pressure (Pa) = force normal to a surface (N) / area of that surface (m2)
Pressure is defined as a how much force is acting upon a certain area. Teachers often introduce the idea by the metaphor of the elephant, or the lady in the stiletto. Which would you rather have stand on your foot?
Otherwise they sometimes give examples of things which give a high pressure for a small force, for example knives, or things which give a small pressure for a high force, for example a surf board.
An example calculation:
A 4N weight is placed on a 0.25m2 board what pressure is exerted on the surface underneath?
Types of Pressure
Air pressure is caused by the total force of all the particles colliding with a surface.
Water pressure is greater the deeper one goes in a column of water and can be calculated by multiplying the depth by the density by the gravitational field strength.
Solid exert pressures which depend on their forces and their areas, for example a pin which has a small area pointed end, which applies a high pressure to the wall, but a large area end that we can push, so a low pressure is applied to our thumb.
In space there is very little air pressure, as typically there is only one molecule per square meter! Astronaut's suits are pressurised to 1 atmosphere, which is equivalent to pressure at sea level on earth.
Hydraulic systems are ways to multiply forces. They use sets of pistons of different areas to increase or decrease the output force. An example of a use of this is a car jack, where a person needs to be able to lift a car using only the force they can make with their foot.
Hydraulic systems use the principle that liquids are virtually incompressible, so the pressure created in the liquid is equal throughout. The maths seems complicated, but in fact the situation is as simple as multiplying the force in the ratio of the cross sectional areas of the pistons.
You may have to work from a piston diameter, using your equation for the area of a circle to work out your areas....
A very hard question might ask you to work out how far a piston has moved, you'll need to work through the Volume of liquid displaced to do this, using Volume = Area X length
A piston has a 1cm2 master piston and a 5cm2 slave piston. 5N is applied to the master piston. What force is exerted by the slave piston?