Settling Velocity Calculator

Settling velocity, also known as the terminal velocity, is a critical parameter in various fields such as environmental engineering, sedimentology, and chemical engineering. It refers to the speed at which a particle falls through a stationary fluid, reaching a constant velocity where gravitational force is balanced by fluid resistance.

Historical Background

The concept of settling velocity has been a subject of study since the 18th century. It gained significance with the development of Stokes' law in the early 19th century by George Gabriel Stokes, a mathematician and physicist. Stokes' law provides the basis for calculating the settling velocity of spherical particles in a fluid.

Calculation Formula

The settling velocity is calculated using the following formula:

\[ \text{Settling Velocity} = \sqrt{\frac{4gD(\rho_s - \rho_f)}{3C_d\rho_f}} \]

Where:

• \( g \) is the acceleration due to gravity (9.81 m/s²).
• \( D \) is the diameter of the solid particle.
• \( \rho_s \) is the density of the solid particle.
• \( \rho_f \) is the density of the fluid.
• \( C_d \) is the drag coefficient, which depends on the Reynolds number and can be approximated as 24/Re for small particles (Stokes' regime).

Example Calculation

Consider a particle with:

• Density of the solid (\( \rho_s \)): 2600 kg/m³
• Density of the fluid (\( \rho_f \)): 1000 kg/m³
• Diameter of the solid (D): 0.005 m
• Kinematic viscosity (\( \nu \)): 1.004 × 10^-6 m²/s

First, calculate the Reynolds number (Re) to ensure Stokes' regime:

\[ \text{Re} = \frac{\rho_f \times D \times \text{Settling Velocity}}{\mu} \]

Assuming Stokes' regime, the settling velocity is calculated as:

\[ \text{Settling Velocity} = \sqrt{\frac{4 \times 9.81 \times 0.005 \times (2600 - 1000)}{3 \times 24/Re \times 1000}} \]

Importance and Usage Scenarios

Settling velocity is important in:

1. Designing Sedimentation Tanks: In wastewater treatment, to determine the size and operation conditions.
2. Erosion and Sediment Transport: In geology and environmental engineering, to understand particle movement.
3. Chemical Engineering: In designing separators and clarifiers.

Common FAQs

1. Does particle shape affect settling velocity?

   • Yes. Stokes' law applies to spherical particles. For non-spherical particles, shape factors are used.

2. Can settling velocity be used in all fluid types?

   • It's mainly applicable to Newtonian fluids. For non-Newtonian fluids, the formula needs adjustments.

3. Is temperature a factor in settling velocity?

   • Yes, as it affects fluid viscosity and density.