The Slider-Block Problem

We begin by considering the classic slider-block problem that is sketched in Fig. 5-7. Here, a 2D cylindrical body of arbitrary cross section, but with one face that is flat, moves with 

The analysis of the preceding section and the solutions (5-74) and (5-79) can be applied directly to this problem. The geometry, as pictured in Fig. 5-7, is 2D, and most conveniently described in terms of a Cartesian coordinate system with x in the direction of motion. If we describe the problem with a coordinate system that is fixed with respect to the lower boundary, the geometry is time dependent and the Reynolds equations (5 79) takes the form 

If we adopt d as the characteristic gap width elc and L as the characteristic streamwise length scale lc, the dimensionless gap-width function is 

The relative velocity of the slider block and the lower wall is U, and this is an appropriate choice for the characteristic velocity uc, which was used to derive Reynolds equation 

Integrating once with respect to x, we find that 

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