Stokes' Law

Definition

Stokes' Law describes the motion of small spherical particles in a viscous fluid, stating that the force of viscosity acting on the particle is proportional to its radius, the fluid's viscosity, and the velocity of the particle. This law is crucial for understanding how objects move through fluids, particularly in relation to drag force and terminal velocity, and it highlights the impact of fluid resistance on particle motion.

5 Must Know Facts For Your Next Test

1. Stokes' Law is mathematically expressed as F = 6πμrv, where F is the drag force, μ is the fluid's viscosity, r is the radius of the sphere, and v is the velocity of the sphere relative to the fluid.
2. This law applies primarily to small particles moving at low velocities in a viscous medium, where laminar flow conditions are met.
3. The validity of Stokes' Law diminishes for larger particles or higher velocities, where turbulent flow may occur.
4. Stokes' Law can be used to derive expressions for terminal velocity, demonstrating how it depends on particle size and fluid viscosity.
5. Applications of Stokes' Law include predicting sedimentation rates in liquids and understanding the behavior of aerosols in air.

Review Questions

• How does Stokes' Law relate to the concepts of viscosity and drag force in fluid dynamics?
  • Stokes' Law directly connects viscosity and drag force by illustrating how these factors influence a small spherical particle's motion in a viscous fluid. According to Stokes' Law, the drag force experienced by a particle is proportional to the viscosity of the fluid and the particle's size. As viscosity increases, so does the drag force on the particle, leading to slower motion through the fluid. This relationship highlights how viscosity plays a critical role in determining how easily particles can move through different fluids.
• Discuss how Stokes' Law can be applied to calculate terminal velocity for particles falling through a viscous medium.
  • Stokes' Law provides a framework for calculating terminal velocity by equating the gravitational force acting on a falling particle with the drag force described by Stokes' Law. At terminal velocity, these forces balance each other out, leading to no net acceleration. By using F = 6πμrv for drag force and equating it with mg (the gravitational force), we can rearrange the equation to solve for terminal velocity (v), revealing how it depends on factors such as particle size (radius) and fluid viscosity. This application helps understand how different particles behave when falling through various fluids.
• Evaluate the limitations of Stokes' Law when applied to larger particles or at higher velocities, particularly in relation to real-world scenarios.
  • While Stokes' Law provides valuable insights for small particles in low-viscosity environments, its limitations become evident when applied to larger particles or at higher velocities. In these cases, laminar flow transitions to turbulent flow, causing deviations from Stokes' predictions. For example, in sedimentation processes or aerosol behavior in atmosphere dynamics, larger particles experience more complex interactions with surrounding fluid molecules that are not accounted for by Stokes' Law. Consequently, engineers and scientists must use alternative models or empirical data to accurately describe these behaviors in practical applications.

Related terms

Viscosity: A measure of a fluid's resistance to flow, indicating how thick or thin a fluid is and how easily it can deform.

Drag Force: The resistance force experienced by an object moving through a fluid, which opposes its motion and is influenced by factors like shape and speed.

Terminal Velocity: The constant speed that a freely falling object eventually reaches when the resistance of the medium through which it is falling prevents further acceleration.