Page 50 - 48Fundamentals of Compressible Fluid Mechanics
P. 50

12                                          CHAPTER 1. INTRODUCTION

                                            Mumenthaler from UTH University, no copy of the thesis can be found in the orig-
                                                                                                                  40
                                            inal University and perhaps only in the personal custody of the Fanno family .
                                            Fanno attributes the main pressure reduction to friction. Thus, flow that is domi-
                                            nantly adiabatic could be simplified and analyzed. The friction factor is the main
                                            component in the analysis as Darcy  41  was already proposed in 1845. The arrival
                                            of the Moody diagram, which built on Hunter Rouse’s (194x) work made Darcy–
                                            Weisbach’s equation universally useful. Without the existence of the friction factor
                                            data, the Fanno model wasn’t able to produce a prediction useful for the indus-
                                            try. Additionally an understating of the supersonic branch of the flow was unknown
                                            (The idea of shock in tube was not raised at that time.). Shapiro organized all the
                                            material in a coherent way and made this model useful.
                                            Meta
                                                   id Fanno realize that the flow is choked? It appears at least in Stodola’s

                                                 book that choking was understood in 1927 and even earlier. The choking
                                                 was assumed only to be in the subsonic flow. But because the actual Fanno’s
                                                 thesis is not available, the question cannot be answered yet. When was
                                                 Gas Dynamics (compressible flow) as a separate class started? Did the
                                                 explanation for the combination of diverging-converging nuzzle with tube for
                                                 Fanno flow first appeared in Shapiro’s book?

                                            Meta End
                              expanding model by others

                                            1.3.3.5  Isothermal Flow

                                            The earliest reference to isothermal flow was found in Shapiro’s Book. The model
                              If it turned out that no one had
                              done it before Shapiro, this
                                                                                 and it appears that Shapiro was the first
                              Shapiro’s flow. Call for others
                              to help in this information.  one to realize this difference compared to the other models. In reality, the flow is
                                                                            to one for cases that are between Fanno (adi-
                              flow model should be called suggests that the choking occurs at
                                            abatic) and isothermal flow. This fact was evident in industrial applications where
                                            the expectation of the choking is at Mach one, but can be explained by choking at
                                            choked somewhere between
                                            a lower Mach number. No experimental evidence, known by the undersigned, was
                                            ever produced to verify this finding.
                                            1.3.4   External flow
                                            When the flow over an external body is about .8 Mach or more the flow must
                                            be considered to be compressible flow. However at a Mach number above 0.8
                                            (relative of velocity of the body to upstream velocity) a local Mach number (local
                                            velocity) can reach 
   . At that stage, a shock wave occurs which increases
                                            the resistance. The Navier-Stokes equations which describe the flow (or even

                                              40 This material is very important and someone should find it and make it available to researchers.
                                              41 Fanning  based radius is only one quarter of the Darcy  which is based on diameter
   45   46   47   48   49   50   51   52   53   54   55