Myth: Higher airspeed means lower pressure
Reality: High airspeed is almost never linked to lower pressure
The Bernoulli principle expresses the relationship between a flowing fluid’s pressure and velocity. The Bernoulli equation is a statement of the conservation of energy, i.e., It is applicable only when the fluid’s total energy does not change. Few seem to pay attention to, or even understand, what that means. So, we will start by straightening that out.
As stated, the Bernoulli equation is an expression of the conservation of energy of a flowing fluid. The major restriction for it to be applicable, and uniformly violated, is that no energy can be added or subtracted. In the real world with friction and viscosity (resistance to flow), energy is removed so the result is never exact. It can correctly be applied when the fluid is in a confined space, e.g., flowing in a tube, so energy is constant. It does not apply to any situation where the flow is not confined! As discussed in Aeronautics and the Bernoulli Principle, the Bernoulli equation can be used for calculations in the correct reference frame but never as a description of the physics of lift.
We will start with a discussion of the venturi, like in every other discussion of the Bernoulli principle that one will read.
The Venturi
The venturi is discussed first because, for those not deeply involved in fluid dynamics, it is the only application where the Bernoulli equation is correctly applicable. A venturi is a restriction in a pipe as shown in Figure 1. Because the cross-section of the venturi is smaller than the pipe, the fluid must flow faster. A simple statement of the Bernoulli equation is the Total Pressure, which is held constant, is equal to the Static Pressure plus the Dynamic Pressure:
Total Pressure (constant) = Static Pressure + Dynamic Pressure
Static pressure is the pressure that pushes on an object (like you!) equally from all directions. If you’re at sea level, air pressure is pushing on your entire body at approximately 15 psi (pounds per square inch) from all directions. That’s approximately one ton (2000 lbs) per square foot! Granted, you don’t feel it because the pressure inside of you is pushing out equally. This is also true for fish in the ocean. The fish at the bottom of the Marianas Trench are at a pressure of 1000 tons per square foot.
Dynamic pressure is a statement of the kinetic energy (energy due to motion) of the fluid. One riding in the air would not experience dynamic pressure unless the air hits a wall! Technically, dynamic pressure is not a pressure but has the dimensions of pressure.
Total pressure is constant in the few instances where the Bernoulli equation is correctly applied. Since the total pressure is constant, static and dynamic pressure are coupled. That is, if the static pressure is reduced by half, the dynamic pressure would double, and vice versa.
The unfortunate result of this concept is people are led to believe that an unconfined, faster-flowing fluid, i.e., a fluid with a higher dynamic pressure, must have a corresponding lower static pressure. Like the song in Gershwin’s Porgy and Bess, “It Ain’t Necessarily So”. The static pressure of an unconfined fluid is always the same as the surrounding environment. No invisible membrane separates the static pressure of a flowing fluid from the static pressure of the surroundings. What makes the venturi work is that it is confined so there is no opportunity for energy to be added or subtracted.
The Static Port
In unconfined flow, such as the air over the wing, velocity and pressure are not related by the Bernoulli equation. The simplest demonstration of this statement is the static port on an airplane. The static port is a small hole in the side of the fuselage that provides the air pressure to the pitot-static system which comprises the altimeter, airspeed indicator, as well as other instruments. Figures 2 & 3 show an airplane’s static port and a close-up of a static port.
The altimeter displays the aircraft’s altitude and can determine a varying altitude within a few feet via a change in the air pressure. An aircraft on the ramp with the engine shut off, or during the engine pre-flight run up with the propeller causing air to flow over the static port at 100 knots, or in flight at 200 knots, the static port provides the correct air pressure and therefore the correct altitude is displayed. Thus, the air pressure is the same for still air, for fast flowing air over the static port, or the static port moving through still air.
When we discuss lift on a wing, we state the air pressure on the top of a wing has a lower pressure than the air pressure on the bottom of a wing. But the reason for the lower pressure is not because the air is flowing faster over the top of the wing. The lower air pressure on the top of the wing is due to the sloping wing’s surface drawing a vacuum. This creates space that lowers the pressure. The lower pressure accelerates the air above the wing perpendicularly to the wing’s motion. This will be discussed in greater detail in Misapplication #3.
The takeaway is:
The velocity and pressure of unconfined flowing air are not related by the Bernoulli equation. The air coming out of the nozzle of a high-pressure air hose will have a high static pressure that quickly adjusts to the pressure of the surrounding air.