Diameter Of Rotating Cylinder In Fluid Given Reynolds Number Calculator

Formula Used:

\[ D = \sqrt{\frac{Re_w \cdot \nu_k}{\pi \cdot \omega}} \]

Diameter:

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1. What is the Diameter Calculation Formula?

The formula calculates the diameter of a rotating cylinder in fluid based on Reynolds number, kinematic viscosity, and rotational speed. This calculation is important in fluid mechanics and engineering applications involving rotating cylinders.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ D = \sqrt{\frac{Re_w \cdot \nu_k}{\pi \cdot \omega}} \]

Where:

\( D \) — Diameter of the rotating cylinder (m)
\( Re_w \) — Reynolds number (dimensionless)
\( \nu_k \) — Kinematic viscosity (m²/s)
\( \omega \) — Rotational speed (rad/s)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: The formula derives the diameter from the relationship between Reynolds number, fluid properties, and rotational characteristics.

3. Importance of Diameter Calculation

Details: Accurate diameter calculation is crucial for designing rotating machinery, analyzing fluid-structure interactions, and predicting flow behavior around rotating cylinders in various engineering applications.

4. Using the Calculator

Tips: Enter Reynolds number (dimensionless), kinematic viscosity in m²/s, and rotational speed in rad/s. All values must be positive and valid for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What is Reynolds number in this context?
A: Reynolds number (Re_w) characterizes the flow regime around the rotating cylinder, indicating whether the flow is laminar or turbulent.

Q2: Why is kinematic viscosity used instead of dynamic viscosity?
A: Kinematic viscosity (ν) is the ratio of dynamic viscosity to density, which is more convenient for flow calculations involving inertial forces.

Q3: What are typical values for rotational speed?
A: Rotational speed varies widely depending on application, from slow rotations in mixing applications to high speeds in turbine systems.

Q4: Are there limitations to this formula?
A: The formula assumes specific flow conditions and may need adjustments for extreme Reynolds numbers or non-Newtonian fluids.

Q5: What engineering applications use this calculation?
A: This calculation is used in designing mixers, turbines, pumps, and other rotating machinery where fluid interaction is critical.