Coefficient Of Drag Given Settling Velocity Of Spherical Particle Calculator

Formula Used:

\[ C_{ds} = \frac{\frac{4}{3} \times (\gamma_s - \gamma_w) \times D}{\rho_{water} \times (v_s)^2} \]

Unit Weight of Particle (γs):

N/m³

Unit Weight of Water (γw):

N/m³

Diameter (D):

Water Density (ρwater):

kg/m³

Settling Velocity (vs):

m/s

Coefficient of Drag (Cds):

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1. What is the Coefficient of Drag given Settling Velocity?

The Coefficient of Drag given Settling Velocity is a dimensionless quantity used to quantify the drag or resistance experienced by a spherical particle settling in a fluid. It relates the particle's properties and fluid characteristics to its terminal settling velocity.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ C_{ds} = \frac{\frac{4}{3} \times (\gamma_s - \gamma_w) \times D}{\rho_{water} \times (v_s)^2} \]

Where:

\( C_{ds} \) — Coefficient of Drag (dimensionless)
\( \gamma_s \) — Unit Weight of Particle (N/m³)
\( \gamma_w \) — Unit Weight of Water (N/m³)
\( D \) — Diameter of particle (m)
\( \rho_{water} \) — Water Density (kg/m³)
\( v_s \) — Settling Velocity (m/s)

Explanation: This formula calculates the drag coefficient for a spherical particle based on the balance between gravitational force and drag force at terminal settling velocity.

3. Importance of Drag Coefficient Calculation

Details: The drag coefficient is crucial for understanding particle behavior in fluid flows, designing sedimentation systems, predicting particle transport, and analyzing filtration processes in various engineering applications.

4. Using the Calculator

Tips: Enter all values in the specified units. Ensure unit weight values are in N/m³, diameter in meters, water density in kg/m³, and settling velocity in m/s. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range of drag coefficients for spherical particles?
A: For spherical particles in laminar flow, drag coefficients typically range from 0.1 to 2.0, depending on Reynolds number and flow conditions.

Q2: How does particle shape affect the drag coefficient?
A: This formula is specifically for spherical particles. Non-spherical particles have different drag coefficients that depend on their shape and orientation in the flow.

Q3: What assumptions are made in this calculation?
A: The calculation assumes spherical particles, Newtonian fluid behavior, and that the particle has reached terminal settling velocity in still fluid.

Q4: How does temperature affect the calculation?
A: Temperature affects water density and viscosity, which indirectly influence the settling velocity and drag coefficient through fluid properties.

Q5: Can this formula be used for non-aqueous fluids?
A: While the formula is written for water, it can be adapted for other fluids by substituting the appropriate fluid density and accounting for fluid viscosity effects.