Archimedes' Principle
Upthrust on an Object in a Fluid
- Pressure increases with depth in a fluid because of the force exerted by the increased weight of the fluid above
- This change in pressure can be calculated using the equation of hydrostatic pressure:
- This equation can be derived in the following way:
Archimedes' Principle
- Archimedes’ principle states:
An object submerged in a fluid at rest has an upward buoyancy force (upthrust) equal to the weight of the fluid displaced by the object
- The object sinks until the weight of the fluid displaced is equal to its own weight
- Therefore the object floats when the magnitude of the upthrust equals the weight of the object
- The magnitude of upthrust can be calculated by:
- Since m = ρV, upthrust is equal to F = mg which is the weight of the fluid displaced by the object
- Archimedes’ Principle explains how ships float:
Boats float because they displace an amount of water that is equal to their weight
Worked example
Atmospheric pressure at sea level has a value of 100 kPa. The density of sea water is 1020 kg m-3.At what depth in the sea would the total pressure be 250 kPa?A. 20 m B. 9.5 m C. 18 m D. 15 m
Worked example
Icebergs typically float with a large volume of ice beneath the water. Ice has a density of 917 kg m-3 and a volume of Vi.The density of seawater is 1020 kg m-3.What fraction of the iceberg is above the water?A. 0.10 Vi B. 0.90 Vi C. 0.97 Vi D. 0.20 Vi
Exam Tip
When asked about the total pressure remember to also add the atmospheric pressure
Total pressure = Hydrostatic pressure + Atmospheric pressure
Atmospheric pressure (also known as barometric pressure) is equal to 101 325 PaValues for pressure can vary widely and depend on metric prefixes such as kPa or MPa. When you’re doing calculations make sure all the pressures are in the same units (otherwise you may be out by a factor of 1000!). To be on the safe side, you can convert them all to Pascals.
