## WORK OR ENERGY UNIT CONVERSIONS

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## Archimedes Number Calculator

The Archimedes number (Ar) is a dimensionless parameter used in fluid mechanics to characterize the relative importance of buoyancy forces to viscous forces in a fluid flow situation. It’s named after the ancient Greek mathematician, physicist, engineer, and inventor Archimedes.

Archimedes number is proportional to { (gravitational force) / (viscous force) } and is used in momentum transfer in general and buoyancy, fluidization, and motion due to density difference calculations in particular. It is normally defined in the following form :

 Where: g = Gravitational acceleration L = Characteristic length μ = Viscosity ρf = Fluid density ρs = Solid density

The Archimedes number helps determine whether buoyancy or viscous effects dominate the fluid flow behavior. Depending on the value of the Archimedes number, different flow regimes can be identified:

• If Ar ≪ 1, viscous forces dominate over buoyancy forces, and the flow behavior is primarily determined by viscosity. This typically occurs in situations where the fluid’s inertia is negligible, such as in highly viscous or slow-flowing fluids.
• If Ar ≫ 1, buoyancy forces dominate over viscous forces, and the flow behavior is primarily determined by buoyancy. This typically occurs in situations where the fluid’s inertia is significant, such as in natural convection or free surface flows.

The Archimedes number is commonly used in the analysis of various fluid flow problems, including natural and forced convection, fluidized beds, and multiphase flows. It helps engineers and scientists understand and predict the behavior of fluids under different flow conditions.

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