Bernoullis Principle of Lift

Daniel Bernoulli, a Swiss scientist working in the eighteenth century, described the phenomenon of a fluid exerting less pressure as it moves more quickly. He published his findings in “Hydrodynamica” in 1738, but not in a very clear form. His friend, the German mathematician Euler generalized his findings and named them Bernoulli’s principle at a later date. The principle can most easily be seen using a piece of equipment called a venturi tube.

A venturi tube is a cylinder of glass with a narrowed central section and a u-shaped tube attached to the wide and narrow part of the tube from below. If water is passed through the tube as it is held horizontally it has to speed up at the narrow section, and according to Bernoulli’s principle it will be at a lower pressure. This demonstrated by differing water levels in the u-tube.

This is termed a differential pressure, meaning the pressures are different at different parts of the same system. Bernoulli’s principle is also known as Bernoulli’s law of Pressure Differential because of this.

The explanation of the phenomenon is that energy cannot be lost or gained, only changed in form. The energy used in the acceleration of the fluid is lost as pressure. As soon as the system is moved from the horizontal, or other energy sources are applied the system will change in its behavior. This is because other forces are added, for instance gravity will change flow rates and pressure if the tube is not horizontal.

Examples of Bernoulli’s principle can be found around us in our daily life. The fast moving air on the inside of the shower creates a low pressure that pulls the shower curtain inwards, instead of it billowing outwards. Ships in a harbor will move together if a wind blows between them, an effect that can be demonstrated by placing two empty soft drink cans a few centimeters apart and blowing between them. When a pitcher throws a curve or fade ball it is caused by the spin he puts on the ball creating pressure differences in the air around the ball.

Bernoulli’s principle is described in an equation and holds true for all simple incompressible fluid systems. If the fluid is compressible, such as gas, or the speeds of travel are very high, such as at Mach speeds derivatives of the original equation are used. These are known as derivations of the Bernoulli equation. The derivations are based on simple principles such as Newton’s laws of motion.

One example of these differences is the rate of flow of water from the bottom of a water tank. The maximum rate of flow is proportional to the square root of the depth of water in the tank; this is known as Torricelli’s law and is compatible with Bernoulli’s principle. The difference between compressible and incompressible systems can be roughly demonstrated by increasing the viscosity of the fluid in the system.

Air is a fluid and because of this Bernoulli’s principle applies to flight. The shape of an aeroplane wing, flatter on the underside than the top, means that the air passing over the wing has to accelerate over the wing. This means that it is at a lower pressure than the air under the wing, creating lift. Nature tries to fill the lower pressure area above the wing by pushing the wing upwards, and we have lift. The same principle applies to helicopters whose fast spinning blades create a pressure differential.

To demonstrate the same thing with no equipment take sheet of paper and hold it by the narrow edge in front of your mouth. It should flop down, but if you blow over it then the paper will lift. You have just used Bernoulli’s principle to create lift. By blowing over the paper you made the air speed on the top of the paper faster than that under it, and so made air pressure above the paper less than air pressure under it and the paper was lifted.

Bernoulli’s principle states that the faster moving air will be at a lower pressure than the slower moving air; this is the origin of lift. Bernoulli’s principle does not explain why the air is moving faster, just the consequences of that faster motion.