Scaling Chemical Processes

${\mathrm{\Pi }}_1=\frac{D}{D_{\mathrm{C}}}$	${\mathrm{\Pi }}_2=\frac{L}{D_{\mathrm{C}}}$	$\frac{{\mathrm{\Pi }}_2}{{\mathrm{\Pi }}_3}=\frac{L}{L_{\mathrm{C}}}$	$\frac{{\mathrm{\Pi }}_4}{{\mathrm{\Pi }}_1}=\frac{L_{\mathrm{B}}}{D}$
$\frac{{\mathrm{\Pi }}_6}{{\mathrm{\Pi }}_1{\mathrm{\Pi }}_7}=\frac{k}{Dh}=N{u}^{-1}$	${\mathrm{\Pi }}_7=\frac{h}{h_{\mathrm{HM}}}$	$\frac{{\mathrm{\Pi }}_8}{{\mathrm{\Pi }}_9}=\frac{\mu }{{\mu }_{\mathrm{W}}}$	${\mathrm{\Pi }}_{10}=\frac{{\rho }_{\mathrm{SF}}}{{\rho }_{\mathrm{HM}}}$
${\mathrm{\Pi }}_{11}=\frac{h_{\mathrm{HM}}\mathrm{\Delta }T}{{\rho }_{\mathrm{HM}}{v}_{\mathrm{HM}}^3}$	${\mathrm{\Pi }}_{12}{\mathrm{\Pi }}_{13}=N\mathrm{\Delta }t$	$\frac{{\mathrm{\Pi }}_4^2{\mathrm{\Pi }}_{10}{\mathrm{\Pi }}_{13}}{{\mathrm{\Pi }}_8}=\frac{\rho L_{\mathrm{B}}^{2}N}{\mu }$	$\begin{array}{cc}\frac{{\mathrm{\Pi }}_{14}{\mathrm{\Pi }}_{16}}{{\mathrm{\Pi }}_{15}}& =\frac{C_{\mathrm{P},\mathrm{HM}}{\mu }_{\mathrm{HM\; ...}}}{}\end{array}$