Dynamic Viscosity Based On Kozeny Carman Equation Calculator

Kozeny Carman Equation:

\[ \mu = \frac{\frac{dP}{dr} \times (\Phi_p)^2 \times (D_e)^2 \times (\eta)^3}{150 \times (1-\eta)^2 \times v} \]

Pressure Gradient (dP/dr):

N/m³

Sphericity of Particle (Φp):

Equivalent Diameter (De):

Porosity (η):

Velocity (v):

m/s

Dynamic Viscosity (μ):

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1. What is the Kozeny Carman Equation?

The Kozeny Carman equation is a fundamental relationship in fluid dynamics that describes the flow of fluids through porous media. It calculates dynamic viscosity based on pressure gradient, particle sphericity, equivalent diameter, porosity, and fluid velocity.

2. How Does the Calculator Work?

The calculator uses the Kozeny Carman equation:

\[ \mu = \frac{\frac{dP}{dr} \times (\Phi_p)^2 \times (D_e)^2 \times (\eta)^3}{150 \times (1-\eta)^2 \times v} \]

Where:

\( \mu \) — Dynamic viscosity (Pa·s)
\( \frac{dP}{dr} \) — Pressure gradient (N/m³)
\( \Phi_p \) — Sphericity of particle
\( D_e \) — Equivalent diameter (m)
\( \eta \) — Porosity
\( v \) — Velocity (m/s)

Explanation: The equation relates the dynamic viscosity of a fluid to various parameters describing the porous medium and flow conditions.

3. Importance of Dynamic Viscosity Calculation

Details: Dynamic viscosity is a crucial property in fluid mechanics that determines a fluid's resistance to flow. Accurate viscosity calculation is essential for designing fluid transport systems, filtration processes, and understanding flow behavior in porous media.

4. Using the Calculator

Tips: Enter pressure gradient in N/m³, sphericity (dimensionless), equivalent diameter in meters, porosity (between 0-1), and velocity in m/s. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is dynamic viscosity?
A: Dynamic viscosity is a measure of a fluid's resistance to flow when an external force is applied. It quantifies the internal friction between fluid layers.

Q2: What is sphericity of particle?
A: Sphericity is a measure of how closely the shape of a particle resembles that of a perfect sphere, with values ranging from 0 to 1 (perfect sphere).

Q3: What is porosity?
A: Porosity is the ratio of void volume to total volume of a porous medium, expressed as a value between 0 and 1.

Q4: What are typical viscosity values?
A: Water at 20°C has a viscosity of about 0.001 Pa·s, while honey has about 2-10 Pa·s, and air has about 0.000018 Pa·s.

Q5: What are the limitations of the Kozeny Carman equation?
A: The equation works best for laminar flow through porous media with uniform particle size and may not be accurate for highly irregular particles or turbulent flow conditions.