Characteristic Length

Characteristic length, abbreviated as \(l_c\), is a dimension used in physics that defines the scale of a physical system.  The length is used in 2D and 3D systems for fluid dynamics and thermodynamics defining the parameter of the system.  It is usually requited by the construction of a dimensionless quantity, in the general framework of dimensionless analysis.

In computational mechanics, a characteristic length is defined to force localization of a stress softening constructive 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.

The characteristic length is essential because it helps in scaling and simplifying complex systems or phenomena.  By identifying a characteristic length, engineers and scientists can determine relevant parameters, derive dimensionless quantities, and apply appropriate analytical or computational techniques to solve problems efficiently.  The characteristic length is used in various dimensionless parameters, such as the Reynolds number, Nusselt number, and Biot number, to characterize the flow and heat transfer properties of a system.  It is important to note that the choice of a characteristic length may vary depending on the specific problem, and multiple characteristic lengths may be considered in certain situations to capture different aspects of the system under study, the specific application and the geometry of the system.