Question B$\mathrm{.}2$ A lubrication system calls for SAE $30$ oil at $20$ to flow at a rate of $1\mathrm{.}7$ L$/$s between $12$ m $1\mathrm{.}5$ m parallel plates placed $5$ mm apart as illustrated in Figure QB$\mathrm{.}2.$ Assume $=920*+,$# and $=0\mathrm{.}47810(\text{'}$ m#$/$s$.$ The flow velocity distribution at any distance, $,$ from the midpoint between the plates is assumed as $()=2$ #; X$<=<1$Z $($# $$#$),$ where $$ is the half$-$height between the plates and $$ is the streamwise direction. $($a$)$ Check the Reynolds number to determine whether the flow is laminar or turbulent. $[4$ marks$]($b$)$ Obtain the required pressure difference between the inflow and outflow sections. $[5$ marks$]($c$)$ What is the maximum velocity between the plates? $[4$ marks$]($d$)$ By assuming the oil as a Newtonian fluid, calculate the shear stress at the top surface. $[6$ marks$]($e$)$ Calculate the total force must be used to keep the plates from moving. $[6$ marks$]$ Hint. $=29$ Figure QB$\mathrm{.}2$: Flow between parallel plates