Diameter Of Sphere Given Coefficient Of Drag Calculator

Formula Used:

\[ DS = \frac{24 \times \mu}{\rho \times V_{mean} \times C_D} \]

Dynamic Viscosity (μ):

Pa·s

Density of Fluid (ρ):

kg/m³

Mean Velocity (V_mean):

m/s

Coefficient of Drag (C_D):

(dimensionless)

Diameter of Sphere (DS):

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1. What is the Diameter of Sphere Formula?

The diameter of sphere formula calculates the diameter of a spherical object in a fluid environment based on its drag coefficient, fluid properties, and flow conditions. This calculation is essential in fluid dynamics and engineering applications involving spherical particles.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ DS = \frac{24 \times \mu}{\rho \times V_{mean} \times C_D} \]

Where:

\( DS \) — Diameter of Sphere (m)
\( \mu \) — Dynamic Viscosity (Pa·s)
\( \rho \) — Density of Fluid (kg/m³)
\( V_{mean} \) — Mean Velocity (m/s)
\( C_D \) — Coefficient of Drag (dimensionless)

Explanation: This formula derives from the drag force equation and Stokes' law, relating the sphere's diameter to fluid properties and flow characteristics.

3. Importance of Sphere Diameter Calculation

Details: Accurate diameter calculation is crucial for designing filtration systems, analyzing particle behavior in fluids, optimizing industrial processes, and understanding sedimentation phenomena.

4. Using the Calculator

Tips: Enter dynamic viscosity in Pa·s, density in kg/m³, mean velocity in m/s, and coefficient of drag (dimensionless). All values must be positive and non-zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of validity for this formula?
A: This formula is most accurate for small Reynolds numbers (Re < 1) where Stokes' law applies, typically for small particles in slow-moving fluids.

Q2: How does temperature affect the calculation?
A: Temperature affects both dynamic viscosity and fluid density. For accurate results, use viscosity and density values at the actual operating temperature.

Q3: Can this formula be used for non-spherical particles?
A: No, this formula is specifically derived for spherical particles. Non-spherical particles require different drag coefficient correlations.

Q4: What are typical values for drag coefficient?
A: For spheres in laminar flow, drag coefficient typically ranges from 0.1 to 1.0, depending on Reynolds number and surface roughness.

Q5: How accurate is this calculation for real-world applications?
A: The calculation provides good estimates for ideal conditions but may require correction factors for rough surfaces, non-Newtonian fluids, or turbulent flow conditions.