Stokes Law Calculator

Stokes Law Calculator

Stokes Law Calculator is a mathematical tool that is used to find the falling or settling velocity of the small spherical particles of viscous fluid. It is found out by using the particle diameter and density of the particle and medium.

What is settling velocity?

It is the speed at which the force acting on the particle is balanced by the gravitational force pulling it downwards. Settling velocity represents the velocity at which a particle in a fluid reaches a stable and constant speed under the influence of gravity.

Formula of settling velocity:

V_t = gd² (ρ_p - ρ_m)/18μ

Where,

• d = Diameter of the small particles
• V_t = Settling Velocity or Fall velocity of the particles
• g = Gravity Acceleration
• ρ_m = Medium density
• ρ_p = Density of the particle
• μ = medium viscosity

How to determine the settling velocity of small particles?

Example 1:

Determine the settling velocity (V_t) of the small particles if the data for particles are given below using the formula of Stoke’s Law.

• Gravity Acceleration (g) = 25 m/s²
• Diameter of the small particles (d) = 15 m
• Medium density (ρ_m) = 5 kg/m⁴
• Density of the particle (ρ_p) = 10 kg/m³
• Medium viscosity (μ) = 20 kg/m-s

Solution:

Step 1:

Write the data carefully from the above data.

g = 25 m/s², d = 15 m, ρ_m= 5 kg/m⁴, ρ_p = 10 kg/m³, μ = 20 kg/m-s

Step 2:

Write the formula of the settling velocity.

V_t = gd² (ρ_p - ρ_m)/18μ

Step 3:

Put all the values in the above formula.

g = 25, d = 15, ρ_m= 5, ρ_p = 10, μ = 20

V_t = gd² (ρ_p - ρ_m)/18μ

V_t = {25×15² (10-5)}/(18×20)

V_t = {25 × 225 × 5}/(18×20)

V_t = {1875}/(360)

V_t = 78.13m/s

Example 2:

Determine the settling velocity (V_t) of the small particles if the data for particles are given below using the formula of Stoke’s Law.

• Gravity Acceleration (g) = 20 m/s²
• Diameter of the small particles (d) = 10 m
• Medium density (ρ_m) = 12 kg/m⁴
• Density of the particle (ρ_p) = 15 kg/m³
• Medium viscosity (μ) = 22 kg/m-s

Solution:

Step 1:

Write the data carefully from the above data.

g = 20 m/s², d = 10 m, ρ_m= 12 kg/m⁴, ρ_p = 15 kg/m³, μ = 22 kg/m-s

Step 2:

Write the formula of the settling velocity.

V_t = gd² (ρ_p - ρ_m)/18μ

Step 3:

Put all the values in the above formula.

g = 20, d = 10, ρ_m= 12, ρ_p = 15, μ = 22

V_t = gd² (ρ_p - ρ_m)/18μ

V_t = {20×10² (15 -12)}/(18×22)

V_t = {20 × 100 × 3}/(18×22)

V_t = {6000}/(396)

V_t = 15.15 m/s