Settling Velocity Of Spherical Particle Given Coefficient Of Drag Calculator

Settling Velocity Formula:

\[ V_{sc} = \sqrt{\frac{\frac{4}{3} \times (\gamma_s - \gamma_w) \times D_p}{\rho_{water} \times C_D}} \]

Unit Weight of Particle (γs):

N/m³

Unit Weight of Water (γw):

N/m³

Diameter of Particle (Dp):

Water Density (ρwater):

kg/m³

Coefficient of Drag (CD):

Settling Velocity (Vsc):

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1. What is Settling Velocity of Spherical Particle?

The Settling Velocity of a Spherical Particle Given Coefficient of Drag is the terminal velocity at which a spherical particle settles in a fluid under the influence of gravity, considering the drag force acting on it. This is an important parameter in sediment transport, water treatment, and various engineering applications.

2. How Does the Calculator Work?

The calculator uses the settling velocity formula:

\[ V_{sc} = \sqrt{\frac{\frac{4}{3} \times (\gamma_s - \gamma_w) \times D_p}{\rho_{water} \times C_D}} \]

Where:

\( V_{sc} \) — Settling Velocity (m/s)
\( \gamma_s \) — Unit Weight of Particle (N/m³)
\( \gamma_w \) — Unit Weight of Water (N/m³)
\( D_p \) — Diameter of Particle (m)
\( \rho_{water} \) — Water Density (kg/m³)
\( C_D \) — Coefficient of Drag (dimensionless)

Explanation: The formula calculates the terminal settling velocity by balancing gravitational force with drag force acting on the particle.

3. Importance of Settling Velocity Calculation

Details: Accurate settling velocity calculation is crucial for designing sedimentation basins, predicting sediment transport in rivers and oceans, optimizing water treatment processes, and understanding particle behavior in various fluid environments.

4. Using the Calculator

Tips: Enter all values in the specified units. Ensure that unit weight of particle is greater than unit weight of water for settling to occur. All input values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the coefficient of drag?
A: The coefficient of drag quantifies the resistance a particle experiences as it moves through a fluid. It depends on the particle's shape, surface roughness, and the Reynolds number.

Q2: How does particle shape affect settling velocity?
A: This formula is specifically for spherical particles. Non-spherical particles will have different drag coefficients and settling characteristics.

Q3: What is the typical range of settling velocities?
A: Settling velocities vary widely depending on particle size and density, ranging from millimeters per second for fine sediments to meters per second for large, dense particles.

Q4: When is this formula most accurate?
A: The formula is most accurate for isolated spherical particles settling in still water at low to moderate Reynolds numbers.

Q5: How does temperature affect settling velocity?
A: Temperature affects water density and viscosity, which in turn affect the drag coefficient and thus the settling velocity. Warmer water typically results in slightly higher settling velocities.