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consider a liquid film of thickness in steady state laminar flow down a vertical, plane surface (wetted wall).assuming incompressible newtonian fluid with constant viscosity.and using the shell balance method. find the following:

(a)    an expression for the velocity profile. (20 pts.)

(b)    an expression for the shear stress distribution (10 pts)

(c)     average velocity (15 pts)

(d)      maximum velocity (5 pts)

(e)      maximum shear stress (5 pts)

(f)       volumetric flow rate (5pts)

 (g)     sketch the velocity and shear stress distribution (10 pts)

(h)      adjust your results to parts (a) through (c) if the plane surface has angle of inclination with the

            horizontal.(15 pts)