Читать книгу Flight Theory and Aerodynamics - Joseph R. Badick - Страница 63

The continuity equation explains the relationship between velocity and cross‐sectional area. It does not explain differences in static pressure of the air passing through a pipe of varying cross sections. Bernoulli, using the principle of conservation of energy, developed a concept that explains the behavior of pressures in flowing gases.

Consider the flow of air through a venturi tube as shown in Figure 2.6. In Image A, as the mass of air experiences a constriction in the tube and as the velocity of the mass increases, the pressure decreases. A comparative image of a wing experiencing Bernoulli’s principle during flight is in Image B. Note the decreased density toward the rear of the airfoil, this will be a discussion area in Chapters 3 and 4.

The energy of an airstream is in two forms: It has a potential energy, which is its static pressure, and a kinetic energy, which is its dynamic pressure. The total pressure of the airstream is the sum of the static pressure and the dynamic pressure. The total pressure remains constant, according to the law of conservation of energy. Thus, an increase in one form of pressure must result in an equal decrease in the other.

Static pressure is an easily understood concept (see the discussion earlier in this chapter). Dynamic pressure, q, is similar to kinetic energy in mechanics and is expressed by

(2.9)

where V is measured in feet per second. Pilots are much more familiar with velocity measured in knots instead of in feet per second, so a new equation for dynamic pressure, q, is used in this book. Its derivation is shown here:

Figure 2.6 Pressure change in a venturi tube.

Source: U.S. Department of Transportation Federal Aviation Administration (2018).

Substituting in Eq. 2.9 yields

(2.10)

Bernoulli’s equation can now be expressed as

Total pressure (head pressure), H = Static pressure, P + Dynamic pressure, q:

(2.11)

To visualize how lift is developed on a cambered airfoil, draw a line down the middle of a venturi tube. Discard the upper half of the figure and superimpose an airfoil on the constricted section of the tube (Figure 2.7). Note that the static pressure over the airfoil is less than that ahead of it and behind it, so, as dynamic pressure increases, static pressure decreases.

Figure 2.7 Velocities and pressures on an airfoil superimposed on a venturi tube.