In physics, a characteristic length is an important dimension that defines the scale of a physical system. Often, such a length is used as an input to a formula in order to predict some characteristics of the system, and it is usually required by the construction of a
dimensionless quantity, in the general framework of
dimensional analysis and in particular applications such as
fluid mechanics
Fluid mechanics is the branch of physics concerned with the mechanics of fluids (liquids, gases, and plasmas) and the forces on them.
It has applications in a wide range of disciplines, including mechanical, aerospace, civil, chemical and bio ...
.
In computational mechanics, a characteristic length is defined to force localization of a stress softening constitutive equation. The length is associated with an integration point. For 2D analysis, it is calculated by taking the square root of the area. For 3D analysis, it is calculated by taking the cubic root of the volume associated to the integration point.
Examples
A characteristic length is usually the volume of a system divided by its surface:
For example, it is used to calculate flow through circular and non-circular tubes in order to examine flow conditions (i.e., the
Reynolds number
In fluid mechanics, the Reynolds number () is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between inertial and viscous forces. At low Reynolds numbers, flows tend to be domin ...
). In those cases, the characteristic length is the diameter of the pipe or, in case of non-circular tubes, its hydraulic diameter
:
Where
is the cross-sectional area of the pipe and
is its wetted perimeter. It is defined such that it reduces to a circular diameter of D for circular pipes.
For flow through a square duct with a side length of a, the hydraulic diameter
is:
For a rectangular duct with side lengths a and b:
For free surfaces (such as in open-channel flow), the wetted perimeter includes only the walls in contact with the fluid.
Similarly, in the
combustion chamber of a rocket engine, the characteristic length
is defined as the chamber volume divided by the throat area.
Because the throat of a
de Laval nozzle
A de Laval nozzle (or convergent-divergent nozzle, CD nozzle or con-di nozzle) is a tube which is pinched in the middle, making a carefully balanced, asymmetric hourglass shape. It is used to accelerate a compressible fluid to supersonic speeds ...
is smaller than the combustion chamber, the characteristic length is greater than the physical length of the combustion chamber.
References
Physical constants
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