Ex 4 : Effects of Controls
The Bernoulli Principle

The Bernoulli Principle was developed by the Swiss Mathematician Daniel Bernoulli who was born in the 1800's.

His theory explains fluid dynamics, and is the theory that LIFT, and therefore FLIGHT is based on.

Bernoulli' s Principle states:

Total energy in a steady streamline flow remains constant.

He discovered this by placing pressure measuring instruments on, and this is something I heard along the way, on sewerage pipes! (not sure if the sewerage pipe part is true).

There was a total constant pressure running through the pipes. Where there was no blockage, there was a relatively higher pressure. Where there was a partial blockage, there was a relatively lower pressure.

Bernoulli Principle Model:

Bernoulli 's Principle is also known as the venturi effect - it states that a high velocity flow gives a low static pressure.

DEFINITION: velocity = speed with direction

When I was first taught the Bernoulli Principle, it just did not make sense to me. How can fluid / air be pushed through a narrow opening and have the pressure drop? I thought since the opening is narrowed, the pressure MUST increase! That's logical, isn't it?

The fact is, that the pressure does drop when the fluid/air speeds up. Try thinking of it this way. The "blockage" creates a surface area that is further / longer than if there was no "blockage", so the air / fluid particles have further to travel. They have to speed up to cover the increased distance in the same time, and because they speed up over this longer distance, less particles pass each point along the way at one time, so less particles passing over a particular point at one time means less pressure.

If that still doesn't work for you, then look at Bernoulli 's Principle mathematically:

Total Constant Energy =

Pressure Energy


+ Kinetic Energy


Static Pressure is the pressure that is essentially the "weight" of the atmosphere, or the Density of the Air as it rests on a body (from Ex 1)

Dynamic pressure / Kinetic (movement) energy is the pressure we feel from moving air, wind, prop wash, hand out of a moving car... etc. (from Ex 1)

In the Bernoulli Principle equation of Total Constant Pressure,(TCP) we can replace "Pressure Energy" with the Greek symbol "Rho" written "p", which represents air density, and "Kinetic / Dynamic Energy" with 1/2 Rho v squared which describes the pressure of moving air, so we can write the same formula like this:

Consider a basic equation:

10 = 5 + 5
10 = 1 + 9
10 = 3 + 7

(The number 10 for Total Constant Energy is just a number I chose randomly. You can use any numbers you like, this is simply to demonstrate the concept).

The total energy remains constant. So, if the kinetic/dynamic energy increases, then the static pressure must decrease so the total constant pressure can remain the same, and visa versa.

Air behaves like an ideal fluid below 200 knots, above that speed it compresses. For PPL, we only concern ourselves with aircraft that fly below 200 knots. Air pours and flows like an ideal fluid below this speed.

If you take two pieces of paper and hold them next to and parallel to each other an inch apart, then blow between the two pages, will you blow them apart?

No. They will "suck" together. Try it if you don't believe me. This is because the faster air creates a drop in pressure. Things tend to move from a relatively higher pressure to a relatively lower pressure, so the papers move from the relatively higher pressure towards the relatively lower pressure, towards each other.

If the Bernoulli Principle is still not making sense to you, just accept that when the speed over a surface increases, the pressure above it drops. Then we can move on.

Go from the Bernoulli Principle back to Ex 4 overview page.

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Exercises 4 to 18