is $45$ cm wide, is steadily pulled upwards at $V=0\mathrm{.}6\frac{m}{s},$ and both sides of the channel outside the liquid are at $p=101,325Pa.$ Assume that the uncured resin is a Newtonian fluid with a viscosity of $=0\mathrm{.}843*{10}^{-3}N-\frac{s}{m^2},$ a density of $=735k\frac{g}{m^3},$ and experiences laminar fully$-$developed flow, all in the vertical direction. You can assume that the sheet is infinitely large into the page $(z$ direction$).$

Figure $2$: Falling liquid along vertical surface for Problem $2.$

$($a$)$ Determine the velocity profile in the channel between one side $($any side$)$ of the metal sheet and the channel walls, as a function of $x.$

$($b$)$ Find the slope of the velocity profile at the surface of the sheet; that is$,$ find $($you can leave your answer in terms of variables$)$:

$\frac{\text{d}\text{e}\text{l}\text{v}(x)}{\text{d}\text{e}\text{l}\text{x}}{|}_x||=0\mathrm{.}1mm$

$($c$)$ Determine the force per unit length exerted on the sheet when it is in the channel.