At the beginning of last century, aerodynamics began to attract more attention than hydrodynamics with the possibility of flight in air. Because of the concentration of effort, aerodynamics – building upon the theories of hydrodynamics -soon outstripped its parent. It started with the same assumptions as hydrodynamics but with the assumption of incompressibility replacing what was a fact for water. Prandtl showed that the effect of VISCOSITY for flow around streamlined (smooth) bodies was confined to a thin layer immediately adjacent to the body. This region is called the boundary layer. Outside the boundary layer, viscous forces are negligible and consequently potential flow theories apply. The analysis of streamlined bodies enabled airfoil design to advance rapidly.
Whereas smooth, streamlined bodies have an unbroken and stable boundary layer, bluff (unstreamlined) bodies do not. The flow starts to separate because of misbehavior of the boundary layer and potential flow solutions, even away from the body., become inaccurate. Even today, no complete theory for low-speed flow around bluff bodies exists, but an understanding of what happens physically has been built up over the years. As aircraft speeds increased, it was found that the assumption of incompressibility introduced errors. The reason for this phenomenon can be explained by Bernoulli’s equation.
Bernoulli’s equation is a statement of energy conservation in a fluid. A fluid, like any moving body, has KINETIC ENERGY through its motion and potential energy because of its potential to move under the influence of the Earth’s GRAVITATION. At all points in a fluid there is a static pressure proportional to the height of fluid above that point – this is a measure of the potential energy of the fluid at that point. The kinetic energy of the fluid is proportional to the square of the velocity and gives rise to a dynamic pressure. If no energy is added to or taken away from the fluid stream then total energy will be conserved even if there is an interchange between kinetic energy (dynamic pressure) and potential energy(static pressure) – this is the principle behind Bernoulli’s equation.
Because dynamic pressure is proportional to the square of the fluid velocity, the rate at which pressure changes with increasing velocity will depend on the absolute velocity as well as its rate of change. Consequently, the higher the speeds involved, the larger will be the pressure changes and the greater the density changes because of compressibility. Below 126 mph (210 km/h) the density changes can be ignored and air can be treated as incompressible, but above this airspeed the assumption becomes increasingly inaccurate.