Page 182 - 48Fundamentals of Compressible Fluid Mechanics
P. 182

144                                           CHAPTER 9. FANNO FLOW

                                             The symbol “*” denotes the state when the flow is choked and Mach number is
                                                                               Equation (9.39) can be integrated to yield:


                                                                                                               (9.40)
                                            equal to 1. Thus, 
   when

                                                                                  %




                                             In the same fashion the variables ratio can be obtained


                                                                                  %



                                                                                                               (9.41)

                                                                            %








                                                                            %


                                                                                                               (9.42)


                                                                                  %


                                                                                  %




                                                                                                               (9.43)


                                                                                       %





                                             The stagnation pressure decreases can be expressed by

                                                                                       %












                                                                                                               (9.44)
















                                             Utilizing the pressure ratio in equation (9.40) and substituting into equation (9.44)


                                            yields



                                                                                                               (9.45)





                                                                       %
                                                                                           %


                                                                                           %


                                                                       %


                                             And further rearranging equation (9.45) provides




                                                                         "




                                                                                                               (9.46)




                                                                               %


                                                                               %

                                             The integration of equation (9.34) yields     "






                                                                                                               (9.47)












                                                                                 %

                                                                                             "
   177   178   179   180   181   182   183   184   185   186   187