Mechanics of Fluids

220 Laminar flow between solid boundaries
Fig. 6.17
✷
µ� =
65 rev/min × 2π rad/rev
µ
60 s/min
µ is evaluated as µ = 5.36 × 10 −3 Pa · s.
The calculations show that, for the particular design of viscometer
considered here, if the contribution from T b is ignored, a 1% error is
incurred in the magnitude of µ.
6.7 FUNDAMENTALS OF THE THEORY OF
HYDRODYNAMIC LUBRICATION
Another important application of laminar flow arises in the lubrication of
various types of bearings. Although high velocities may be involved, the
thickness of the lubricant film is usually small. Hence the Reynolds number
is low enough for laminar motion to be assumed.
The primary function of the lubricant is to separate the bearing surfaces,
and so long as the lubrication is effective there is no direct contact between
properly finished surfaces. If the film of lubricant is to keep the bearing surfaces
apart it must be capable of sustaining a load. One way of achieving
this is to supply the fluid lubricant to the space between the surfaces at a
sufficiently high pressure from some external source. This provides hydrostatic
lubrication. But in many instances a high pressure may be more readily
produced in the lubricant as a result of the shape and relative motion of the
bearing surfaces themselves. This action gives hydrodynamic lubrication.
The theory of it can give rise to considerable mathematical complexity and
no attempt will be made here to consider more than very simple examples.
Nevertheless, we shall see how the clearances that must be allowed between
the surfaces may be determined; also the degree of smoothness to which they
must be finished, the viscosity and the rate of flow of the lubricant necessary
to prevent the bearing surfaces coming into direct contact.
The simplest form of bearing is the slipper or slide-block moving over
a horizontal plane surface as illustrated in Fig. 6.17. For the purpose of
our analysis we shall assume that the bearing plate is infinite in extent
and that the slipper is infinitely wide in the horizontal direction perpendicular
to its motion (i.e. perpendicular to the diagram). Thus the flow
of the lubricant may be considered two-dimensional; in other words,
there is no component of velocity in the direction perpendicular to the
diagram.