What shape is a spirit level bubble?

[DC31kParticipant @dc31k]

As title, if I wanted to model the bubble in a spirit level, what shape is it?

The vial of a spirit level comes in two options.

The first is a segment of a torus (a cylinder bent into a circle of large radius). The inside bore is thus circular in cross section.

The other is the same shape as the inside of a barrel (so it has a linear axis but its cross section varies in diameter).

Maybe this is a physics question (surface tension?) not a CAD question.

Thanks.

[JasonBModerator @jasonb]

Surface tension and distortion of what you see through the glass probably both come into play.

Depends on how close you want the 3D model to be. Simple would be to draw a 1/2 ellipse and rotate that into a solid though lengths of bubbles can vary and then do a boolean subtraction of the profile of the glass

[CirclipParticipant @circlip]

Why? Bubble is a symmetrical shape in plan view but can’t be in side elevation.

Regards  Ian

[SillyOldDufferModerator @sillyoldduffer]

Yikes!

Trying to keep it simple:

• The top of the bubble must be the same shape as the vial.  (Easy)
• The bottom of the bubble must be flat.  (Easy)

Now it gets seriously hard, I think.  The bubble must follow a curve defined by the shape of the vial, which depends on how big the bubble is.   However, the liquid side of the bubble is effectively covered by a plastic layer created by surface tension.  I’ve no idea how thick the layer is, or how far up the vial the layer will be pulled up by surface tension, or if the join at the edge will be convex or concave.  I’m only certain it’s unlikely to be a straight chamfer!

Unless the image has to be photo realistic, I’d be inclined to try and fake it by keeping the CAD in the ‘easy’ zone.   Without trying though, I’ve no idea how good or bad the fake might be.

Dave

[Bob WorsleyParticipant @bobworsley31976]

Any decent bubble is barrel shaped, otherwise it is too hard to work out which side is top when fitting.

 

[John HaineParticipant @johnhaine32865]

Are you modelling it in software in order to display?  If so I suggest you play around with some elliptical shapes until you find something that looks right.

[HopperParticipant @hopper]

Spirit level bubbles are thin at one end, much thicker in the middle, and then thin again at the far end.

[DC31k]

On 2 September 2024 at 08:52 DC31k Said:

 

The first is a segment of a torus (a cylinder bent into a circle of large radius). The inside bore is thus circular in cross section.

 

I used to buy small ones used in rifle foresights as the yellow liquid gradually fades in sunlight. They were the first shape you suggest.

[Bob Worsley]

On Bob Worsley Said:

Any decent bubble is barrel shaped

 

I think you mean ‘vial’, the container in which the bubble is housed, not the bubble itself.

A barrel-shaped interior to the vial is expensive to produce, especially in (ground) glass.

I think there is an old ME article on making a precision level which used a cylindrical glass tube, restrained at the two ends, with a jacking screw under its centre. That would put a very slight curve in the tube.

—

Thanks for all the replies: it is a difficult question.

I am not sure an ellipse works: if you look at pictures of a level in plan view, the shape of the bubble is not elliptical. It is difficult to describe, but the ends are not pointed enough. With an ellipse, you can only specify the ratio between the major and minor axes.

It is easy enough to malke an ellipse of varying eccentricity in Desmos or Geogebra but they do not look correct. To me, the shape looks closer to an olympic running track where the straights are not straight, but bowed slightly outwards.

—

If we changed from a ‘linear’ level  to a ‘bullseye’ level, I do not know if that makes it easier to answer. I guess the inside of a bullseye vial is spherical, but the shape the bubble in one of those makes is not like slicing the top off an orange. The bubble retains some other shape.

[FulmenParticipant @fulmen]

Unless you’re using ray tracing software the correct shape probably won’t look right, there is a lot of refraction going on. I would just make it so it looks right to me.

[duncan webster 1Participant @duncanwebster1]

No way is the bottom of the bubble flat, surface tension will always make it curved.

[Robert Atkinson 2Participant @robertatkinson2]

As mentioned by DC31k we need to be precise about  terminology i.e. “vial” and “bubble”. The vial is the container and the bubble is the airspace in the liquid.

SoD, The bottom of the bubble is not flat. It is a meniscus. Depending on the shape of the vial, relative sizes of bubble / vial and surface tension of the liquid this can significantly affect the shape of the bottom of the bubble. In “bullseye” level the  bottom of the bubble is roughly hemispherical.

Robert.

[DC31kParticipant @dc31k]

Thanks for the further thoughts.

I found this (also available on ResearchGate, where you can request a copy from the authors) which appears to be close to the problem. It deals with a horizontal cylindrical tube, so not quite the same situation as a spirit level, but possibly useful nonetheless. Interesting that it is from February 2024, so quite recent.

https://www.sciencedirect.com/science/article/abs/pii/S0301932224000119

[Robert Atkinson 2]

On Robert Atkinson 2 Said:

…

SoD, The bottom of the bubble is not flat. It is a meniscus. Depending on the shape of the vial, relative sizes of bubble / vial and surface tension of the liquid this can significantly affect the shape of the bottom of the bubble….

