Inverse Hydrodynamic Methods Applied to Mr. Beauchamp Tower’s Experiments of 1885

The experiments of Mr. Beauchamp Tower and their subsequent interpretation by Professor Osborne Reynolds form the basis of all hydrodynamic lubrication theory. In the experiments described in his second report, Tower made nine pressure tappings in a 157 deg partial arc bearing. Reynolds assumed that the film shape corresponded to a circular bearing and analyzed the results on this assumption. Inverse hydrodynamic theory allows the calculation of the actual film shape from this measured pressure distribution. It is found that the film was a slightly convergent wedge which does not correspond to a fitted bearing as assumed by Tower and certainly not to the clearance bearing assumed by Reynolds. Existing methods of inverse hydrodynamic analysis require the second differential of the pressure profile (or its equivalent in the two-dimensional case) to become zero at some point in the film. The film thickness can be found directly at this point and then elsewhere by the solution of a cubic equation. Two separate and more general methods are developed in this paper in which this requirement for the second differential is unnecessary.