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
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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Question
![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F23b4efbc-43a5-46bd-be37-8b4e183c086e%2Fbfa0a5d0-177d-48d2-a12f-97795daf6c88%2Faclvz5i.png&w=3840&q=75)
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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