Definition
- Pressure is the force per unit area acting normal (at right angles) to a surface
- The same force concentrated into a smaller area produces a higher pressure. That's why a sharp knife slices and a blunt one doesn't, and why a sleeping bag is more comfortable on a wide foam mat than on a single rope
The pressure equation
P = F / A
- where:
- P = pressure (pascals, Pa, where 1 Pa = 1 N/m²)
- F = force acting perpendicular to the surface (N)
- A = area over which the force is applied (m²)
- Rearrangements:
- F = P × A (the total force a fluid pressure exerts on a surface of known area)
- A = F / P
Everyday consequences
- Small area + ordinary force = high pressure:
- Drawing pins taper to a tiny tip on the wall side. A modest push from a fingertip becomes a huge pressure at the point, driving it into the wood
- Nails and needles work the same way
- Sharp knives cut better than blunt ones because the cutting edge is a much smaller area
- Stiletto heels focus the wearer's weight onto a few square millimetres and can dent wooden floors
- Large area + ordinary force = low pressure:
- Tractor tyres are very wide. The same vehicle weight spread over more rubber gives a lower ground pressure, so the tractor doesn't sink into wet soil
- Caterpillar tracks on tanks and bulldozers do the same thing, distributing the weight over a long track footprint
- Snow shoes and skis stop a person sinking into soft snow by spreading their weight across a much larger area than a pair of boots would
- A camel's foot broadens when it pushes down, spreading the camel's weight on sand
Example — a hydraulic jack has a piston with a cross-sectional area of 0.40 m². The pump delivers a pressure of 2400 Pa to the underside of the piston. Calculate the upward force exerted on the piston.
- Rearrange P = F / A to F = P × A
- F = 2400 × 0.40 = 960 N
Example — a stiletto-heeled shoe presses on a wooden floor over a contact area of 0.50 cm². The wearer's weight on that one heel is 350 N. Calculate the pressure on the floor.
- Convert the area to SI: 0.50 cm² = 0.50 × 10⁻⁴ m² = 5.0 × 10⁻⁵ m²
- P = F / A = 350 / (5.0 × 10⁻⁵) = 7 000 000 Pa = 7.0 MPa
- A staggering pressure for the wood, which is why stilettos can leave dents that an elephant's broad foot would not