Motion in a Viscous Medium
Motion in a Viscous Medium
Aim
The aim of this experiment is to measure the terminal velocity of spherical beads falling under gravity in a liquid determine, and hence determine its viscosity using Stoke’s law.
Introduction
When a stationary solid object is complete or partially immersed in a fluid, it experiences an upthrust or buoyant force. According to Archimedes’ principle, this buoyant force B is given by
where ρ is the density of the fluid, Vs is the immersed volume of the solid object, and g is the acceleration due to gravity. As its name implies, this force acting on the solid object by the fluid is always directed upwards.
If the solid object now moves through the fluid, it will have to push the fluid out of the way. By Newton’s third law, the fluid pushes back on the object with an equally strong reaction in the opposite direction. This is experienced by the object as fluid resistance f to its motion. Depending on the speed v of the solid object, as well as the nature of the fluid, this fluid resistance can be proportional to the speed, i.e. f ~ v (skin drag or viscous drag), or proportional to the square of the speed, i.e. f ~ v2 (form drag or inertial drag). Viscous drag is the dominant fluid resistance at low Reynolds numbers, whereas inertial drag is the dominant fluid resistance at high Reynolds numbers. The Reynolds number
is a dimensionless ratio of inertial forces to viscous forces. Here, ρ is the density of the fluid, v is the typical speed of the fluid flow, L is the typical distance the fluid has to flow around, and η is the viscosity of the fluid.
For a sphere of radius r moving with speed v in an infinite fluid with viscosity η, the viscous drag has been worked out by Sir George Stokes in 1851 to be
(1) if the fluid at the surface of the sphere is always at rest with respect to the sphere. This has since come to be known as Stokes’ law. In this experiment, spherical beads are dropped into a
Aim
The aim of this experiment is to measure the terminal velocity of spherical beads falling under gravity in a liquid determine, and hence determine its viscosity using Stoke’s law.
Introduction
When a stationary solid object is complete or partially immersed in a fluid, it experiences an upthrust or buoyant force. According to Archimedes’ principle, this buoyant force B is given by
where ρ is the density of the fluid, Vs is the immersed volume of the solid object, and g is the acceleration due to gravity. As its name implies, this force acting on the solid object by the fluid is always directed upwards.
If the solid object now moves through the fluid, it will have to push the fluid out of the way. By Newton’s third law, the fluid pushes back on the object with an equally strong reaction in the opposite direction. This is experienced by the object as fluid resistance f to its motion. Depending on the speed v of the solid object, as well as the nature of the fluid, this fluid resistance can be proportional to the speed, i.e. f ~ v (skin drag or viscous drag), or proportional to the square of the speed, i.e. f ~ v2 (form drag or inertial drag). Viscous drag is the dominant fluid resistance at low Reynolds numbers, whereas inertial drag is the dominant fluid resistance at high Reynolds numbers. The Reynolds number
is a dimensionless ratio of inertial forces to viscous forces. Here, ρ is the density of the fluid, v is the typical speed of the fluid flow, L is the typical distance the fluid has to flow around, and η is the viscosity of the fluid.
For a sphere of radius r moving with speed v in an infinite fluid with viscosity η, the viscous drag has been worked out by Sir George Stokes in 1851 to be
(1) if the fluid at the surface of the sphere is always at rest with respect to the sphere. This has since come to be known as Stokes’ law. In this experiment, spherical beads are dropped into a