Consider flow through a two-dimensional slipper-pad

Chapter 10, Problem 30P

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Problem 30P

Consider flow through a two-dimensional slipper-pad bearing with linearly decreasing gap-height from h 0 to h L (Fig. P10-24), namely, h = h 0 + αx, where α is the nondimensional convergence of the gap, α -(hL - h 0)/L. We note that tan α ≡ α for very small values of α, Thus, α is approximately the angle of convergence of the upper plate in Fig. P10-24 (α is negative for this case). Assume that the oil is exposed to atmospheric pressure at both ends of the slipper-pad, so that P = P0 = P m at x = 0 and P = P L = P m at x = L. Integrate the Reynolds equation (Prob. 10-30) for this slipper-pad bearing to generate an expression for P as a function of x.