## Flying Cups & Bernoulli

Level: Elementary to H.S.

Time involvement: 10–15 minutes.

Daniel Bernoulli, 1700-1782, a Swiss mathematician first put numbers to the strange behavior of fluids. He likened the effect to the concept that “There is no free lunch in the world of science.” Just as kinetic energy and potential energy are interchangeable, the total energy available is constant. So too, Pressure and Velocity are interchangeable. If the velocity is increased there will be a simultaneous decrease in pressure.

The practical application of this principle is evident in Nature. The wind of a hurricane or tornado doesn’t simply “rip” the roof of houses it “lifts” the roof off due to the increased velocity on the outside compared to the inside. The wings of birds and insects create lift, in part due to the higher velocity of air moving over the top of the wing compared to the velocity on the bottom. A skilled baseball pitcher can throw a “curve ball” by imparting a spin to the ball at the moment of releasing the pitch. Early paint sprayers, bug sprayers, perfume atomizers, even automobile carburetors utilized this principle. The difficulty of teaching this principle is that it is counter-intuitive. Striking a dish with a hammer needs little explanation to understand. Invisible moving air is mysterious. Physical convincing demonstrations are needed to clarify the puzzling principle. You can be a teacher who unlocks a difficult concept for adult minds and will be even more memorable to young inquiring minds.

The foam cup demonstration is an inexpensive fun way to visualize the Bernoulli Principle (Effect). By simply taping together the bottom of two foam cups and winding a string with a rubber band at one end, around the joined region, the affair can launch the spinning cups forward. Depending on whether the string is held above or below the cups the direction of spin can be either forward (top moving faster) or backward, (bottom moving faster). The instant effect will be a sharply curved path. In the case of the “top spin”, the cups quickly descend and, in fact, will begin a bit of backward travel. In the case of “back spin” the opposite effect will occur. The rapidly spinning cups will begin an immediate upward path but the aerodynamic air friction and gravity terminates progress before long. If you want to be clever you can hold the cups vertically and simulate the effect of the pitcher’s curve ball technique.

A second demonstration I have created required a bit of light woodworking. I have chosen to name my “invention” the “Bernoulli Effect Doubt Remover”. It is not copyrighted so feel free to create your own version of it. Because of the likelihood of germ transmission I discourage students from trying my “Teacher Model”. (One year I got ambitious and built a personal model for each student to take home.) As shown in the accompanying photo, the “mouthpiece” is a piece of wood with a long hole drilled through it. The bottom has a 2-3 inch wood disk attached. The “long hole” align with a similar hole in the center of the disk. A 2-3 inch thin plastic disk has been fitted with a small short nail to keep the disk from sliding off the matching wood disk. The demonstration is brief and simple but is convincing! Begin by taking a deep breath. While holding the apparatus downward and lightly holding the plastic disk in position begin blowing in the hole. Remove your hand. The plastic disk remains “attached”. The harder you blow the more firmly the disk sticks! After a few seconds your lungs will empty and the disk falls off. With careful breath control the effect can be sustained for 10-15 seconds. (Try breaking your own record).

I first saw the idea in book. It used an empty thread spool, a playing card and a pin. I tried this with disappointing results, thus my “improved model”. Be creative by experimenting with empty food containers, scissors, and hot glue.

A YouTube video uses a pair of inflated balloons supported by strings and separated by an inch or two. The demonstrator uses a straw to direct a stream of air between the balloons. Immediately the balloons are drawn together. The set-up is good science but needs a careful explanation so students understand the lesson.

Discussion: You may choose several different directions to lead a discussion. The first direction probably should be to clarify exactly what is happening to the air molecules at the surface of the cups. If you consider the almost microscopic region of the junction of the cup surface and the air you will confuse yourself and the student’s understanding of the true principle involved. Think instead, of the friction effect of the spinning surface. In the case of the “back spin” the upper surface will speed up the flow of air across the “shape” of the cups. This may take a little thought because the surface is moving “backward” in relation to the forward movement. Conversely, the opposite action is occurring at the bottom of the cup. Even though the “relative speed” of the air molecules compared to the surface molecules is higher this “microscope region” does constitute the Bernoulli Effect. If you and your students can ignore the “spinning action” and just visualize the “big picture” it may help to grasp the how the principle is working.

The Bernoulli “Doubt Remover” is more immediate and clearly shows that the device creates a believable space where the air velocity is increased. The “Wow Factor” is that the harder you blow the harder the disk sticks. Naturally, of course, there is little need for this device in your “kitchen tools” but it can be a very effective teaching tool.

A simple variation on the wooden model (“Doubt Remover”) is to take a small empty soda bottle, cut off and discard the lower half, obtain a ping-pong ball, add a vacuum cleaner with a “blowing” outlet and a hose. The difficult part here is finding a vacuum cleaner with a blowing outlet (some shop models may have this feature), and making a secure connection between the hose and soda bottle. The big advantage here is that there is no problem with germ transmission and your lungs will not get overworked repeating the demo.

Notes: The Bernoulli Effect is one of the most difficult to grasp because it involves invisible air. Play with the demonstrations long enough so you can do them smoothly. Emphasize to students that the brightest minds did not grasp this concept for thousands of years! From the smallest insect to the largest jumbo jet this principle applies. By visiting You Tube you will be introduced to a number of demonstrations that attempt to physically illustrate the principle. One demonstration I would discourage using is the leaf blower rapidly unrolling a roll of toilet paper.