Stokes' Law Calculator

How to Use the Stokes' Law Calculator

The Stokes' Law Calculator is specifically designed to calculate the settling velocity of a particle in a fluid. It takes into account parameters such as particle radius, fluid viscosity, particle density, fluid density, and acceleration due to gravity. By inputting these values into the calculator, you can obtain the settling velocity, which is the velocity at which the particle falls through the fluid under the influence of gravity and viscous drag.

Primary Applications

The primary applications of the Stokes' Law Calculator include:

• Sedimentation Studies: Determining the settling velocity of particles in sedimentation processes.
• Particle Characterization: Assessing the behavior and motion of particles in fluid systems.
• Environmental Engineering: Analyzing the settling behavior of particles in water treatment and wastewater processes.

Instructions for Utilizing the Calculator

To effectively utilize the Stokes' Law Calculator, follow these steps:

Input Fields

• Particle Radius: Enter the radius of the particle you want to calculate the settling velocity for.
  • The particle radius represents the size of the particle.
  • Provide the value in any suitable unit, such as meters (m) or millimeters (mm).
• Fluid Viscosity: Input the viscosity of the fluid in which the particle is settling.
  • Fluid viscosity is a measure of a fluid's resistance to flow.
  • Provide the value in any suitable unit, such as pascal-seconds (Pa·s) or centipoise (cP).
• Particle Density: Specify the density of the particle.
  • The particle density represents the mass per unit volume of the particle material.
  • Provide the value in any suitable unit, such as kilograms per cubic meter (kg/m³) or grams per cubic centimeter (g/cm³).
• Fluid Density: Enter the density of the fluid in which the particle is settling.
  • Fluid density represents the mass per unit volume of the fluid.
  • Provide the value in the same unit used for the particle density.
• Acceleration Due to Gravity: Input the acceleration due to gravity.
  • The acceleration due to gravity represents the force of gravity on the particle.
  • Provide the value in any suitable unit, such as meters per second squared (m/s²) or centimeters per second squared (cm/s²).

Output Fields

Upon submitting the form, the Stokes' Law Calculator will display the following output:

1. Particle Radius: This field displays the particle radius value inputted.
   • The particle radius represents the size of the particle.
2. Fluid Viscosity: This field showcases the fluid viscosity value inputted.
   • Fluid viscosity represents the resistance to flow of the fluid.
3. Particle Density: This field exhibits the particle density value inputted.
   • The particle density represents the mass per unit volume of the particle.
4. Fluid Density: This field presents the fluid density value inputted.
   • Fluid density represents the mass per unit volume of the fluid.
5. Acceleration Due to Gravity: This field displays the acceleration due to gravity value inputted.
   • The acceleration due to gravity represents the force of gravity on the particle.
6. Settling Velocity: This field showcases the calculated settling velocity of the particle.
   • The settling velocity is determined based on the input parameters and Stokes' Law.
   • It represents the velocity at which the particle falls through the fluid under the influence of gravity and viscous drag.

Stokes' Law Calculator Formula

The settling velocity calculation is performed using Stokes' Law formula:

Settling Velocity = (2/9) * (Particle Density - Fluid Density) * Acceleration Due to Gravity * Particle Radius^2 / Fluid Viscosity

In plain English, the settling velocity is calculated by subtracting the fluid density from the particle density. This difference is multiplied by the acceleration due to gravity, the square of the particle radius, and a constant factor of 2/9. The result is then divided by the fluid viscosity.

Illustrative Example

Let's consider an example to better understand the calculation process:

Suppose you have a particle with the following properties:

• Particle Radius: 0.1 millimeters
• Fluid Viscosity: 0.01 pascal-seconds
• Particle Density: 2500 kilograms per cubic meter
• Fluid Density: 1000 kilograms per cubic meter
• Acceleration Due to Gravity: 9.8 meters per second squared

Using the Stokes' Law Calculator, you input the above values into the respective fields.

Upon calculation, the settling velocity will be displayed as follows:

• Particle Radius: 0.1 millimeters
• Fluid Viscosity: 0.01 pascal-seconds
• Particle Density: 2500 kilograms per cubic meter
• Fluid Density: 1000 kilograms per cubic meter
• Acceleration Due to Gravity: 9.8 meters per second squared
• Settling Velocity: 0.000041 meters per second

In this example, the settling velocity of the particle is determined to be 0.000041 meters per second.

Illustrative Table Example

The following table showcases multiple rows of example data to demonstrate the functionality of the Stokes' Law Calculator:

The table presents various scenarios with different input parameters, showcasing the corresponding settling velocities.

The Stokes' Law Calculator provides a convenient and efficient solution for calculating the settling velocity of a particle in a fluid based on Stokes' Law. By inputting the particle radius, fluid viscosity, particle density, fluid density, and acceleration due to gravity, you can quickly obtain the settling velocity. This calculator is invaluable in sedimentation studies, particle characterization, and environmental engineering applications. Embrace the convenience and accuracy of the Stokes' Law Calculator to enhance your understanding of particle settling behavior and optimize various processes.