Parameter Convention List¶

Table 2 Relevant Dimensions¶

Dimension Abbreviation Base Unit

Length $[L]$ meter

Mass $[M]$ kilogram

Time $[T]$ second

If you would like to be able to ctrl+f some variables, click on ‘View page source’ on the top right of this window. If you want to know what a greek variable is but don’t know what it’s called, you can view the source text on the file where you found the variable. nu, mu, eta, who actually remembers what these all look like? The letter ‘v’ should sue ‘nu’ for copyright infringement. Or is it the other way around?

Table 3 Parameter Guide¶

Parameter Description Units

$m$ Mass $[M]$

$z$ Elevation $[L]$

$L$ Length $[L]$

$W$ Width $[L]$

$H$ Height $[L]$

$D$ Diameter $[L]$

$r$ Radius $[L]$

$A$ Area $[L]^2$

$\rlap{-} V$ Volume $[L]^3$

$v$ Velocity $\frac{[L]}{[T]}$

$Q$ Flow rate $\frac{[L]^3}{[T]}$

$n$ Number, Amount Dimensionless

$C$ Concentration $\frac{[M]}{[L]^3}$

$p$ Pressure $\frac{[M]}{[L][T]^2}$

$g$ Acceleration due to Gravity $\frac{[L]}{[T]^2}$

$\rho$ Density $\frac{[M]}{[L]^3}$

$\mu$ Dynamic viscosity $\frac{[M]}{[T][L]}$

$\nu$ Kinematic viscosity $\frac{[L]^2}{[T]}$

$h$ Head, Elevation $[L]$

$h_L$ Headloss $[L]$

$h_{\rm f}$ Major Loss (friction) $[L]$

$\epsilon$ Surface roughness $[L]$

$\rm{f}$ Darcy-Weisbach friction factor Dimensionless

${\rm Re}$ Reynolds Number Dimensionless

$h_e$ Minor Loss (expansion) $[L]$

$K$ Minor Loss coefficient Dimensionless

$\Pi$ Dimensionless Proportionality Ratio Dimensionless

$\Pi_{vc}$ Vena Contracta Area Ratio Dimensionless

$\Pi_{Error}$ Linearity Error Ratio Dimensionless

$M$ Fluid Momentum $\frac{[M][L]}{[T]^2}$

$F$ Force $\frac{[M][L]}{[T]^2}$

$t$ Time $[T]$

$\theta$ Residence Time $[T]$

$G$ Velocity Gradient/Fluid Deformation $\frac{1}{[T]}$

$\varepsilon$ Energy Dissipation Rate $\frac{[L]^2}{[T]^3}$

$\Pi_{\bar G}^{G_{Max}}$ $\frac{G_{Max}}{\bar G}$ Ratio in a Reactor Dimensionless

$\Pi_{\bar \varepsilon}^{\varepsilon_{Max}}$ $\frac{\varepsilon_{Max}}{\bar \varepsilon}$ Ratio in a Reactor Dimensionless

$\Pi_{HS}$ Height to Baffle Spacing in a Flocculator Dimensionless

$H_e$ Height Between Flow Expansions in a Flocculator $[L]$

$S$ Spacing Between Two Objects $[L]$

$B$ Center-to-Center Spacing Between Two Objects $[L]$

$T$ Object Thickness $[L]$

$P$ Power $\frac{[M][L]^2}{[T]^3}$

$\eta_K$ Kolmogorov Length Scale $[L]$

$\lambda_\nu$ Inner Viscous Length Scale $[L]$

$\Pi_{K\nu}$ Ratio of Inner Viscous Length Scale to Kolmogorov Length Scale Dimensionless

$\Lambda$ Distance Between Particles $[L]$