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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.
x is the characteristic length; Ra x is the Rayleigh number for characteristic length x; g is acceleration due to gravity; β is the thermal expansion coefficient (equals to 1/T, for ideal gases, where T is absolute temperature). is the kinematic viscosity; α is the thermal diffusivity; T s is the surface temperature
A powerful tool in physics is the concept of dimensional analysis and scaling laws. By examining the physical effects present in a system, we may estimate their size and hence which, for example, might be neglected. In some cases, the system may not have a fixed natural length or time scale, while the solution depends on space or time.
L = characteristic length of robot, U = characteristic speed. The analysis of a microrobot using the Strouhal number allows one to assess the impact that the motion of the fluid it is in has on its motion in relation to the inertial forces acting on the robot–regardless of the dominant forces being elastic or not.
In physics, critical phenomena is ... the defining property of criticality is that the characteristic length scale of the structure of the physical system, ...
Dimensionless numbers (or characteristic numbers) have an important role in analyzing the behavior of fluids and their flow as well as in other transport phenomena. [1] They include the Reynolds and the Mach numbers, which describe as ratios the relative magnitude of fluid and physical system characteristics, such as density, viscosity, speed of sound, and flow speed.
[n 1] These definitions generally include the fluid properties of density and viscosity, plus a velocity and a characteristic length or characteristic dimension (L in the above equation). This dimension is a matter of convention—for example radius and diameter are equally valid to describe spheres or circles, but one is chosen by convention.
The Froude number is based on the speed–length ratio which he defined as: [2] [3] = where u is the local flow velocity (in m/s), g is the local gravity field (in m/s 2), and L is a characteristic length (in m). The Froude number has some analogy with the Mach number.