Bernoulli’s Principle & Lift

Lift is the backbone of aviation. Over the years, we’ve encountered many different explanations for lift — some more accurate than others. While simplicity is great, it’s important to stay grounded in reality. So let’s see how Bernoulli’s Principle explains lift.

Explore this Article:

> What is Bernoulli’s Principle?
> The Principle Explained.
> Applying Bernoulli’s Principle to Lift.
> Other Factors Influencing Lift.
> Conclusion.
> Frequently asked Questions.

What is Bernoulli’s Principle?

Bernoulli’s Principle applied to aerodynamics tells us that:

“In a streamlined flow of an ideal fluid, the sum of static pressure and the dynamic pressure remains constant.”

Daniel Bernoulli, Swiss mathematician. Published in Hydrodynamics – 1738.

To start, let’s clarify Bernoulli’s Principle which operates under the assumption that air behaves like an “ideal fluid.” This means:

It’s incompressible
(its volume doesn’t change with pressure fluctuations).

It has no viscosity
(it doesn’t create friction or stick to surfaces or itself).

While these assumptions aren’t entirely accurate, they are generally accepted for subsonic airspeeds (below Mach 0.4) where the effects of compressibility and viscosity are minimal.

Seeing as not much went over 260 Knots in 1738, we will give him the benefit of the doubt.

With that clarified, let’s explore the principle itself.

Bernoulli's Principle Explained

Imagine a tube that has airflow going through it:

Bernoulli’s Principle tells us that the sum of static and dynamic pressure within a stream of fluid (like air) remains constant throughout. This is referred to as Total Pressure.

So, what does all this mean?

Essentially, it demonstrates that the total pressure within the stream tube remains constant, regardless of changes in the other two pressures.

The principle can be expressed through a simplified equation:

Showing that no matter what happens to static or dynamic pressure, the total pressure will not change.

This concept ties into the Law of Continuity, which states that when the cross-sectional area of a tube decreases, the airflow velocity increases.

So Lets pinch the tube at one end…

As the tube narrows, the airflow velocity rises, the dynamic pressure increases while static pressure decreases to maintain constant total pressure.

This little exchange keeps the total pressure constant!

To summarise, if either static or dynamic pressure increases, the other one decreases – and vice versa. Total pressure will always remain the same.

So what does any of this have to do with lift?

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Applying Bernoulli’s Principle to Lift

So how does this relate to lift? The shape of an aircraft’s wing creates a narrower stream of air on top than beneath it. As airflow speeds up over the curved top of the wing, dynamic pressure increases while static pressure drops. This difference in pressure between the upper and lower surfaces of the wing generates an upward force—lift!

However, Bernoulli’s Principle is just one aspect of what produces lift. There are other key factors to consider.

Lets recap, if the air flowing past the top surface of an aircraft wing is moving faster than the air flowing past the bottom
surface, then Bernoulli’s principle implies that the pressure on the surfaces of the wing will be lower above than below generating Lift.

This pressure difference results in an upwards lifting force. Whenever the distribution of speed past the top and bottom surfaces of a wing is known, the lift forces can be calculated (to a good approximation) using Bernoulli’s equations. For our purposes though we know the pressure above the wing is relatively lower than that below.

Other Factors Influencing Lift

To fully understand lift, let’s have a look at the lift equation:

Clearly there’s more to it that just reducing pressure above the wing. Don’t be put off by all the formulae.

Let’s go over each variable, and its relationship with the outcome of lift.

Density (ρ)

Rho represents air density, which determines how much air the wing can interact with to generate lift.

Both pressure and temperature have a direct impact on air density:

– As pressure increases ⬆️, air density increases ⬆️.
– As temperature rises ⬆️, air density decreases ⬇️.

This explains why aircraft performance decreases significantly in hotter, higher, or more humid conditions — due to the effects of density altitude.

Lift Coefficient (CL)

The lift coefficient (CL) represents the effectiveness of a wing at generating lift.

It’s mainly influenced by the shape of the wing, the angle of attack, and something called a Reynolds Number.

A Reynolds number is determined by the air velocity, viscocity, (we’ll cover this one in another article).

In general, the higher the angle of attack, the higher the CL value, up to the point of stall where CL reduces massively.

True Airspeed (TAS)

Airspeed doesn’t just increase lift
— it does so exponentially.

Doubling your airspeed quadruples the amount of lift due to the square relationship between lift and airspeed.

Wing or Surface Area

Larger wings generate more lift since both Bernoulli’s pressure reduction and Newton’s deflection of air act over a bigger surface area.

Doubling the wing area results in twice as much lift.

Conclusion

Lift is a fundamental concept that often doesn’t get the focus it deserves during a pilot’s career.

Grasping Bernoulli’s Principle is key to truly understanding lift. However, it’s equally important to acknowledge that this principle is just one part of a larger picture. Other factors such as air density, lift coefficient, airspeed, Newton’s Third Law, and wing surface area also play vital roles in the generation of lift.

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