Developing a long-pipe approximation to the full compressible flow equations

4 Developing a long-pipe approximation to the full compressible flow equations 

By equation (4.43), the conductance. Cl, is related to the total velocity head drop, Kr, by  

Note that this flow model assumes that the thermodynamic properties of the fluid just inside the inlet are equal to those in the upstream vessel, so that no distinction need be made Iwtween fluid properties at station T and station 2 . However, it is not possible to assume that the pressure just inside the outlet of the pipe, p3, will be equal to the pressure of the receiving vessel, Pa, at all times. Whenever the pipe is choked, the pressure, pi, will be equal to its critical value, pj, which will depend on both the type of gas being passed and on the frictional loss in velocity heads. Hence  

Fortunately the relationship Pic/P versus Kt may be calculated in advance and values are included in Tables A2.1 to A2.4 for four important specific-heat ratios, y. Furthermore, it is a relatively simple matter to approximate the resulting function using polynomials, as is shown in Section A2.6. 

But it remains to determine the average specific volume in the pipe, Vav, and the correction parameter, b.  

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