**Class topic –** **Bernoulli’s equation**

Let’s start with one of my favorite demonstrations. I do not recall the origin of this demonstration though I am sure that it is widely used. The basic idea is to have students blow Ping-Pong balls out of standard kitchen funnels with the funnels pointing down (there is another version of this with the funnel pointing up but the physics is different, and the result less dramatic).

**Equipment**

Funnels – the one I use has a 9.5cm diameter mouth and 1cm diameter neck. The inside of the funnel should be smooth (some funnels have ridges on the inside and they will not work with this demonstration). If the neck diameter is too small it can be hard to get the flow rate needed for the demonstration to work. If it is too large the velocity can be too low.

Ping-Pong Balls – they need to be smooth and light. Plastic golf balls and balls with holes will not work.

Alcohol wipes – they are used to clean the funnels and balls between use so that as many students as possible feel comfortable trying.

**Demonstration**

I generally try to set this demonstration up as a competition between the student volunteers to see who can blow the Ping-Pong ball out of the funnel fastest. The trick is that the harder they blow the more the ball gets stuck in the funnel. The procedure is

- Hold the Ping-Pong ball in the funnel with one hand holding the funnel vertically with the mouth facing the floor.
- On the count of three have them all blow as hard as they can while simultaneously letting go of the ball. This can take some practice to get the timing right.
- Repeat step 2 a few times discussing whose ball landed first and perhaps suggesting that those students whose ball got stuck that they need to blow harder.

If the timing is right and the students blow hard enough then the ball should rattle around in the funnel before falling out when the student runs out of breath.

**Class Discussion**

Following the demonstration I thank the students who participated and ask the class to discuss what they observed. The two main observations that are most relevant are:

- The ball gets stuck in the funnel while the person in blowing down
- There is a rattling noise so the ball is moving about during the time it is suspended.

**Analysis**

The explanation for why the ball gets stuck is presented as follows:

- On the board draw sketch of the funnel with the ball very close to the funnel sides. Then draw a control volume that covers the funnel mouth and passes across the funnel sides into the ball at the narrowest point.
- Add a streamline to the diagram going from the small gap (1) to the funnel mouth (2) (see figure for complete diagram)
- Write down conservation of volume (U
_{1}A_{1}=U_{2}A_{2}). Given that A_{1}<<A_{2}then U_{1}>>U_{2}. - Now write down Bernoulli’s equation. The pressure at (2) is atmospheric (zero). If you assume that the hydrostatic pressure variation from (1) to (2) is negligible then the pressure at (1) is given by U
_{2}^{2}/2g-U_{1}^{2}/2g implying that there is a negative pressure over the upper portion of the ball. There is, therefore, a net upward pressure force on the ball.

The rattling is due to the ball periodically blocking the flow. When the student first blows into the funnel the ball drops slightly opening up the small gap where the low pressure is induced. This draws the ball back up into the funnel blocking the flow. The pressure on top of the ball is now the stagnation pressure from the student blowing and the ball is pushed out. This process repeats until the student runs out of breath. If the funnel has ridges along the inside the gap between the ball and the funnel can be too large to get the velocity high enough and the pressure low enough to levitate the ball. The ball needs to be very light so that it can change direction rapidly during the rattling stage.

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