Skimmers are used to remove viscous fluids, such as oil, from the surface of water. As shown on the diagram in Figure P10.24, a continuous belt moves upward at velocity \(v_{s}\) through the fluid and the more viscous liquid (with density, \(ho\), and viscosity, \(\mu\) ) adheres to the belt. A film with thickness, \(h\), forms on the belt. Gravity tends to drain the liquid, but the upward belt velocity is such that net liquid is transported upward. Assume the flow is fully developed, laminar, with zero pressure gradient, and zero shear stress at the outer film surface where air contacts it. Determine an expression for the velocity profile and flow rate. Use a differential analysis, similar to that used for fully developed laminar flow through an inclined pipe. Clearly state the velocity boundary conditions at the belt surface and at the free surface.

Transcribed Image Text:

FIGURE P10.24 X