Characteristic Length

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

Characteristic length, abbreviated as \(l_c\), is 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.

Examples of:

Characteristic Length Formula

\(\large{ l_c = \frac{ V } { A }  }\)        

\(\large{ l_c =  \sqrt   { \frac{ \alpha \; t }{ Fo }  }   }\)     (Fourier number)

\(\large{ l_c =\frac{ Nu \; k }{ h  }    }\)     (Nusselt number)

\(\large{ l_c =  \frac {Pe \;  k}{ v \; \rho \;  C }  }\)     (Peclet number)

\(\large{ l_c = \frac{ Re \; \mu }{\rho \; v }  }\)     (Reynolds number)

\(\large{ l_c = \frac { Sh \; D}    {K} }\)     (Sherwood number)

Where:

\(\large{ l_c }\) = characteristic length

\(\large{ A }\) = area of object surface

\(\large{ \rho }\)  (Greek symbol rho) = density

\(\large{ D }\) = diffusion coefficient

\(\large{ \mu }\)  (Greek symbol mu)  = dynamic viscosity

\(\large{ Fo }\) = Fourier number

\(\large{ C }\) = heat capacity

\(\large{ h }\) = heat transfer coefficient

\(\large{ K }\) = mass transfer coefficient

\(\large{ Nu }\) = Nusselt number

\(\large{ Pe  }\) = Peclet number

\(\large{ Re }\) = Reynolds number

\(\large{ Sh }\) = Sherwood number

\(\large{ k }\) = thermal conductivity

\(\large{ \alpha }\)  (Greel symbol alpha) = thermal diffusivity

\(\large{ t }\) = time

\(\large{ v  }\) = velocity

\(\large{ V }\) = volume