Pressure in a fluid
A fluid is anything that can flow, so both liquids and gases are fluids. A fluid exerts pressure on any surface it touches, and this pressure in fluids has three important features: it increases with depth, it increases with the density of the fluid, and it acts equally in all directions at a given point.
Key idea
Pressure in a liquid P = h ρ g, where h is the depth, ρ is the density of the liquid and g is the gravitational field strength. Pressure does not depend on the shape of the container.
Pascal's principle
Pascal's principle states that pressure applied to an enclosed fluid is transmitted equally and undiminished throughout the fluid in all directions. This idea is used in hydraulic systems. In a hydraulic jack or the hydraulic brakes of a car, a small force on a small piston creates a pressure that is transmitted through the liquid to a large piston, producing a much larger force. The liquid must be incompressible for this to work.
Example
At a depth of 2 m in water (density 1000 kg m⁻³, g = 10 N kg⁻¹), the pressure due to the water is P = 2 × 1000 × 10 = 20 000 Pa.
Buoyancy
When an object is placed in a fluid, the fluid pushes up on it with an upward force called the buoyant force (upthrust). By Archimedes' principle, this force equals the weight of fluid displaced by the object. An object floats when the buoyant force is equal to its weight; this is why a heavy steel ship can float — its shape displaces a large weight of water.
Remember
A denser liquid, or a greater depth, gives a greater pressure. Buoyant force does not depend on the object's weight but on the weight of fluid it pushes aside.