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Additional resources for Lurie Modeling of Oil Product and Gas Pipeline Transportation

Example text

It is required to find the temperature at the end of the section. Solution. 36 K. 8 · 2 Using Eq. 5 C. 27 28 1 Mathematical Modeling of One-Dimensional Flows of Fluid and Gas in Pipelines Exercise 2. 004) provided with ideal heat insulation (κ = 0)? Solution. In this case it is impossible to use at once Eq. 45) since κ = 0. To use Eq. 47) one should go to the limit at κ → 0, therefore it would be better to use Eq. 004 · 150 · 103 /1950 ∼ = 3 K. Exercise 3. It is required to obtain the temperature of oil pumping over the pipeline section of length 150 km in cross-sections x = 50, 100 and 125 km, if the temperature at the beginning of the pipeline T0 = 60 ◦ C, that at the end TL = 30 ◦ C, and that of the environment Tex = 8 ◦ C.

It changes in total quantity from one form into another. 35) that is the change in total energy (Ekin + Ein ) of an arbitrary volume of the transported medium happens only due to the exchange of energy with surrounding bodies owing to external inflow of heat dQ ex and the work of external forces dAex . 7 Total Energy Balance Equation In Eq. 35) Ein is the internal energy of the considered mass of transported medium, unrelated to the kinetic energy, that is the energy of heat motion, interaction between molecules and atoms and so on.

1 A scheme of force interactions in a fluid. Modeling of Oil Product and Gas Pipeline Transportation. Michael V. Lurie Copyright  2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-40833-7 32 2 Models of Transported Media with this there are two models: the model of an ideal fluid and the model of a viscous fluid. 2 Models of Ideal and Viscous Fluids In the model of an ideal fluid it is assumed that tangential friction forces between fluid particles separated by an elementary surface are absent, not only in the state of rest but also in the state of flow.

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