Archimedes number

The Archimedes number (formula symbol: ${\mathit {Ar}}$ ) is a dimensionless ratio named after the ancient scholar Archimedes. It can be interpreted as the ratio of buoyancy force to friction force and is defined as

${\begin{aligned}{\mathit {Ar}}&={\frac {\Delta \rho \,g\,L^{3}}{\rho \,\nu ^{2}}}=\left({\frac {\rho _{\mathrm {K} }}{\rho }}-1\right)\cdot {\frac {g\,L^{3}}{\nu ^{2}}}\\&={\frac {\rho \,\Delta \rho \,g\,L^{3}}{\eta ^{2}}}\end{aligned}}$ .

The incoming variables are

Other definition

An alternative definition of Archimedes number, which can be interpreted as the ratio of buoyant force to inertial force, or between free and forced convection, is identical to the definition of Richardson number and reads:

${\mathit {Ar}}={\frac {\Delta T\,g\,L\,\beta }{{u_{\infty }}^{2}}}={\frac {\mathit {Gr}}{{\mathit {Re}}^{2}}}$ .

Thereby

$\beta$ is the isobaric expansion coefficient
$\Delta T=T_{\infty }-T_{\text{Wand}}$ the driving temperature difference
$u_{\infty }$ the ambient velocity
${\mathit {Gr}}$ : Grashof number
${\mathit {Re}}$ : Reynolds number.

Questions and Answers

Q: What is the Archimedes number?

A: The Archimedes number is a dimensionless number used in viscous fluid dynamics to represent the ratio of gravitational forces to viscous forces.

Q: Who was Archimedes?

A: Archimedes was a Greek mathematician and scientist who lived in the 3rd century BC.

Q: What does Ar represent?

A: Ar represents the ratio of gravitational forces to viscous forces in viscous fluid dynamics.

Q: What is the relationship between Ar and other variables?

A: The relationship between Ar and other variables has the form of gL3ρℓ(ρ−ρℓ)/μ2, where g is gravity, L is length, ρℓ is density of liquid, ρ is density, and μ is viscosity.

Q: How can Ar be used?

A: Ar can be used when motion of fluids are affected by density differences.

Q: Is it possible to calculate Ar?

A: Yes, it is possible to calculate Ar using the equation given above with known values for gravity, length, densities, and viscosity.