Dynamic Similarity

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Dynamic Similarity

• Scale-Up

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Longhorn Pipeline
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Specifications

• 700 mi.
• 24 diameter commercial steel(k 0.0018 in.)
• 250,000 bbl/day gasoline, Jet fuel, dieselJet-A
  0.81g/cm3, 1.3 cP

What ?P is required to pump gasoline through the
pipeline?
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Dynamic Similarity
If the two dimensionless groups on the right-hand
side are the same in both a model system and
production (field) system, the left-hand quantity
is also the same.
The magnitude of the individual variables doesnt
matter!
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So
Here V4Q/pD2 has been substituted.
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Caveats
Correlation is only valid when LgtgtD
?
and
Flow is turbulent (NRe gt 2100)
?
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We have 3 equations What are the knowns and
unknowns
Known (D, L, k, Q, µ, ?)pipeline, (?P)model
Unknown (D, L, k, Q, µ, ?)model, (?P)pipeline
With 3 equations and 7 unknowns we must fix 4
unknowns arbitrarily. But since the ones we need
to fix deal with the model, we must keep in mind
that the model materials should be inexpensive,
readily available and safe.
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Model Design
Fix the diameter of the model pipe first. This
can be chosen arbitrarily, but we probably want
to use a smaller more manageable diameter than
the actual pipeline.
Note that the pipe material and diameter are
related via one of our equations
and
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Model Design (contd)
So unless we choose a smoother pipe the pipeline
and model diameters must be equivalent. Smoother
pipes include plastic, glass, and drawn metal
tubings. These all have k0.00006. Choosing
plastic
Now the k values are approximations so we are
free to choose any pipe of this approximate
diameter. Schedule 40, ¾ in pipe has an I.D. of
0.824 in. which is fortuitous (and probably
available at Home Depot).
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Model Design (contd)
We must also choose a fluid for the model. We
probably dont want to pump Jet fuel in a lab
setting. Whats a safe liquid?
H2O µ 1 cP ? 1 g/cm3
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The Experiment
Still need a length. This can be any length that
conveniently fits into the laboratory setting.
Take L 10 ft. for this example
We have the following experimental
design Plastic ¾ in Schedule 40 pipe 10
ft Water pumped at a rate of 156 gpm
We then set up the experiment and measure ?P for
the model. Lets assume that we measure 20 psi
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The Result
The Euler Number similarity then gives