by solving the small fluid-mass limit of the generally unsolvable Navier-Stokes equations
Don Carnage said:Hi -
Is it possible to derive Stokes law or is it an emprirical law.?
Stokes Law, also known as the law of viscous drag, is a fundamental physical principle that describes the behavior of small particles in a fluid medium. It was first formulated by Sir George Gabriel Stokes in the 19th century and is commonly used in various fields such as fluid dynamics, sedimentation, and rheology.
Stokes Law states that the drag force experienced by a small spherical particle moving through a viscous fluid is directly proportional to the particle's velocity, radius, and the viscosity of the fluid. This relationship is described by the equation F = 6πηrv, where F is the drag force, η is the viscosity, r is the particle radius, and v is the velocity.
Stokes Law was first derived by Sir George Gabriel Stokes in 1851 as a mathematical solution to the problem of a small sphere moving through a viscous fluid at a constant velocity. Stokes used the principles of fluid mechanics and Newton's laws of motion to develop this law.
Stokes Law is widely used in various scientific and engineering fields to understand and predict the behavior of small particles in a fluid medium. Some common applications include understanding sedimentation rates in the ocean, predicting the behavior of particles in pharmaceuticals and paints, and analyzing the flow of blood cells in the human body.
Stokes Law is based on certain assumptions, such as the particle being spherical and the fluid being incompressible and Newtonian. These assumptions may not hold true in all real-life situations, leading to discrepancies between the predicted and actual behavior. Additionally, Stokes Law is only applicable to small particles in low Reynolds number flow, and it may not accurately describe the behavior of larger particles or in high-speed flows.