Читать книгу Flight Theory and Aerodynamics - Joseph R. Badick - Страница 62

Consider the flow of air through a pipe of varying cross section as shown in Figure 2.5. There is no flow through the sides of the pipe: air flows only through the ends. The mass of air entering the pipe, in a given unit of time, equals the mass of air leaving the pipe, in the same unit of time. The mass flow through the pipe, must remain constant. The mass flow at each station is equal. Constant mass flow is called steady‐state flow. The mass airflow is equal to the volume of air multiplied by the density of the air. The volume of air, at any station, is equal to the velocity of the air multiplied by the cross‐sectional area of that station.

The mass airflow symbol Q is the product of the density, the area, and the velocity:

(2.6)

The continuity equation states that the mass airflow is a constant:

(2.7)

The continuity equation is valid for steady‐state flow, both in subsonic and supersonic flow. For subsonic flow, the air is considered to be incompressible, and its density remains constant. The density symbols can then be eliminated; thus, for subsonic flow,

(2.8)

Velocity is inversely proportional to cross‐sectional area: as cross‐sectional area decreases, velocity increases.

Figure 2.5 Flow of air through a pipe.