NAVWEPS 00401-80  BASIC AERODYNAMICS  be an unbalance of force to provide the ac-  celeration. Since there is only air within the  tube, the unbalance of force is provided by  the static pressure  at station 1 being greater  than the static pressure at the constriction,  station 2.  the pressure  forces created on an aerodynamic  surface can be studied in a simple form which  at first neglects the effect of friction and vis-  cosity of the airflow.  The most appropriate  means of visualizing the effect of airflow and  the resulting aerodynamic pressures  is to study  the fluid flow within a closed tube.  (2) The total energy of the air stream in  the tube is unchanged. However, the air-  stream energy may be in two forms.  The  airstream may have a potential energy which  is related by the static pressure  and a kimtic  energy by virtue of mass and motion.  As  the total energy is unchanged, an increase  in  velocity (kinetic energy) will be accompa-  nied by a decrease  in static pressure  (poten-  tial energy). This situation is analagous to  a ball rolling along-a smooth surface. As  the ball rolls downhill, the potential energy  due to position is exchanged for kinetic  energy of motion.  If .friction- were negli-  gibie, the change of potential energy would  equal the change in ki,netic energy. This- is  also the case for the airflow within the tube.  The relationship of static pressure  and veloc-  Suppose a stream of air is flowing through  the tube shown in figure 1.2.  The airflow at  station 1 in the tube has a certain velocity,  static pressure, and density.  As the airstream  approaches  the constriction at station 2 certain  changes must take place. Since the airflow  is enclosed within the tube, the mass flow at  any point along the tube must be the same and  the velocity, pressure, or density must change  to accommodate  this continuity of flow.  BERNOULLI ’ S  EQUATION.  A  distin-  guishing feature of submnic airflow is that  changes in pressure and velocity take place  with sniall and negligible changes in density.  For this reason the study of subsonic airflow  can be simplified by neglecting the variation  of density in the flow and assuming the flow  to be incomprmiblc. Of course, at high flow  speeds  whjch approach the speed of sound, the  flow must be considered as compressible and  “compressibility effects” taken into account.  However, if the flow through the tube of  figure 1.2 is considered subsonic, the density of  the airstream is essentially constant at all sta-  tions along the length.  ity is maintained throughout the length of the  tube. As the flow moves past the constriction  toward station 3, the velocity decreases  and  the static pressure  increases.  The Bernoulli equation for incompressible  flow is most readily explained ,by accounting  for the energy of the~airflow within the tube.  As the airstream has no energy added or sub-  tracted at any point, the sum of the potential  +id  kinetic energy must be constant.  The  kinetic energy of an object is found by:  “KE. =%MV=  where K;E. = kinetic energy, ft.-lbs.  M = mass, slugs  V ’ =velocity, ft./set.  The kinetic energy of a cubic foot of air is:  K&x,,  where g=  kinetic energy per cu. ft., psf  p=air density, slugs per cu. ft.  V=ait velocity, ft./set.  If the density of the flow remains constant,  static pressure and velocity are the variable  quantities.  As the flow approaches the con-  striction of station 2 the velocity must increase  to maintain the same mass flow.  As the  velocity increases  the static pressure will de-  crease  and the decrease  in static pressure  which  accompanies the increase in velocity can be  verified in two ways:  (I) Newton ’ s laws of motion state the  requirement of an unbalanced force to pro-  duce an acceleration (velocity change). If  the airstream experiences  an increase  in veloc-  ity approaching the constriction, there must  6 