# 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:

## Formulas that use Characteristic Length

 $$\large{ l_c = \frac{ V } { A } }$$ $$\large{ l_c = \sqrt { \frac{ \alpha \; t }{ Fo } } }$$ (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

$$\large{ V }$$ =