The formula
- Pressure from force and area
p = F / A- Pressure at depth in a fluid of constant density
p = p₀ + ρgh- Weight, when the force is an object resting on a surface
F = mg
What the symbols mean
| Symbol | Meaning | Unit |
|---|---|---|
p | Pressure | Pa (1 Pa = 1 N/m²) |
F | Force perpendicular to the surface | N |
A | Area the force is spread over | m² |
p₀ | Pressure at the surface, usually atmospheric at 1.013 × 10⁵ Pa | Pa |
ρ | Density of the fluid | kg/m³ |
g | Acceleration due to gravity | 9.80 m/s² |
h | Depth below the surface of the fluid | m |
m | Mass of the object | kg |
When it applies
- Only the component of force perpendicular to the surface counts. A force pushing sideways along the surface contributes nothing.
- p = F / A gives the average pressure over the contact area, so use the area actually touching.
- The depth formula assumes a fluid at rest with constant density, which is a good model for water in a tank or a pool.
Worked example
Problem. A 45 kg crate rests on a floor on a base measuring 0.60 m by 0.40 m. What pressure does it exert on the floor?
- Find the force. The crate presses down with its weight: F = mg = (45 kg)(9.8 m/s²) = 441 N.
- Find the contact area: A = 0.60 m × 0.40 m = 0.24 m².
- Divide: p = F / A = 441 N / 0.24 m² = 1837.5 Pa.
- Round to two significant figures: p = 1.8 × 10³ Pa, which is 1.8 kPa.
Answer. About 1.8 kPa, roughly one fifty-fifth of atmospheric pressure.
Common mistakes
- Using the object's whole surface area rather than the part actually in contact.
- Substituting mass in kilograms where the formula needs force in newtons. Convert with F = mg first.
- Confusing gauge pressure with absolute pressure. A tire gauge reading 220 kPa means 220 kPa above atmospheric.
- Thinking pressure at depth depends on the width of the container. It depends only on depth, density and the pressure at the surface.
Related formulas
- Bernoulli's equation:
p + ½ρv² + ρgy = constant - Newton's second law:
ΣF = ma - Ideal gas law:
pV = nRT