Question

Assuming Stokes flow, find the settling velocity for a 100 micron diameter particle falling through water at 20°C. The particle has density 1.75 g/m³. What is the reynolds number? Note: For spherical particles, Fdrag = Fstokes = -6πμαU

Answer 1

The settling velocity of a particle in Stokes flow can be calculated using Stokes' law. The formula involves the density and radius of the particle, the density of the fluid, the acceleration due to gravity, and the dynamic viscosity of the fluid. Plugging in the given values will give the settling velocity of the particle.

Step-by-step explanation:

The settling velocity of a particle in Stokes flow can be calculated using Stokes' law. The formula for the settling velocity of a spherical particle in Stokes flow is given by:

U = (2/9) * [(p_p - p_f) * g * a^2] / µ

Where:

• U is the settling velocity of the particle
• p_p is the density of the particle
• p_f is the density of the fluid
• g is the acceleration due to gravity
• a is the radius of the particle (which can be calculated as half the diameter)
• µ is the dynamic viscosity of the fluid

In this case, the particle has a diameter of 100 microns, so the radius is 50 microns. The density of the particle is 1.75 g/m³, and the fluid is water at 20°C. The dynamic viscosity of water at 20°C is approximately 1.002 × 10^-3 Pa·s. Plugging these values into the formula, we get:

U = (2/9) * [(1.75 g/m³ - 1000 kg/m³) * 9.8 m/s² * (50 × 10^-6 m)²] / (1.002 × 10^-3 Pa·s)

Calculating this equation will give us the settling velocity of the particle.