Pressure is fundamentally related to the concept of buoyancy in fluids. Buoyancy is the upward force that a fluid exerts on an object submerged in it. This force is a result of pressure differences within the fluid: the pressure at the bottom of the object is greater than the pressure at the top, creating a net upward force. According to Archimedes' principle, the magnitude of this buoyant force is equal to the weight of the fluid displaced by the object. This principle explains why objects float or sink in fluids depending on their density relative to the fluid.

In a hydraulic system, pressure is used to transmit force from one point to another through an incompressible fluid, typically oil. When a force is applied at one point in the fluid, it creates pressure in the system. According to Pascal's principle, this pressure is transmitted undiminished throughout the fluid, allowing a force applied to a small area to be transmitted to a larger area. This results in a magnified force at the output, allowing hydraulic systems to lift or move heavy loads. This principle is widely used in various mechanical systems, including car brakes, hydraulic jacks, and heavy machinery.

Pressure plays a significant role in determining weather patterns. Weather systems are largely driven by differences in atmospheric pressure, which cause air to move from high-pressure areas to low-pressure areas. High-pressure systems are generally associated with clear, calm weather, as they involve descending air that inhibits cloud formation. Low-pressure systems, on the other hand, often lead to unsettled weather conditions, including rain and storms, due to rising air that promotes cloud development. Meteorologists use barometers to measure atmospheric pressure, helping them predict weather changes and providing crucial information for weather forecasts.

Atmospheric pressure decreases with an increase in altitude. This is because atmospheric pressure is a result of the weight of the air above the point of measurement. As altitude increases, there is less air above the point, thus exerting less pressure. This decrease in atmospheric pressure with altitude has several implications. For instance, it affects the boiling point of water, which decreases at higher altitudes due to the lower pressure. It also has physiological effects on the human body, such as altitude sickness, caused by reduced oxygen levels at high altitudes. In aviation, understanding these changes in atmospheric pressure is crucial for altitude measurement and cabin pressurisation.

Deep-sea divers experience greater pressure as they dive deeper due to the increasing weight of the water above them. Water is much denser than air, so the pressure increases rapidly with depth. The pressure experienced by a diver at a certain depth is calculated using the hydrostatic pressure equation, P = ρgh. Here, ρ is the density of the water, g is the acceleration due to gravity, and h is the depth of the water. As the diver goes deeper, h increases, leading to an increase in pressure. This increased pressure can have physiological effects on divers, such as decompression sickness, and requires careful management through decompression stops and specialised equipment.