Your ears hurt when you dive deep in a pool, and your body feels lighter in a bath──these are effects of water pressure and buoyancy.
Basic Knowledge
Water pressure is pressure caused by the weight of water and increases in proportion to depth. The water pressure at depth h [m] is found using the following formula:Water pressure P = ρgh ( ρ: density of water 1000 kg/m³ , g: acceleration due to gravity 9.8 m/s² )
Water pressure acts on an object in water from every direction. However, comparing the top and bottom, the pressure from below is greater, leaving a net upward force. This is buoyancy.
Archimedes' principle: A buoyant force acts with a magnitude equal to the weight of the liquid (water) displaced by an object.Buoyant force = ρ × V × g ( V: volume of the submerged part )
Water pressure (pressure caused by the weight of water. Proportional to depth)
Buoyancy (the upward force acting on an object in a liquid or gas)
Archimedes' principle (buoyant force = weight of displaced liquid)
Density ρ (mass per unit volume. Water is approximately 1000 kg/m³ = 1 g/cm³)
Condition for floating (an object floats when its density is less than that of the liquid)
Condition for sinking (an object sinks when its density is greater than that of the liquid)
Further Exploration (Background and Significance)
Archimedes (third century BCE) is said to have measured volume from the rise in water level when a crown was placed in water and calculated its density to determine whether it was pure gold (“Eureka” episode).
A ship floats even though it is made of iron because the ship's overall average density (including the internal spaces filled with air) is less than that of water.
A submarine controls surfacing and diving by filling its ballast tanks with water to change its overall average density.
Water pressure increases by approximately 1 atmosphere (approximately 10万Pa) for every 10m of water depth. In the Mariana Trench, with a depth of 1万m, the environment reaches approximately 1000 atmospheres.
Buoyancy also occurs in air (an object feels slightly lighter because of air buoyancy). Balloons and airships float because of air buoyancy.
- Water pressure is proportional to depth ( P = ρgh )
- Water pressure increases by approximately 1 atmosphere at a depth of 10m
- Buoyant force = weight of displaced liquid (Archimedes' principle)
- Density of water: approximately 1000 kg/m³ = 1 g/cm³
- Condition for floating: object density < liquid density
- Reason ships float: average density including internal spaces is less than that of water
- Submarines adjust density with ballast tanks
Points to Note (Easily Confused)
① Water pressure is proportional to depth and acts from all directions. ② Buoyancy is determined by the volume of the submerged part (not the total mass of the object). ③ Archimedes' principle applies to gases as well as liquids. ④ Whether an object floats or sinks in water is determined by the density of the object and liquid. It cannot be judged from mass or size alone.
Practice
- Briefly state how water pressure changes with depth.
- Explain Archimedes' principle in words.
- Explain why a ship made of iron floats.