Calculate Mass Transfer Rate

$\frac{a_w}{a_t}=1-e^{-1\mathrm{.}45(\frac{S_c}{s}{)}_{N_{re}}^{0\mathrm{.}75}{?}^{0\mathrm{.}01}{N}_{Fr}-0\mathrm{.}05}{N}_{we}0\mathrm{.}2$

$\frac{1}{(K{)}_{LA}}=\frac{1}{Ha{K}_G{a}_w}+\frac{1}{K_{\text{I}}{a}_w}$

Calculate the Liquid Mass Velocity

$L={}_L\frac{Q_L}{A}$

$L=998\mathrm{.}19(\frac{0\mathrm{.}021618}{0\mathrm{.}413419})$

$L=30\mathrm{.}466\frac{Kg}{m^2(s)}$

Calculate the following dimensionless Numbers to determine

Calculate Reynolds Number

$N_{re}^{0\mathrm{.}1}=(\frac{1}{a_t})\frac{V_L^{{}_L}}{{}_L}$

$N_{re}^{0\mathrm{.}1}=(\frac{1}{157})\frac{0\mathrm{.}0305998\mathrm{.}19}{0\mathrm{.}0010042}$

$N_{re}^{0\mathrm{.}1}=1\mathrm{.}693$

Calculate Froude's Number

$N_{Fr}^{-0\mathrm{.}05}=a_i\frac{V_L^2}{g_c}$

$N_{Fr}^{-0\mathrm{.}05}=157\frac{(0\mathrm{.}0305{)}^2}{9\mathrm{.}807}$

$N_{Fr}^{-0\mathrm{.}05}=1\mathrm{.}23411$

Can you please explain why calculating these are important to the design of a packed column air stripper?