In viscous
fluid dynamics, the Archimedes number (Ar), is a
dimensionless number used to determine the motion of
fluids due to
density differences, named after the ancient Greek scientist and mathematician
Archimedes.
It is the ratio of gravitational forces to viscous forces and has the form:
:
where:
*
is the local external field (for example
gravitational acceleration), ,
*
is the
characteristic length of body, .
*
is the
submerged specific gravity,
*
is the
density of the fluid, ,
*
is the density of the body, ,
*
is the
kinematic viscosity, ,
*
is the
dynamic viscosity, ,
Uses
The Archimedes number is generally used in design of tubular
chemical process reactors. The following are non-exhaustive examples of using the Archimedes number in reactor design.
Packed-bed fluidization design
The Archimedes number is applied often in the engineering of
packed beds, which are very common in the chemical processing industry.
A packed bed reactor, which is similar to the ideal
plug flow reactor model, involves packing a tubular
reactor with a
solid catalyst, then passing
incompressible or
compressible fluids through the solid bed.
When the solid particles are small, they may be "fluidized", so that they act as if they were a fluid. When fluidizing a packed bed, the pressure of the
working fluid is increased until the
pressure drop between the bottom of the bed (where fluid enters) and the top of the bed (where fluid leaves) is equal to the weight of the packed solids. At this point, the
velocity of the fluid is just not enough to achieve fluidization, and extra pressure is required to overcome the
friction of particles with each other and the wall of the reactor, allowing fluidization to occur. This gives a minimum fluidization velocity,
, that may be estimated by:
:
where:
*
is the diameter of sphere with the same volume as the solid particle and can often be estimated as
, where
is the diameter of the particle.
Bubble column design
Another use is in the estimation of gas holdup in a
bubble column
Bubble, Bubbles or The Bubble may refer to:
Common uses
* Bubble (physics), a globule of one substance in another, usually gas in a liquid
** Soap bubble
* Economic bubble, a situation where asset prices are much higher than underlying fundame ...
. In a bubble column, the gas holdup (fraction of a bubble column that is gas at a given time) can be estimated by:
:
where:
*
is the gas holdup fraction
*
is the
Eötvos number
*
is the
Froude number
*
is the diameter of holes in the column's
spargers (holed discs that emit bubbles)
*
is the column diameter
* Parameters
to
are found empirically
Spouted-bed minimum spouting velocity design
A
spouted bed is used in drying and coating. It involves spraying a liquid into a bed packed with the solid to be coated. A fluidizing gas fed from the bottom of the bed causes a spout, which causes the solids to circle linearly around the liquid. Work has been undertaken to model the minimum velocity of gas required for spouting in a spouted bed, including the use of
artificial neural network
Artificial neural networks (ANNs), usually simply called neural networks (NNs) or neural nets, are computing systems inspired by the biological neural networks that constitute animal brains.
An ANN is based on a collection of connected unit ...
s. Testing with such models found that Archimedes number is a parameter that has a very large effect on the minimum spouting velocity.
See also
*
Viscous fluid dynamics
*
Convection
*
Convection (heat transfer)
*
Dimensionless quantity
*
Galilei number In fluid dynamics, the Galilei number (Ga), sometimes also referred to as Galileo number (see discussion), is a dimensionless number named after Italian scientist Galileo Galilei (1564-1642).
It may be regarded as proportional to gravity forces div ...
*
Grashof number
*
Reynolds number
*
Froude number
*
Eötvös number In fluid dynamics the Eötvös number (Eo), also called the Bond number (Bo), is a dimensionless number
measuring the importance of gravitational forces compared to surface tension forces for the movement of liquid front. Alongside the Capillary nu ...
*
Sherwood number
References
{{DEFAULTSORT:Archimedes Number
Dimensionless numbers of fluid mechanics
Fluid dynamics