# Bernoullis Principle

 Physics, Engineering: Pressure, Bernoulli's Principle, Lift Grade Range: Elementary School, Middle School, High School Format: Hands-on, Stage

This is one of our most commonly performed demonstrations. It is easy to perform, easy to understand, and the topic matter is easily adjusted for all grades and age levels.

## Materials

• Shop Vacuum/Blower with Hose
• Ribbon Wand
• Beach Ball
• Round-bottom Plastic Bottle
• Optional: Roll of Toilet Paper

## Safety Precautions

Please read the Physical Demonstration section of the Demonstration Safety page before performing this demonstration.

## Demonstration

Preparation: Blow up the beach ball. Make sure the hose is in the blower side, and plug it in. Make sure that there is a small amount of water in the soda bottle.

1. Choose a volunteer from the audience and have them hold the ribbon wand. Explain to the audience that you will be making the beach ball fly by using the blower, but you want them to guess if the air will be blowing over or under the beach ball. Take a vote to see how many think the air should blow over or under.
2. Turn on the blower on the "LOW" setting. Hold the hose at an angle slightly above 45 degrees, and lift the ball into the air stream. It will lift off into the air, and it will float! Have the volunteer hold the ribbons first under the ball, and see that the air isn't blowing underneath! Then, have them hold the ribbon wand over the ball to see the ribbons move, and show that the air blows over the ball!
3. Let the volunteer return to their seat. Turn off the blower, and explain the demonstration.
4. Call on a new volunteer, and have them hold the soda bottle in one hand. Turn on the blower on the "HIGH" setting. Holding the hose at about a 70 degree angle, have the volunteer place the rounded side of the bottle into the air stream. It should float in the air! After showing this for a minute, turn off the blower and explain.
5. Optional: To end the show, call up one more volunteer. give them the ribbon wand, and have them hold it sideways, turned towards the audience. put the toilet paper roll on the wand, with the roll over side towards the audience. Turn on the blower on the "HIGH" setting, and aim above the roll a little above a 45 degree angle. The roll will unravel into the audience!

## Why This Works

### Short Explanation

Bernoulli's Principle states that if you have an object inside of a fluid, then the object will move to the part of the fluid that exerts the least amount of pressure upon it. To understand what this means, first look at the beach ball. Before we use the blower, the air is still around the ball. This means that the Air Pressure, or the force the air exerts across all sides of the ball, is equal on all sides. Because it is equal on all sides, the net force will cancel out, leaving the force of gravity as the only force on the ball and pulling it down. When the blower is used, the air above the ball is now moving. The moving air above the ball no longer pushes equally in all directions, and instead pushes mostly in one direction (forward) and weakly in the direction of the ball (downward). The air under the ball is not moving, and so the force it applies on the ball (upward) is now much stronger than the downward force of air from above and the force of gravity. The Lift, or the net upward force, holds the ball up into the moving air stream and keeps it suspended.

The bottle helps to get across how useful this knowledge is. Even though it has more mass to it, we can still get it to hover in the air by using this concept. The curve of the bottle's base allows it to float, much like the curve on a plane's wing will allow it to fly. A plane is able to fly thanks to utilization of this concept, along with a lot of important engineering to make the plane able to ascend, descend and turn in the air.

### Full Explanation

In fluid dynamics, we can show that, If you have a fluid with velocity v moving past another fluid with a substantially lower velocity, that the amount of pressure P that it exerts on any suspended objects perpendicular to its motion is lower than what the slower fluid exerts. This can be shown with Bernoulli's equation:

 Compressible (Gases) Incompressible (Liquids) 1/2 v2 + (P/d) = C 1/2 v2 + (g * z) + (P/d) = C v = Velocity g = Gravity P = Pressure z = Elevation d = Density C = Constant, in units (m/s)^2

The Bernoulli's Equation has slightly different forms for compressible fluids, such as air and other gases, and incompressible fluids, such as water and other liquids. For this demonstration, we are looking at the form for compressible fluids. There are three variables that can be changed; the velocity (how fast the fluid is moving), the pressure the fluid is exerting externally at the chosen point, and the density of the fluid. Prior to the use of the blower, we can sample the air on all sides of the ball and show that, since it is still air, it is all at the same velocity (that is, it is un-moving) and therefore it is all equally dense, and also exerting equal pressure on all sides of the ball. It is important to note that when we are looking at the pressure exerted on the ball, we are looking at the pressure as being perpendicular to the direction of movement. In still air, this is a null point to make, but it is important once we turn on the blower. In total, we can get a constant value at the end of our equation, which carries over to this next step.

When the blower is on and aimed across the top of the ball, we now have a velocity value for our equation. The constant we found for still air is the same for this system, so to keep the equation balanced the points across the top have to adjust either the density or pressure. Remember: the pressure measured is perpendicular to the direction of movement. Also, although air is compressible, and therefore the density could adjust, the moving air isn't separated from the still air around it by any walls; in other words, the moving air could only adjust in density if the still air around it also changes density. Pressure, however, is directional, and so it will be applied primarily in the direction of movement. For the forward pressure to increase, the perpendicular pressure must decrease. Therefore, the pressure value shrinks to accommodate the air velocity. Since the pressure value for the moving air is smaller, this means the net force is no longer balanced, but rather is applied upwards. This net upward force is called Lift, and it is the reason why the ball stays suspended in the air!

To summarize: When we lift the ball into the stream of moving air, the top of the ball is placed inside of a high velocity, low pressure area while the bottom is still in a low velocity, high pressure area. The fast moving air applies much lower pressure on the ball, since it is perpendicular to the direction of movement, and so it is lifted into this low pressure area by the high pressure air below it. The ball cannot be lifted above the low pressure zone, due to the counter force of gravity, so if the ball rises too high in the stream, then the net force on it will point downward. Likewise, if the ball drops low, then the net force on it will be upward. This is why the ball will stay above the ground, bobbing slowly in the air stream as it gets pushed by the air all around it.

This also helps us to understand one of the more tricky parts of this principle, which is that the reason why this happens is, surprisingly enough, due to the Conservation of Mass. We often hear the statement that it is the difference in air pressure on the sides of a plane's wings that creates lift. However, this difference is not caused directly by the shape of the wing. As a plane is ascending, we are correct in thinking that the air on top of the wings exerts less pressure than the air under the wing. However, this happens because the air has equal density throughout. Think of the wings of the plane cutting through the air much like a knife cutting through water. The knife separates the water as it slides through straight, but the water meets again right behind the knife. If you slide the knife through the water while angled slightly upwards, you will see that the water above the knife will become turbulent as you glide the knife through, and that the knife will feel pushed towards it. This is because a plane's wings are designed to use an Angle of Attack, or upward angle while having a forward velocity. This angle of attack results in the air under the wing applying more pressure than the air above the wing, and the plane having lift! When the plane then wants to descend, it needs to simply adjust the flaps on the back of the wings so the angle of attack isn't as severe. This, paired with slight deceleration, allows the plane to descend slowly to the runway. Stunt planes have flaps that can be adjust more freely, which allows them to do loops and spins in the air, and even fly upside down!