pressure is lower than standard and the temperature is above standard for that altitude, which results in lower air density (higher density altitude).As discussed, density altitude influences aircraft performance; the higher the density altitude, the lower the aircraft performance. So, in the previous problem, even though the aircraft is at an indicated altitude of 1800 ft, the density altitude for performance calculations is 3500 ft. Low air density equals a higher density altitude; high air density equals a lower density altitude. Therefore, aircraft performance charts are provided for various density altitudes.
Application 2.2
A non‐pressurized, single‐engine aircraft departs for a cross‐country flight at 6500 ft. A portion of the route crosses rising terrain with peaks at 5000 ft. The pilot is only concerned with maintaining an indicated altitude of 6500 ft as filed on the visual flight rules (VFR) flight plan.
What other altitudes must the pilot consider along the route of flight? What are the implications of failing to adjust the altimeter setting if the barometric pressure is decreasing along the route? Consider the FAA definition of Maximum Elevation Figure (MEF) on VFR Sectionals and if nonstandard pressure and temperature may impact obstacle clearance.
CONTINUITY EQUATION
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.
BERNOULLI’S EQUATION
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
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.
AIRSPEED
