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In a small (4.5 KW) diesel engine, Laser Induced Fluorescence (LIF) has been used to produce detailed oil film thickness measurements around the top piston ring and liner near midstroke. The flow is “Newtonian” under the ring in the sense that using a high shear rate viscosity at the liner temperature is appropriate. The geometry corresponds everywhere to that required for a valid Reynolds approximation. Classical boundary conditions are not applicable for the high strain rates (106-107 s-1) under the piston rings of typical modem engines. A new boundary condition is developed to explain the data. The exit surface shear stress is shown to scale with a Marangoni-like (surface tension gradient) effect. By increasing surface tension, it is possible to make substantial reductions in friction for a fixed high shear viscosity.

In a recent paper (Hoult & Meador, [1]) a novel method of estimating the costs of parts, and assemblies of parts, was presented. This paper proposed that the metric for increments of cost was the function log (dimension/tolerance). Although such log functions have a history,given in [1], starting with Boltzman and Shannon, it is curious that it arises in cost models. In particular, the thermodynamic basis of information theory, given by Shannon [2], seems quite implausible in the present context. In [1], we called the cost theory “Complexity Theory”, mainly to distinguish it from information theory. A major purpose of the present paper is to present a rigorous argument of how the log function arises in the present context. It happens that the agrument hinges on two key issues: properties of the machine making or assembling the part, and a certain limit process. Neither involves thermodynamic reasoning.