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The flow pattern in bearing lubrication can be illustrated by Fig. P4.83, where a viscous oil (p, 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), v = w = 0. Neglecting gravity, reduce the Navier-Stokes rquations .. to a single differential equation for u(y). What are the proper boundary conditions? Integrate and show that 1 dp ( – yh) + U( и 2д dx where h = h(x) may be an arbitrary, slowly varying gap width. ( Oil inlet Fixed slipper block Oil outlet ho h(x) и (у) Moving wall

The flow pattern in bearing lubrication can be illustrated by Fig. P4.83, where a viscous oil (p, 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), v = w = 0. Neglecting gravity, reduce the Navier-Stokes rquations .. to a single differential equation for u(y). What are the proper boundary conditions? Integrate and show that 1 dp ( – yh) + U( и 2д dx where h = h(x) may be an arbitrary, slowly varying gap width. ( Oil inlet Fixed slipper block Oil outlet ho h(x) и (у) Moving wall

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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The flow pattern in bearing lubrication can be illustrated by Fig. P4.83, where a viscous oil (p, 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), v = w = 0. Neglecting gravity, reduce the Navier-Stokes rquations .. to a single differential equation for u(y). What are the proper boundary conditions? Integrate and show that 1 dp ( – yh) + U( и 2д dx where h = h(x) may be an arbitrary, slowly varying gap width. ( Oil inlet Fixed slipper block Oil outlet ho h(x) и (у) Moving wall
Transcribed Image Text:The flow pattern in bearing lubrication can be illustrated by Fig. P4.83, where a viscous oil (p, 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), v = w = 0. Neglecting gravity, reduce the Navier-Stokes rquations .. to a single differential equation for u(y). What are the proper boundary conditions? Integrate and show that 1 dp ( – yh) + U( и 2д dx where h = h(x) may be an arbitrary, slowly varying gap width. ( Oil inlet Fixed slipper block Oil outlet ho h(x) и (у) Moving wall
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