This is a neat little demonstration that illustrates a slightly odd manometer behavior and can be used as a lead in to a quantitative manometer example in class.

**Equipment**

- A circular bucket
- Transparent plastic tubing long enough that it can be wrapped around the bucket at least 5 times
- A jug of water with food coloring added
- A funnel for filling the tube with the dyed water
- Duct tape

**Demonstration**

- Lay the bucket on its side.
- Wrap the tube around the drum at least five turns leaving about a foot at one end to extend above the bucket
- Fix the funnel into the tubing at the vertical end which extends above the bucket
- Tape down the end of the tube in contact with the bucket leaving it open to the atmosphere
- Have a volunteer pour the water slowly into the funnel. It will fill up the tube and a little will spill over into the second loop. You may find that a little more will spill over into the third loop, but that should be about as far as the fluid will go.
- If you keep filling, the water will back up and overflow out of the funnel.

You should try this before doing it in class just to make sure that you have sufficient tubing and liquid, and just to make sure that it will work for you.

**Analysis**

Wrapping the tube around the bucket forms a manometer that is essentially sinusoidal in shape when stretched out. See the schematic figure below.

As the second loop starts to fill the air path from the first loop to the outlet is blocked off. As such, the pressure on the left surface of the second loop is no-longer atmospheric. As such, the water will rise more on the right hand side of that loop than the left had side. If any water gets into the third loop, then the process is repeated. Eventually, this buildup of pressure causes the water to back up in the first loop and overflow at the funnel.

Based on the diagram above, and ignoring the hydrostatic pressure variation in the trapped air, we can write a series of expressions relating the pressures at the labeled points:

P_{a}=0

P_{b}=P_{a}+γ(H_{a}-H_{b})

P_{b}=P_{c}

P_{c}=P_{d}+γ(H_{d}-H_{c})

P_{d}=0

I always write out the equations for each column of water separately in the form P_{lower point}=P_{upper point}+γ(change in height). Done this way I find that it is harder for students to make mistakes with signs.

Solving this set of equations leads to

H_{a}-H_{b} = H_{d}-H_{c}

Therefore, when the height difference of the water in the second loop (or the sum of the height differences in the 2^{nd} and 3^{rd} loops) equals the height difference between the top of the first loop and the funnel, the funnel will overflow.

An index of all the demonstrations posted on this blog can be found here. Don’t forget to follow @nbkaye on twitter for updates to this blog. If you have a demonstration that you use in class that you would like to share on this blog please email me (nbkaye@clemson.edu). I also welcome comments (through the comments section or via email) on improving the demonstrations.

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