Bernoulli’s Principle and Subsonic Flow

in Physics

The basic concept of subsonic airflow and the resulting pressure differentials was discovered by Daniel Bernoulli, a Swiss physicist. Bernoulli’s principle, as we refer to it today, states that “as the velocity of a fluid increases, the static pressure of that fluid will decrease, provided there is no energy added or energy taken away.” A direct application of Bernoulli’s principle is the study of air as it flows through either a converging or a diverging passage, and to relate the findings to some aviation concepts.


A converging shape is one whose cross-sectional area gets progressively smaller from entry to exit. A diverging shape is just the opposite, with the cross-sectional area getting larger from entry to exit. Figure 3-54 shows a converging shaped duct, with the air entering on the left at subsonic velocity and exiting on the right. Looking at the pressure and velocity gauges, and the indicated velocity and pressure, notice that the air exits at an increased velocity and a decreased static pressure. Because a unit of air must exit the duct when another unit enters, the unit leaving must increase its velocity as it flows into a smaller space.

Figure 3-54. Bernoulli’s principle and a converging duct.

Figure 3-54. Bernoulli’s principle and a converging duct.

In a diverging duct, just the opposite would happen. From the entry point to the exit point, the duct is spreading out and the area is getting larger. [Figure 3-55] With the increase in cross-sectional area, the velocity of the air decreases and the static pressure increases. The total energy in the air has not changed. What has been lost in velocity (kinetic energy) is gained in static pressure (potential energy).

Figure 3-55. Bernoulli’s principle and a diverging duct.

Figure 3-55. Bernoulli’s principle and a diverging duct.

In the discussion of Bernoulli’s principle earlier in this section, a venturi was shown in Figure 3-46.

Figure 3-46. Bernoulli’s principle and a venturi.

Figure 3-46. Bernoulli’s principle and a venturi.

In Figure 3-56, a venturi is shown again, only this time a wing is shown tucked up into the recess where the venturi’s converging shape is. There are two arrows showing airflow. The large arrow shows airflow within the venturi, and the small arrow shows airflow on the outside heading toward the leading edge of the wing. In the converging part of the venturi, velocity would increase and static pressure would decrease. The same thing would happen to the air flowing around the wing, with the velocity over the top increasing and static pressure decreasing.

Figure 3-56. Venturi with a superimposed wing.

Figure 3-56. Venturi with a superimposed wing.

In Figure 3-56, the air reaching the leading edge of the wing separates into two separate flows. Some of the air goes over the top of the wing and some travels along the bottom. The air going over the top, because of the curvature, has farther to travel. With a greater distance to travel, the air going over the top must move at a greater velocity. The higher velocity on the top causes the static pressure on the top to be less than it is on the bottom, and this difference in static pressures is what creates lift.

For the wing shown in Figure 3-56, imagine it is 5 ft wide and 15 ft long, for a surface area of 75 ft2 (10,800 in2). If the difference in static pressure between the top and bottom is 0.1 psi, there will be 1⁄10 lb of lift for each square inch of surface area. Since there are 10,800 in2 of surface area, there would be 1,080 lb of lift (0.1 × 10,800).