Show that when $R{e}_P>1000$ and $C_D$ is governed by:

$d{}_o{}_f$~$=0\mathrm{.}41\frac{v_f}{v_m}=0\mathrm{.}11R{e}_{p}R{e}_p[\frac{{}_f^3}{1\mathrm{.}75}(\frac{{}_o-}{})gd{]}^{\frac{1}{2}}$

Given that ${}_f$~$=0\mathrm{.}41$ and $\frac{v_f}{v_m}=0\mathrm{.}11.$ That $is,$ there $is$ approximately $a10-$fold range $of$ feasible velocities $at$ high $R{e}_p,in$ contrast $to$ the $100-$fold range $at$ low $R{e}_p.$