TRANSPORT PHYSICS / DIMENSIONLESS RATIO
Compare density-driven body force with viscous resistance for a particle or inclusion at a stated fluid condition and length scale.
METHOD / WORKED EXAMPLE
Compare density-driven body force with viscous resistance for a particle or inclusion at a stated fluid condition and length scale. The ratio becomes dimensionless only when every property uses coherent units and one physical state.
WORKED DEFAULT
For a 1 mm scale in the displayed liquid and density contrast, the numerator is 0.01471 and Ar is about 14,710.
READ THE RESULT
The ratio compares body-force and viscous scales; it does not return settling speed or select a drag law.
ASSUMPTIONS AND LIMITS
Shape, orientation, confinement, particle interactions, non-Newtonian response, drag regime, and terminal velocity require separate analysis.
COMMON QUESTIONS
Use one coherent SI unit system, physical state, geometry, and documented characteristic scale across every input. Density contrast is supplied as a positive magnitude. Fluid properties and length match one particle model. Confirm whether each property belongs to the fluid, solid, interface, particle, or transported quantity named by the formula. Mixed conventions can produce a plausible number whose physical meaning is wrong.
The ratio compares body-force and viscous scales; it does not return settling speed or select a drag law. A dimensionless group compares selected mechanisms under a stated model; it does not prove a regime, transition, instability, similarity, or safe design. Geometry, boundary conditions, property variation, measurement uncertainty, and the validity range of downstream correlations still require separate review.
No. This educational calculator performs displayed arithmetic on supplied SI values; it is not simulation, experimental validation, a correlation selector, material data, or engineering approval. Shape, orientation, confinement, particle interactions, non-Newtonian response, drag regime, and terminal velocity require separate analysis. Retain source values, units, property temperatures, geometry definitions, and uncertainty, then obtain qualified review before using the result for design or safety decisions.
RELATED TOOLS
Use boundary
Cube particle length, multiply by gravity, fluid density, and density difference, then divide by squared dynamic viscosity.
Ar = g L^3 rho_f Delta rho / mu^2.