Problem $\backslash$#$9$

Oil $\backslash (\backslash$left$(\backslash$mu$=0\mathrm{.}38\backslash$mathrm$\{$~N$\}\backslash$right$.\backslash ).$s$.\backslash (\backslash$left$.\backslash$mathrm$\{$m$\}^\{-2\}\backslash$right$)\backslash )$ flows steadily between two

fixed horizontal infinite parallel plates with a spacing of $4$ mm $($see Figure $1).$ The flow is laminar with a pressure gradient of $30$ kPa per unit meter. Determine:

$($a$)$ volume flowrate per unit width,

$($b$)$ magnitude and direction of the shear stress on the lower plate,

$($c$)$ centerline velocity.

rigure $1.$