Consider the laminar flow of an incompressible, viscous liquid down an inclined plate. The inclina-

tion angle of the plate is 0. The thickness of the film h is constant. The density of the fluid is p, and

the viscosity of the fluid is µ. Neglect pressure changes. The velocity profile for this flow is given as

(1)

1.

2.

3.

u = ky(2h-y),

v=w = 0.

Find in terms of p, g, u, and 0.

Find the mass flow rate per unit width.

Find the velocity potential if it exists. If it does not exist, prove it mathematically.

Figure 5: Sketch

(v)