constantly and from every direction.

🔑No single particle "is" the pressure. Pressure is a statistical, collective effect — the combined result of an enormous number of tiny collisions, averaged into one smooth, measurable quantity.
8.2.B.28.2.B.3Math

Absolute Pressure, Gauge Pressure, and Depth

At any point in a fluid, the absolute pressure is the sum of a reference pressure P₀ (usually atmospheric pressure) and the gauge pressure — the extra pressure contributed by the fluid itself:

P = P₀ + P_gauge

For a vertical column of fluid, gauge pressure depends on exactly three things — the fluid's density, gravity, and how deep the point is:

P_gauge = ρgh

Deeper point, denser fluid, or stronger gravity — any of the three increases gauge pressure. Combine the two equations and you get the full picture: P = P₀ + ρgh.

Drag depth and pick a fluid. Watch absolute pressure climb — and watch the particle collisions below speed up as pressure increases.

Depth h (m)3.0 m
Density ρ (kg/m³)1000
Gauge Pressure
29.4 kPa
Absolute Pressure
130.7 kPa
vs. Atmospheric
1.29×
P (kPa)depth h (m) →
particle collisions against the surface

Higher pressure means more frequent, harder collisions — that's what pressure actually is at the particle level.

ExampleGuided Example — Absolute Pressure at Depth

A diver is swimming 3.0 m below the surface of a freshwater lake (ρ = 1000 kg/m³). Atmospheric pressure at the surface is P₀ = 1.01×10⁵ Pa. Find the absolute pressure at the diver's depth. (g = 9.8 m/s²)

Step 1Calculate gauge pressure
P_gauge = ρgh = (1000)(9.8)(3.0) = 29,400 Pa
← Back to Lesson 8.2Lesson 8.3 — Fluids and Newton's Laws — is next.