Density upthrust and viscosity

Density measures the mass packed into a unit volume and is calculated using:

ρ = m/V

where m is the mass and V is the volume. The SI unit of density is kg m⁻³.

Key Definition When an object is immersed in a fluid, the surrounding fluid exerts an upward force called upthrust, which equals the weight of the fluid that the object displaces.

This principle (Archimedes' principle) explains why objects made of dense material can still float if their shape allows them to displace enough fluid.

As a sphere moves through a fluid, it also experiences viscous drag described by Stokes' Law:

F = 6πηrv

where η is the viscosity of the fluid, r is the radius of the sphere and v is its speed. This relationship holds provided the sphere is small, the speed is low, and the flow remains laminar.

Together, weight, upthrust and viscous drag determine the motion of a sphere falling through a liquid. When these three forces balance, the resultant force is zero and the sphere falls at terminal velocity.

This balance is the basis of Core Practical 2, where measuring the terminal velocity of a ball bearing falling through a liquid allows the viscosity of that liquid to be calculated.

Viscosity is strongly temperature dependent and decreases as temperature rises, so controlling the temperature is essential to obtaining reliable measurements.