Stokes' Law Calculator
Stokes' Law Calculator is a convenient online tool that helps you calculate the terminal velocity of a spherical particle settling through a liquid under the influence of gravity. This useful tool is ideal for students, scientists, and researchers who are interested in understanding the behavior of particles in suspension. With the Stokes' Law Calculator, you can easily input the variables related to the particle size, fluid viscosity, and fluid density, and receive a precise result in seconds. This tool is both easy to use and accurate, making it an essential tool for anyone interested in fluid dynamics. Whether you are working on a research project, studying for an exam, or simply need to calculate the terminal velocity of a particle, this tool has got you covered. With its user-friendly interface and fast calculation time, the Stokes' Law Calculator is a must-have for anyone in need of reliable and accurate particle settling calculations.Stokes' Law Calculator
Calculate the settling velocity of a particle in a fluid
Stokes' Law Calculator Results | |
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Particle Radius | 0 |
Fluid Viscosity | 0 |
Particle Density | 0 |
Fluid Density | 0 |
Acceleration Due to Gravity | 0 |
Settling Velocity | 0 |
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:
- Particle Radius: This field displays the particle radius value inputted.
- The particle radius represents the size of the particle.
- Fluid Viscosity: This field showcases the fluid viscosity value inputted.
- Fluid viscosity represents the resistance to flow of the fluid.
- Particle Density: This field exhibits the particle density value inputted.
- The particle density represents the mass per unit volume of the particle.
- Fluid Density: This field presents the fluid density value inputted.
- Fluid density represents the mass per unit volume of the fluid.
- 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.
- 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:
Particle Radius (mm) | Fluid Viscosity (Pa·s) | Particle Density (kg/m³) | Fluid Density (kg/m³) | Acceleration Due to Gravity (m/s²) | Settling Velocity (m/s) |
---|---|---|---|---|---|
0.1 | 0.01 | 2500 | 1000 | 9.8 | 0.000041 |
0.05 | 0.005 | 2000 | 900 | 9.8 | 0.000027 |
0.2 | 0.02 | 3000 | 1200 | 9.8 | 0.000073 |
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.