Archimedes' Principle (OCR A Level Physics) : Revision Note

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:

• Hydrostatic pressure is the pressure at any given point within a fluid, that is exerted by the weight of the fluid above that point 

• If the fluid is at rest, then all the points within the fluid are in equilibrium

• Therefore, the pressure acts in all directions at each point

Pressure on a point in a fluid

The hydrostatic pressure on area A is due to the weight, W, of the volume of fluid above it

• The weight, W, of the fluid above area A is given by:

• Using the density equation, mass can be given as:

• Substituting this expression for mass into the weight equation gives:

• Therefore, the pressure exerted on area A can be given as:

• Within the volume of the cube V, there is a change in pressure between the top and bottom surfaces

Change in pressure through a volume of fluid

The pressure at the bottom of the cube with volume V is greater than the area A at the top of the cube, because there is an increasing amount of fluid above, which increases the force of weight W acting upon it

• The change in pressure can be found by considering the change in height of the volume of fluid above the lower surface

• This gives the equation for hydrostatic pressure:

• Where:

  • Δp = change in pressure in pascals (Pa)

  • ρ (Greek letter rho) = density of fluid in kilograms per metre cubed (kg m^-3)

  • Δh = change in height in metres (m)

  • g = gravitational field strength in newtons per kg (N kg^-1)

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