A slipper-pad bearing (Fig. P10-24) is often encountered

Chapter 10, Problem 23P

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Problem 23P

A slipper-pad bearing (Fig. P10-24) is often encountered in lubrication problems. Oil flows between two blocks; the upper one is stationary, and the lower one is moving in this case. The drawing is not to scale; in actuality, h ≪ L. The thin gap between the blocks converges with increasing x. Specifically, gap height h decreases linearly from h0 at x = 0 to hL at x = L. Typically, the gap height length scale h0 is much smaller than the axial length scale L.This problem is more complicated than simple Couette flow between parallel plates because of the changing gap height. In particular, axial velocity component u is a function of both x and y, and pressure P varies nonlinearly from P = P0 at at x = 0 to P = PL at x = L (∂i/∂x) is not constant), Gravity forces are negligible in this flow field, which we approxiiri.ate as two-dimensional steady, and laminar. In fact, since h is so small and oil is so viscous, the creeping flow approximation? are used in the analysis of such lubrication problems. Let the characteristic length scale associated with x be L and let that associated with y be h0 (x ~ L and y ~ h0). Let u ~ V. Assuming creeping flow, generate a characteristic scale for pressure difference AP = P - P0 in terms of L h0, μ and V.

FIGURE P10-24