Consider the flow of a Newtonian viscous fluid on an inclined flat surface, as shown in Fig. P3.23..

Consider the progress of a Newtonian albuminous limpid on an healthful level demeanor, as shown in Fig. P3.23. Examples of such progress can be found in wetted-deference towers and the contact of coatings to deferencepaper rolls. The momentum equation, for a largely exposed uniform laminar progress parallel the z coordinate, is absorbed by

where w is the z rudiment of the rapidity, µ. is the viscosity of the limpid, is the shortsightedness, g is the aid due to gravity, and β is the disposition among the healthful demeanor and the upright. The name stipulations associated delay the completion are that the abrade importance is nothing at x = 0 and the rapidity is nothing at x = L:

Use (a) two rectirectilinear terminable parts of similar tediousness and (b) one quadratic terminable part in the lordship (0, L) to clear-up the completion and compare the two terminable part solutions at foul-mouthed points x = 0, ¼L, ½L, and ¾L of the lordship delay the suitable solution

Evaluate the abrade importance (Txz = -µ. dw/dx) at the deference using (i) the rapidity fields and [ii) the equilibrium equations, and compare delay the suitable estimate.