The Blake$-$Kozeny equation for the pressure drop $(p_1-p_2)$ in laminar flow of a fluid of viscosity $$ through a packed bed of length $L,$ particle diameter $D_p,$ and void fraction $,$ is given by:

$\frac{p_1-p_2}{L}=150(\frac{u_0}{D_p^2})[\frac{(1-{)}^2}{{}^3}]$

a$.$ What are the units of $?$ Explain your reasoning.

b$.$ Given $p_1-p_2=75l\frac{b_f}{i}{n}^2,D_p=0\mathrm{.}1in.,L=6\mathrm{.}0ft,=0\mathrm{.}22P,$ and $u_0=0\mathrm{.}1f\frac{t}{s},$ compute the value of $.$