Download - Rough and Smooth Pipes
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Rough and smooth pipesclassification criteria and velocity distribution
Submitted by- Deepak ahuja
Scholar number- 091111052
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Hydro dynamically Smooth and Rough Boundaries
The classification of rough and smooth boundary is based onboundary characteristics. Rather for proper classification, theflow and fluid characteristics should also be considered
In general, the type of boundary depend on average height ofirregularities projecting from the surface of the boundaryIf the value of k is less then it is called smooth boundary andif value of k is more then it is called rough boundary.
As in the case of turbulent flow the flow is divided inboundary characteristics depend on laminar sub layer depth
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From Nikuradses experiment
If is less than .25, the boundary is called smooth boundary
If is between .25 to 6.0, the boundary is in transition
If is more than 6.0, the boundary is called rough boundary
Where, k is average height of the irregularities projecting from the
surface of a boundary, height of laminar sub layer from boundary
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Roughness in the term of reynolds number
Instead of value of is used to classify the
type of boundary and limits for these type of flow
is
100, then rough boundary
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Criterion for Turbulent vs. Laminar Flow in a Pipe
The behavior of flow in pipes is determined by the Reynolds
number Re.
Flow tends to become turbulent when Re > 3000.
Flow is always laminar when Re < 2000.
For 2000 < Re < 3000, the behavior is unpredictable and
often switches back and forth between laminar and
turbulent.
When conditions are carefully controlled so that the flow
is perfectly motionless at the inlet of the pipe and the pipe
is free of vibrations, then it is possible to maintain laminar
flow even at Re > 3000.
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Turbulent flow is less efficient than laminar flow:
Velocity profilefor turbulent flow
Velocity profileif flow were laminar
everywhere
Thin, laminar boundary layer
If flow could remain laminar, the pipe could transport morefluid for a given pressure gradient.
The swirls and eddies associated with turbulence make
the fluid appear as though it had a much higher viscosity
where flow is turbulent.
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Same concept, different way of looking at it:
The effective mean stress (or apparent stress) is much
greater than the stress expected for laminar flow.Within the turbulent flow, this stress is approximately
linear with radius.
The apparent stress depends on the turbulent velocity
perturbations u and v.
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Velocity distribution in smooth pipes:
Laminar Turbulent
Experiments show:
for
for
where
(laminar
boundary
layer)
(note logarithmic scales)
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More empirical (experimental) relations for smooth pipes:
where for laminar flow
shear stress at wall
head loss (Darcy-Weisbachequation)
For turbulent flow
with Re > 3000
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Rough Pipes
Velocity distribution
k is a parameter that characterizes the height of the
roughness elements.
B is a parameter that is a function of the type, concentration,
and the size variation of the roughness.
y is distance from wall.
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Rough Pipes
Low Reynolds number or small
roughness elements:Roughness unimportant, pipe
considered smooth
High Reynolds number or large
roughness elements:
Fully rough, f independent of
Reynolds number.
and are still valid
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