Consider flow through a two-dimensional slipperpad bearing with linearly decreasing gap height from h₀ to h_L (Fig. P10–23), namely, h = h₀ + αx, where a is the nondimensional convergence of the gap, α = (h_L – h₀)/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. P10–23 (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_atm at x = 0 and P = P_L = P_atm at x = L. Integrate the Reynolds equation for this slipper-pad bearing to generate an expression for P as a function of x.

FIGURE P10–23

Transcribed Image Text:

T ho u(x, y) V X L- h(x) μ hL