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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.
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.
Substituting this length scale into the Debye–Hückel equation and neglecting the second and third terms on the right side yields the much simplified form () = ().As the only characteristic length scale in the Debye–Hückel equation, sets the scale for variations in the potential and in the concentrations of charged species.
The Brezina equation. The Reynolds number can be defined for several different situations where a fluid is in relative motion to a surface. [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 ...
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.
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.
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
The characteristic length depends on the geometry. For a circular pipe the characteristic length would be the diameter. For non circular ducts, the characteristic length would be: L=4A/p where A is the cross-sectional area of the duct, P would be the wetted perimeter. Note that for a circular pipe: L=4*(pi*D^2/4)/(pi*D) = D For flat plates, the ...