Video of the “Manometers – the curious case of the coiled manometer” demonstration

Here is a video of the “Manometers – the curious case of the coiled manometer” demonstration. The full video is here and shows the rest of the demonstration up to when the funnel (off screen) overflows (on screen).

coiled

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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Manometers – the curious case of the coiled manometer

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

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

Photo Aug 18, 8 37 09 AM

Demonstration

  1. Lay the bucket on its side.
  2. Wrap the tube around the drum at least five turns leaving about a foot at one end to extend above the bucket
  3. Fix the funnel into the tubing at the vertical end which extends above the bucket
  4. Tape down the end of the tube in contact with the bucket leaving it open to the atmosphere
  5. 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.
  6. 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.

coil

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:

Pa=0

Pb=Pa+γ(Ha-Hb)

Pb=Pc

Pc=Pd+γ(Hd-Hc)

Pd=0

I always write out the equations for each column of water separately in the form Plower point=Pupper 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

Ha-Hb = Hd-Hc

Therefore, when the height difference of the water in the second loop (or the sum of the height differences in the 2nd and 3rd 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.

Measuring specific gravity of oil with a U-tube manometer

This is a really simple demonstration that allows you to measure the specific gravity of oil using a u-tube manometer. It also gives students the opportunity to visualize a multi-fluid manometer.

Equipment

  1. A 4 foot length of clear flexible tubing with a diameter of about a half to one inch
  2. A funnel
  3. A bucket of water
  4. A jug of oil (cheap cooking oil is perfect)
  5. A tape measure or ruler
  6. A chalk or white board with appropriate marker.
  7. A student volunteer

Photo Jan 10, 3 56 42 PM

Demonstration

  1. Draw a horizontal line on the board.
  2. Hold the tubing at each end forming a u-tube.
  3. Have the student pour water into the tube until there is about 9 inches of air between the top of the water and the top of the tube ends
  4. Show the students that the water levels are at the same height on both sides of the u-tube
  5. Have the student slowly pour the oil into one side of the u-tube until there is about 2-3 inches of air between the top of the oil and the top of the tube.
  6. Hold the u-tube up so that the bottom of the column of oil is at the height of the line drawn on the board.
  7. Measure the height of the column of oil (Hoil) and the height of the water (Hwater) above the same horizontal line.

Photo Jan 10, 3 58 17 PM Photo Jan 10, 4 01 47 PM Photo Jan 10, 4 02 15 PM

Analysis

Because hydrostatic pressure does not vary horizontally across the connected water, the pressure in the u-tube at the height of the line on the board is the same on both sides. Starting at the oil free surface you can write that the pressure at the line is

Plineoil g Hoil

The pressure at the line can also be calculated starting at the free surface of the water,

Plinewater g Hwater

Equating these two pressures gives

Plinewater g Hwateroil g Hoil

which can be re-written as

S.G.oiloilwater= Hwater/Hoil

For the example in the pictures the depths were Hwater=15cm and Hoil=18cm such that S.G.oil=0.83. You can then compare this to online data tables for various oil densities.

The demonstration is also good for discussing measurement errors as there is error in both height measurements. Re-doing the S.G. calculation with, for example, the low estimate of Hoil and the high estimate of Hwater (or vice versa) will give a different result. In this case the uncertainty in the measurement is at least 0.5 cm so the S.G ranges from 0.78 to 0.89.

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. If you do not wish to register with twitter or wordpress to get updates then send me an email and I will add you to the list I send update notifications to.