NAVWEPS OCMOT-60  HIGH SPEED AERODYNAMICS  exist in both compressible and incompressible  cases.  The example of subsonic incompressible flow  is simplified by the fact that the density of  flow is constant throughout the tube. Thus,  as the flow approaches a constriction and the  streamlines converge, velocity increases and  static pressure decreases. In other words, a  convergence  of the tube requires an increasing  velocity to accommodate the continuity of  flow.  Also, as the subsonic incompressible  flow enters a diverging section of the tube,  velocity decreases  and static pressure increases  but density remains unchanged.  The behavior  of subsonic incompressible flow is that a con-  vergence  causes  expansion (decreasing  pressure)  while a divergence causes compression (in-  creasing pressure).  It is important to note that compressibility  effects are not limited to flight speeds at and  above the speed of sound. Since any aircraft  will have some aerodynamic shape and will  be developing lift there will  be local flow  velocities on the surfaces which arc greater  than the flight speed. Thus, an aircraft can  experience compressibility effects at flight  speeds well below the speed of sound. Since  there is the possibility of having both subsonic  and supersonic flows existing on the aircraft  it is convenient to define certain regimes of  flight.  These regimes are defined approxi-  mately as follows:  Subsonic-Mach numbers below 0.75  Transonic-Mach  numbers from 0.75 to  1.20  Supersonic-Mach numbers from 1.20 to  5.00  The example of supersonic  compressible  flow  is complicated by the fact that the variations  of flow density are related to the changes  in velocity and static pressure. The behavior  of supersonic compressible flow is that a con-  vergence  causes  compression  while a divergence  causes expansion. Thus, as the supersonic  compressible flow approaches a constriction  and the streamlines converge, velocity dc-  creases and static pressure increases.  Con-  tinuity of mass flow is maintained by the  increase  in flow density which accompanies  the  decrease  in velocity. As the supersonic com-  pressible flow enters a diverging section of the  tube, velocity increases, static pressure de-  creases,  and density decreases  to accommodate  the condition of continuity.  Hypersonic-Mach numbers above 5.00  While the flight Mach numbers used to define  these regimes of flight are quite approximate,  it is important to appreciate the types of flow  existing in each area.  In the subsonic regime  it is most likely that pure subsonic airflow  exists on all parts of the aircraft. In the  transonic regime it is very probable that flow  on the aircraft components may be partly sub-  sonic and partly supersonic. The supersonic  and hypersonic’ flight regimes will  provide  definite supersonic flow velocities on all parts  of the aircraft.  Of course, in supersonic flight  there will be some portions of the boundary  layer which are subsonic but the predominating  flow is still supersonic.  The previous comparison points out three 1  significant differences  between supersonic corn- 1  pressible and subsonic incompressible flow.  The principal differences between subsonic  and supersonic flow are due to the cmprrs-  Jibi&  of the supersonic flow.  Thus, any  change of velocity or pressure  of a supersonic  flow will produce a related change of density  which must be considered and accounted for.  Figure 3.2 provides a comparison of incom-  pressible and compressible flow through a  closed tube.  Of course, the condition of con-  tinuity must exist in the flow through the  closed tube; the mass flow at any station along  the tube is constant.  This qualification must  (a) Compressible flow includes the addi-  tional variable of flow density.  (b) Convergence  of flow causes  expansion  of incompressible flow but compression of  compressible flow.  (c) Divergence of flow causes  compression  of incompressible flow but expansion of  compressible  flow.  204  Revised January 1965 