$($c$)$ A mechanobiological experiment is used to examine the biochemical response of cells to

a fluid shear stress in $2$D monolayer culture. For this experiment a parallel plate flow

chamber is used, and the internal dimensions of the chamber are $0\mathrm{.}45mm($height$)$ and

$55mm($width$).$

i$.$ Assuming that the viscosity of perfusion media is $8\mathrm{.}9{10}^{-4}Pa.$s$,$ and the density

of media is $997kg{m}^{-3},$ estimate the required flow velocity of the media if a shear

stress of $2Pa$ is to be imparted onto the cell monolayer.

ii$.$ Determine whether these flow conditions result in a laminar flow regime.

iii. Calculate the entry length for plane Poiseuille flow to develop.