By Mikhail V. Lurie, Emmanuil Sinaiski
In response to a good tried-and-tested lecture on the Russian kingdom collage of Oil and gasoline, this available method of the idea of pipeline transportation offers systematic insurance of varied varieties of fluids, sponsored by means of real-world examples. From the contents:* basics of mathematical modeling of one-dimensional flows* types of transported media* constitution of laminar and turbulent fluid flows* Modeling and calculation of steady-state regimes * Closed mathematical versions of one-dimensional fluid and gasoline flows * Dimensional idea* actual modeling of phenomena* size and similarity in mathematical modeling of processesEnd-of-chapter difficulties make this sensible e-book constant and appropriate for self-study.
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4 2 4 2 From this it transpires that the friction resistance is proportional to the square of the ﬂuid mean velocity and hence this type of ﬂow is called square ﬂow. 002·(Re−2320) is the intermittency factor (Ginsburg, 1957). It is obvious that the form of the last formula assures continuous transfer from the Stokes formula for laminar ﬂow to the Blasius formula for turbulent ﬂow in the zone of hydraulic smooth pipes. 21 22 1 Mathematical Modeling of One-Dimensional Flows of Fluid and Gas in Pipelines To calculate the hydraulic resistance factor λ of the gas ﬂow in a gas main, where the Reynolds number Re is very large and this factor depends only on the condition of the pipeline internal surface, Eq.
H The expression in parentheses characterizes the loss of mechanical energy within the pump. Usually this factor is taken into account by insertion of the pump efﬁciency η η= 1− −1 x2 i/ H dx <1 x1 so that Nmech = ρgQ · H . 21) is the main formula used to calculate the power of the pump generating head H in ﬂuid pumping with ﬂow rate Q. 6 Equation of Change in Internal Motion Kinetic Energy At the beginning of the previous section it was noted that the total kinetic energy of the transported medium consisted of two terms – the kinetic energy of the center of mass of the particle and the kinetic energy of the internal motion of the center of mass, so that the total energy of a particle is equal to αk ρv2 /2, where αk > 1.
1934). 2 Formulas for Calculation of the Factor λ(Re, ε) Details of methods to ﬁnd and calculate the factor of hydraulic resistance λ in Eqs. 29) and one of the primary factors in hydraulics and pipeline transportation will be given in Chapter 3. Here are shown several formulas exploiting the practice. 1) is used λ= 64 . 6 Equation of Change in Internal Motion Kinetic Energy As the Reynolds number increases (Re > 2300) the ﬂow in the pipeline gradually loses hydrodynamic stability and becomes turbulent, that is vortex ﬂow with mixing layers.
Modeling of Oil Product and Gas Pipeline Transportation by Mikhail V. Lurie, Emmanuil Sinaiski