Answer Happy

2. Oil film with thickness t, density p, and viscosity μ moves down an infinitely large inclined solid surface as shown in Fig. P2. The flow is parallel and fully developed and there is no applied pressure driving the flow, the fluid moves down by gravity alone. Pressure at the free surface (at z = t) is constant and known to be Po. Use the notation and the coordinate system shown in Fig. P2, clearly state the assumptions, analyze continuity and Navier-Stokes equations as we did in the lectures, apply boundary conditions, and: a) Determine the velocity field. Hint: The fact that shear stress at the free surface is zero will be used as one of the boundary conditions. b) Determine the pressure field. H c) Determine the volumetric flow rate per unit width (in y-direction) as a function of p, μ, t, 0, and g. d) Plot nondimensional velocity u* vs. nondimensional coordinate z* for 0 = 60°. Use and t as pgt² the scaling parameters for velocity u and coordinate z, respectively. Note that u will be plotted on the abscissa and plot range will be confined to 0 ≤ u ≤ 0.5 and 0 ≤ z* ≤ 1. 1 of 2 Z X oil Fig. P2 8