diff --git a/uni/mmme/2xxx/2047_thermodynamics_and_fluid_dynamics/dimensional_analysis.md b/uni/mmme/2xxx/2047_thermodynamics_and_fluid_dynamics/dimensional_analysis.md index e173dd9..abda66c 100755 --- a/uni/mmme/2xxx/2047_thermodynamics_and_fluid_dynamics/dimensional_analysis.md +++ b/uni/mmme/2xxx/2047_thermodynamics_and_fluid_dynamics/dimensional_analysis.md @@ -120,4 +120,44 @@ where $M$, $L$, and $T$ are units of mass, length, and time respectively. The two equations results in some simple simultaneous equations to solve to find the coefficients $a$, $b$, $c$, $d$, $e$, $f$. +# Standard Nondimensional Groups in Fluids + +This is not an exhaustive list. + +## Reynolds Number + +$$\text{Re} = \frac{\rho U L}{\mu}$$ + +Represents ratio of intertial forces over viscous forces. +Important in all viscous flows. + +## Froude Number + +$$\text{Fr} = \frac{U^2}{gL}$$ + +Represents ratio of inerital forces over gravitational forces. +Important in flows with interfaces (e.g. gas-liquid). + +## Weber Number + +$$\text{We} = \frac{rho U^2 L}{\sigma}$$ + +where $\sigma$ is the surface tension coeffecient. + +Represents ratio of inertial to capillary forces. +Important to flows with strong surface tension effects (e.g. droplets, +bubbles, jets) + +## Strouhal Number + +$$\text{St} = \frac{fL}{U}$$ + +where $f$ is frequency. + +Important in flows with velocity oscillations. + +## Mach Number + +$$\text{Ma} = \frac U a$$ +