| \(m\) |
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 |
\([L]\) |