Part $2$a: Flow Through a Packed Bed

Bioengineers consider flow through packed beds and$/$or porous

materials all the time $($for example in filtration systems$).$ For pressure$-$

driven flow of a Newtonian liquid through a tube packed with stationary

porous material, the pressure difference between the inlet and the

outlet $(P)$ is related to the viscosity of the fluid $(),$ the length of the

tube $(L),$ the fluid volumetric flow rate $(Q_v,$ which has dimensions of

volume$/$time$),$ the cross$-$sectional area of the tube $(A_c),$ and a constant $k$

$($which has units$/$dimensions that are as$-$of$-$yet$-$unknown$).$

$P=\frac{L{Q}_v}{A_{c}k}$

$[10$ points$]$ What are the units $($or dimensions$)$ of the constant k$?$ You may put your answer in

terms of SI units $($e$.$g$.m,s,kg)$ or in more generalized units $($e$.$g$.$ length, time, mass$).$

$[10$ points$]$ Would this equation work for the shear$-$thickening cornstarch solution that we

discussed in class? Why or why not?