Bernoulli Effect Myths

A commonly taught idea is that "A fast moving stream of air will have a lower pressure than the surrounding still air." This is often stated as "The Bernoulli Effect."

(1) This statement is contradicted by observation, and

(2) It is not a predicted result of the Bernoulli Equation.

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(1) Experiment:

In order to test the statement experimentally, we can use the following setup:

A water manometer with three tubes connected to a common reservoir. Blow a stream of air over the top of each tube (with a hair dryer or air track blower or leaf blower), and use the water level to measure changes in pressure. (Thanks to Evan Jones for the idea of the flat plate on top of a tube.)

• For a bare tube with no surface on top - water in tube rises, indicating lower pressure.
• For tube with flat top - no change in pressure is observed.
• For tube with concave top - pressure goes up.
• For tube with convex top - pressure goes down.

The observation is that the pressure in a fast moving stream of air is the same as that of the surrounding air unless its direction is altered by some surface. The shape of the surface is an important variable in determining the pressure in the stream, and the effect will be larger as the speed increases.

Here is a video with several more experiments that test the idea that "fast moving air has lower pressure."

(2) Theory

Bernoulli's principle is a statement of conservation of energy of a mass of fluid at different points along it's path. It compares pressure, speed, and height of the fluid at points 1 and 2, which are along the same streamline. The assesrtion is that if no work is done on a bit of fluid by outside forces, the energy of that bit will remain constant.

Here is a mechanical analogy:

If the cart starts at rest at the top of the track, and then later increases its speed and kinetic energy, we know that it must have lost gravitational potential energy, don't we? Could we make a rule of thumb that says "a faster cart will be at a lower height?"

The answer is: Yes ... IF no work is done on the cart by outside forces. If the cart is given a push by a hand or a motor, it can obviously gain kinetic energy without needing to lose gravitational potential energy, and it could speed up even on a level track.

Bernoulli's equation is the same kind of thing for fluids:

Here we consider some volume of fluid moving along stream lines. There are three forms of energy it might have: gravitational potential (mgh), kinetic (1/2 mv^2) and internal energy from being "pressurized" (PV).

Bernoulli's equation is usually written as energy per unit volume rather than the energy of a little mass: (divide each term by V)

E = ρgh + 1/2ρv^2 + P = constant

If energy is conserved and there is no work done by outside forces, then if the bit of fluid increases its kinetic energy, it must decrease some other form of energy. If it stays at the same height, then its internal energy, and thus its pressure, must decrease. The rule of thumb for this is "fast moving air will have a lower pressure."

BUT... if there is an outside force (such as a fan) that does work on a bit of fluid, that force can certainly cause an increase in the KE of that bit, without any need for a corresponding decrease in height (GPE) or pressure (internal energy).

Our rule of thumb is no longer valid. In this case, we could easily have a fast moving bit of air (or other fluid) that is at the same pressure as the surrounding still air without any violation of conservation of energy. And since this bit of air is in contact with the surrounding air, it makes sense that the pressures would be equal. This is in fact what is observed in the above experiment with the flat topped tube, when the air is not diverted.

Does the rule of thumb hold for airplanes? Since the apparent speed of the wind past the wing is maintained by burning fuel in the airplane, we have a situation with outside forces, and so conservation of E doesn't require the air on top of the wing to be at lower than atmospheric pressure. We also know that paper airplanes can fly with planar wings, so we know that the airfoil shape is helpful but not necessary.

So what is it that causes lift? The short answer is that if air is diverted down by an object in any way, there will be a net upward force on that object, by Newton's Third Law. This accounts for 100% of lift. (it must, unless it violates N's 3rd Law). The microscopic mechanism by which the curved top of a wing diverts air downward is complicated. It is often called the Coanda effect.