Characteristic Length
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 formulas
| \(\large{ l_c = \frac{ V } { A } }\) | |
| \(\large{ l_c = \sqrt { \frac{ \alpha \; t }{ Fo } } }\) | (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