Short on time? This page is the recap. For diagrams, the column derivation and worked examples, use the full study guide. This is the algebra-based course: no calculus is needed.
Recap
- Pressure is the perpendicular force on a surface divided by the area it acts on. A force along the surface adds nothing to the pressure.
- Pressure is a scalar. At a point in a fluid, it has one value. The force it makes on any surface is perpendicular to that surface.
- A fluid’s pressure comes from countless particle collisions with a surface. Particles move every way, so a fluid pushes on every surface it touches.
- An incompressible liquid keeps the same volume and density however hard it is squeezed.
- Absolute pressure is the total. Gauge pressure is the amount above a reference, usually the atmosphere.
- Pressure increases with vertical depth because each layer supports the weight of the fluid above it.
Key relationships
| Relationship | Symbols and units | Use it to |
|---|---|---|
| P = F⊥ / A | P in Pa (N/m²), F⊥ in N, A in m² | pressure from a force |
| P = P₀ + P_gauge | P₀ often P_atm = 1.0 × 10⁵ Pa | switch between absolute and gauge |
| P_gauge = ρgh | ρ in kg/m³, g = 9.8 m/s², h in m (vertical depth) | pressure under a column of fluid |
| F = PA (perpendicular to surface) | N | force from a pressure on a flat surface |
| slope of P–h graph = ρg | Pa/m | find density from a pressure–depth line |
Assumptions behind the numbers
- The fluid is at rest and incompressible, so ρ is the same at every depth.
- g is uniform: 9.8 m/s².
- The pressure on a horizontal surface is the same everywhere on it. On a tall vertical wall it is not, because depth varies.
- Atmospheric pressure is taken as 1.0 × 10⁵ Pa unless stated.
Mistakes to avoid
- Calling pressure a force or a vector. It is force per area, and a scalar.
- Using the whole force when it acts at an angle. Use F⊥ only.
- Mixing gauge and absolute pressure. Check which one the question wants.
- Using the slanted length of a tube as h. Use the vertical depth.
- Thinking a wider or fuller container has more pressure at the same depth. It does not.
- Doubling absolute pressure when depth doubles. Only gauge pressure doubles.
- Leaving depth in cm or area in cm². Convert to m and m².
Quick self-check
- A 300 N crate rests on a base of area 0.25 m². Pressure on the floor? (1.2 × 10³ Pa)
- Gauge pressure 2.0 m below the surface of fresh water? (2.0 × 10⁴ Pa, or 19,600 Pa)
- Absolute pressure at the same point? (1.2 × 10⁵ Pa)
- Two tanks of the same liquid, one narrow and one wide, are filled to the same depth. Which has the greater pressure at the bottom? (Neither: the pressures are equal.)
Next: practice questions.