Chapman-Rubesin Factor Calculator

Chapman–Rubesin Factor Formula:

\[ C = \frac{\rho \cdot \nu}{\rho_e \cdot \mu_e} \]

Density (ρ):

kg/m³

Kinematic Viscosity (ν):

m²/s

Static Density (ρe):

kg/m³

Static Viscosity (μe):

Pa·s

Chapman-Rubesin Factor (C):

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1. What is the Chapman-Rubesin Factor?

The Chapman-Rubesin factor is a dimensionless parameter used in fluid dynamics, particularly in boundary layer theory. Chapman and Rubesin assumed a linear relationship between the coefficient of dynamic viscosity and temperature, leading to this factor that relates density and viscosity properties of a fluid.

2. How Does the Calculator Work?

The calculator uses the Chapman-Rubesin formula:

\[ C = \frac{\rho \cdot \nu}{\rho_e \cdot \mu_e} \]

Where:

\( C \) — Chapman-Rubesin factor (dimensionless)
\( \rho \) — Density of the material (kg/m³)
\( \nu \) — Kinematic viscosity (m²/s)
\( \rho_e \) — Static density (kg/m³)
\( \mu_e \) — Static viscosity (Pa·s)

Explanation: The factor relates the product of density and kinematic viscosity to the product of static density and static viscosity, providing insight into fluid behavior under different conditions.

3. Importance of Chapman-Rubesin Factor

Details: The Chapman-Rubesin factor is crucial in boundary layer analysis, heat transfer calculations, and aerodynamic studies where viscosity-temperature relationships significantly influence fluid behavior and heat transfer rates.

4. Using the Calculator

Tips: Enter all values in appropriate SI units (kg/m³ for densities, m²/s for kinematic viscosity, and Pa·s for static viscosity). All values must be positive and non-zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the physical significance of the Chapman-Rubesin factor?
A: It represents the ratio of momentum diffusivity to thermal diffusivity under specific assumptions about viscosity-temperature relationships in boundary layer flows.

Q2: In which engineering applications is this factor most commonly used?
A: Primarily in aerodynamics, heat transfer analysis, and boundary layer studies where temperature-dependent viscosity effects are significant.

Q3: What are typical values for the Chapman-Rubesin factor?
A: The value typically ranges between 0.5-2.0 for most common fluids, but can vary significantly depending on temperature and fluid properties.

Q4: How does temperature affect the Chapman-Rubesin factor?
A: Since both density and viscosity are temperature-dependent, the factor changes with temperature, reflecting the changing relationship between momentum and heat transfer.

Q5: Can this factor be used for compressible flows?
A: Yes, the Chapman-Rubesin approach is particularly useful for compressible boundary layer flows where temperature variations significantly affect fluid properties.