Archimedes Number Calculator

Archimedes Number Formula:

\[ Ar = \frac{[g] \times L_c^3 \times \rho_{Fluid} \times (\rho_B - \rho_{Fluid})}{\mu_{viscosity}^2} \]

Characteristic Length (Lc):

Density of Fluid (ρFluid):

kg/m³

Density of Body (ρB):

kg/m³

Dynamic Viscosity (μ):

Pa·s

Archimedes Number (Ar):

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1. What Is The Archimedes Number?

The Archimedes Number (Ar) is a dimensionless number used to determine the motion of fluids due to density differences. It is named after the ancient Greek scientist and mathematician Archimedes and represents the ratio of gravitational forces to viscous forces.

2. How Does The Calculator Work?

The calculator uses the Archimedes Number formula:

\[ Ar = \frac{[g] \times L_c^3 \times \rho_{Fluid} \times (\rho_B - \rho_{Fluid})}{\mu_{viscosity}^2} \]

Where:

\( [g] \) — Gravitational acceleration (9.80665 m/s²)
\( L_c \) — Characteristic length (m)
\( \rho_{Fluid} \) — Density of fluid (kg/m³)
\( \rho_B \) — Density of body (kg/m³)
\( \mu_{viscosity} \) — Dynamic viscosity (Pa·s)

Explanation: The Archimedes Number quantifies the relative importance of buoyancy forces compared to viscous forces in fluid dynamics.

3. Importance Of Archimedes Number

Details: The Archimedes Number is crucial in various engineering applications, including fluidized beds, sedimentation processes, natural convection, and particle motion in fluids. It helps predict flow patterns and behavior in systems where density differences drive fluid motion.

4. Using The Calculator

Tips: Enter characteristic length in meters, densities in kg/m³, and dynamic viscosity in Pa·s. All values must be positive and valid for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the physical significance of Archimedes Number?
A: The Archimedes Number represents the ratio of buoyancy forces to viscous forces, indicating whether buoyancy or viscosity dominates in a particular fluid flow situation.

Q2: How does Archimedes Number relate to Reynolds Number?
A: While Reynolds Number characterizes flow regimes (laminar vs turbulent), Archimedes Number specifically addresses flows driven by density differences and buoyancy effects.

Q3: What are typical values of Archimedes Number?
A: Values can vary widely depending on the system. Small values indicate viscous dominance, while large values indicate buoyancy dominance in the flow.

Q4: In which industries is Archimedes Number commonly used?
A: It's widely used in chemical engineering, petroleum industry, environmental engineering, and materials processing where density-driven flows are important.

Q5: Can Archimedes Number be negative?
A: No, since it involves squared terms in the denominator and physical properties that are always positive, the Archimedes Number is always a positive dimensionless quantity.