$(1.$b$)$ Consider steady, incompressible, parallel,

laminar flow of a viscous fluid falling between

two infinite vertical walls. The distance between

the walls is $h,$ and gravity acts in the negative

$z-$direction $($downward in the figure$).$ There is no

applied $($forced$)$ pressure driving the flow $-$ the

fluid falls by gravity alone. The pressure is

constant everywhere in the flow field.

i$.$ Derive an expression velocity field.

ii$.$ Prove that the axial velocity $(w)$ is function

of $(x)$ only if normal velocity $u=0$

everywhere.

iii. Beginning with the continuity and

momentum equations, determine the

velocity distribution between the plates as

function of $x.$

iv$.$ Determine the shear stress.