Terminal Velocity of a Particle in Fluid
In a laboratory experiment, a small particle is dropped into a fluid contained in a vertical cylinder. As the particle sinks through the fluid, it experiences a viscous drag force that opposes its motion. This fluid has a density of 1,000 kg/m3 and a dynamic viscosity of 0.001 Pa·s. The particle has a radius of 0.01 m. Assuming that the particle reaches terminal velocity, which occurs when the net force on the particle is zero, what is the relationship between the gravitational force and the viscous drag force acting on the particle?
To analyze the situation, consider the following forces: the force of gravity acting downward, calculated as Fgravity = mg, where m is the mass of the particle, and the buoyant force acting upward, calculated using Archimedes' principle. The viscous drag force can be calculated using Stokes' Law: Fdrag = 6πηrv, where η is the dynamic viscosity, r is the radius of the particle, and v is the velocity of the particle.