A block slides down a long, straight, inclined wall at speed V, riding on a thin film of oil of thickness h (Fig. P9–123). The weight of the block is W, and its surface area in contact with the oil film is A. Suppose V is measured, and W, A, angle α, and viscosity μ are also known. Oil film thickness h is not known. 

(a) Generate an exact analytical expression for h as a function of the known parameters V, A, W, α, and μ. 

(b) Use dimensional analysis to generate a dimensionless expression for h as a function of the given parameters. Construct a relationship between your ∏’s that matches the exact analytical expression of part (a).

FIGURE P9–123

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