Problem 4: Consider again Problem 3 with a constant pressure gradient (Fig. 5) in the x-direction (dp/dx) and: a) Simplify the governing equations (continuity and momentum) for the flow; b) Apply the boundary conditions and determine the velocity profile; c) Develop expressions for the flow rate and mean velocity from the velocity profile. ignore anything that referenes drilling engineering (i.e. part D). I realize there isn't a drilling engineering expert but that isn't the point of the question either.. Problem 3 is attached for reference.
Problem 4: Consider again Problem 3 with a constant pressure gradient (Fig. 5) in the x-direction (dp/dx) and: a) Simplify the governing equations (continuity and momentum) for the flow; b) Apply the boundary conditions and determine the velocity profile; c) Develop expressions for the flow rate and mean velocity from the velocity profile. ignore anything that referenes drilling engineering (i.e. part D). I realize there isn't a drilling engineering expert but that isn't the point of the question either.. Problem 3 is attached for reference.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Problem 4: Consider again Problem 3 with a constant pressure gradient (Fig. 5) in the x-direction (dp/dx)
and:
a) Simplify the governing equations (continuity and momentum) for the flow;
b) Apply the boundary conditions and determine the velocity profile;
c) Develop expressions for the flow rate and mean velocity from the velocity profile.
ignore anything that referenes drilling engineering (i.e. part D). I realize there isn't a drilling engineering expert but that isn't the point of the question either.. Problem 3 is attached for reference.

Transcribed Image Text:Problem 3: Consider incompressible Newtonian fluid flow
between parallel plates (Fig. 4) that are horizontal and a distance h
apart. The plates can be considered as very wide and very long so
that the flow is essentially axial; hence, u ‡ 0 but v = w = 0 and
a/az-0. B represents the plate width. The flow is fully developed
laminar and steady.
a) Simplify the governing equations (continuity and
momentum) for this flow;
B
Fixed
Fig. 4
u(y)
b) Apply the boundary conditions and determine the velocity profile;
c) Develop expressions for the flow rate and mean velocity from the velocity profile.
h

Transcribed Image Text:Problem 4: Consider again Problem 3 with a constant pressure gradient (Fig. 5) in the x-direction (dp/dx)
and:
a) Simplify the governing equations (continuity and momentum) for the flow;
b) Apply the boundary conditions and determine the velocity profile;
c) Develop expressions for the flow rate and mean velocity from the velocity profile.
d) Discuss how these formulas can be used in drilling applications (Applied Drilling Engineering,
pages 165-166)
y
h
Fig. 5 Flow between parallel plates with pressure gradient
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