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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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