The flow pattern in bearing lubrication can be illustrated by Fig. P4.83, where a viscous oil (ρ, μ) is forced into the gap h(x) between a fixed slipper block and a wall moving at velocity U. If the gap is thin, h L, it can be shown that the pressure and velocity distributions are of the form p = p(x), u = u(y), υ = w = 0. Neglecting gravity, reduce the Navier-Stokes equations (4.38) to a single differential equation for u(y). What are the proper boundary conditions? Integrate and show that
u = 1/ 2μ dp/ dx (y2 €“ yh) + U (1 €“ y/h)
Where h = h(x) may be an arbitrary slowly varying gap width. (For further information on lubrication theory, see Ref. 16.)

Transcribed Image Text:

Oil inlet Fixed slipper block Oil outlet ho h) Moving wall