House paint is formulated so that, if applied properly, it will not run down a vertical surface before it dries. It can be modeled as a Bingham fluid.

(a) Suppose that a latex paint with a density like that of water is brushed on a wall at a thickness H = 0.5 mm. What is the minimum yield stress τ₀ that is needed to avoid running?

(b) Assume now that the paint is applied carelessly, such that H exceeds the film thickness that can be immobilized by the yield stress. Determine v_x(y) for steady, fully developed flow, using the coordinates in Fig. 7.5. What is the maximum velocity?

Transcribed Image Text:

y X Liquid +H Gas W g Figure 7.5 Liquid film of thickness H flowing down a flat, vertical surface.