Pressure and speed
The pressure and the relative speed of the air flow vary considerably from one point to another around an aircraft. When the air flows from a region of high pressure to one at a lower pressure, it is accelerated. Conversely, flow from a low pressure to a higher one results in a decrease of speed. Regions of high pressure are therefore associated with low flow speeds, and regions of low pressure are associated with high speeds, as illustrated in Fig. 1.10.
When the air pressure is increased quickly, the temperature and density also rise. Similarly, a rapid reduction in pressure results in a drop in temperature. The rapid pressure changes that occur as the air flows around an aerofoil are, therefore, accompanied by changes in temperature and density. At low flow speeds of less than about one half of the speed of sound, however, the changes in temperature and density are small enough to be neglected for practical purposes. The speed of sound is about 340 m/s (760 mph) at sea level, and its significance will be explained in Chapter 5.
Although we have generally avoided the use of mathematics or formulae, we will include one or two relationships which are fundamental to the study of aerodynamics, and which also enable us to define some important terms and quantities. The first of these expressions is the approximate relationship between pressure and speed for low flow speeds.
pressure + HI density x (speed)1 is constant or in mathematical symbols,
P + 1pV1 is constant
Where p is the pressure, p is the density and V is the speed.
You will see that this fits the behaviour of the air, as described above, in that an increase in pressure must be accompanied by a decrease in speed, and vice versa. Readers who are familiar with Bernoulli’s equation, may recognise that the above expression is just a version in which the height term has been ignored, because changes in this term are negligible in comparison with changes in the other two.
This simple Bernoulli relationship between speed and pressure, given above, applies without significant error, as long as the aircraft speed is less than about half the speed of sound. At higher speeds, some form of correction becomes necessary, and once the aircraft approaches the speed of sound, a much more complicated expression has to be used.