Page 64 - Tribology in Machine Design

Basic principles of tribology 51

The distance between the boundaries is 2/z, so that t;=0 when y= ±h.
Hence the constant A is zero and

It follows from this equation that the pressure gradient dp/dx is negative,
and that the velocity distribution across a section perpendicular to the
direction of flow is parabolic. The pressure intensity in the film falls in the
direction of flow. Further, if Q represents the volume flowing, per second,
across a given section

where ). — 2h is the distance between the boundaries. This result has
important applications in lubrication problems.

2.13.4. Shear stress variations within the film
For the fluid film in simple shear, q is constant, so that

and p is also constant. In the case of parallel flow between plane boundaries,
since Q must be the same for all sections, dp/dx is constant and p varies
linearly with x. Further

2.13.5. Lubrication theory by Osborne Reynolds
Reynolds' theory is based on experimental observations demonstrated by
Tower in 1885. These experiments showed the existence of fluid pressure
within the oil film which reached a maximum value far in excess of the mean
pressure on the bearing. The more viscous the lubricant the greater was the
friction and the load carried. It was further observed that the wear of