Robert.

agreed, and Duncan says the same.  But I was suggesting assuming the bubble to be flat was a reasonable  starting point because it’s easy to model.

I tried, and obviously failed, to cover the difference between easy and realistic models of the bubble in the next paragraph covering why this is a hard question :  However, the liquid side of the bubble is effectively covered by a plastic layer created by surface tension. I’ve no idea how thick the layer is, or how far up the vial the layer will be pulled up by surface tension, or if the join at the edge will be convex or concave.

Love to blame Robert and Duncan’s failure to understand my brilliant words on them being a pair of  thickos!  Sadly for me, they’re both clever chaps, plus I did a Technical Writing course where it was cruelly explained it’s the writers responsibility to be clear.

🙁

Dave

[Robert Atkinson 2Participant @robertatkinson2]

The join at the edge (liquid/air/vial interface) curvature will depend on the surface activity relative to the liquid. In simple terms for water is the surface hydrophobic or hydrophillic. When I was working in biotech instrumentation we did some work on flattening the top sirface of liquid in small wells by selectively coating the hydrophillic base material with a hydrophobic material. This worked quite well. The purpose was to image cells growing at the bottom of the wells with minimum distortion.

Sorry if I diddn’t read you post properly SoD.

[Nicholas FarrParticipant @nicholasfarr14254]

Hi, just to give you an idea, the vial in the photo below is 60mm long and 10mm diameter, I can’t remember the resolution, but it’s not less than 0.005mm /250mm, the bubble is 25mm long. It’s a little out of focus in places, as it was a bit difficult to get it right with manual focus, and auto focus wasn’t having anything to do with it.

Regards Nick.

[John HaineParticipant @johnhaine32865]

If we know why a model was needed it could help.  Maybe the best approach would be to take a photo of an actual bubble from right above and fit a curve to its outline?

[John Haine]

On John Haine Said:

If we know why a model was needed it could help.

Maybe that is why this forum has ‘engineer’ in its title, not ‘scientist’, because everything here needs an immediate application. Do we need to know why? Is intellectual curiosity not sufficient?

Paper referred to above is available to download here:

https://www.tara.tcd.ie/handle/2262/104846

When equation 1 of the paper is a triple integral, that is 2 1/2 integrals outside my comfort zone.

[DC31k]

On DC31k Said:

On John Haine Said:

If we know why a model was needed it could help.

Maybe that is why this forum has ‘engineer’ in its title, not ‘scientist’, because everything here needs an immediate application. Do we need to know why? Is intellectual curiosity not sufficient?

Paper referred to above is available to download here:

https://www.tara.tcd.ie/handle/2262/104846

When equation 1 of the paper is a triple integral, that is 2 1/2 integrals outside my comfort zone.

Good grief!  As a professional engineer all my life, I would never start trying to model something unless I had some idea of the requirements that the model had to fulfil.  If the OP just wanted to show an emulated bubble on a screen, i.e. a 2D image, then it’s a much easier problem than trying to compute the 3D shape of the bubble, though the latter could yield the former.

[Michael GilliganParticipant @michaelgilligan61133]

It seems reasonable enough to me, John … the question was asked for the sake of understanding, not for any specific purpose.

Mankind’s progress has benefitted from such inquisitiveness

Solutions to problems that we may not yet know exist.

… remember the Ape with the bone, in Kubrick’s 2001 ?

MichaelG.

.

Ref. __ https://youtu.be/2ZGUm3uQxMg?feature=shared

 

[Speedy Builder5Participant @speedybuilder5]

Would the bubble be affected by the Coriolis effect, if so it would depend upon the positioning of the level – but then that would be stupid – Wouldn’t it ?

Bob

[SillyOldDufferModerator @sillyoldduffer]

Though I’m not proud of it, this is a promising start with  SolidEdge 2024, using my two ‘easy’ assumptions, which are the top of the bubble is the shape of the tube, and the bottom is flat.

The Vial is modelled as a bent tube, 300mm diameter, material declared as glass to make it transparent.

The inner liquid was modelled by extruding a new square section inside the tube, such that a gap is left inside the tube.   The gap is the bubble.

I expected to be able to colour the flat bottom as a face, but it appears solid edge considers the whole interior to be a face (like a sphere), so I’ve not been able to colour the model effectively.   The software failing to identify the flat bottom as a face, also means I can’t fillet the line to fake a meniscus.   It’s also created two unwanted artifacts right and left by colouring the contents of the tube, which is not wanted.

Like as not my method is flawed because I’ve tried to model the vial and contents as a single body when two are needed.  Might try to make the flat bubble by joining two boolean parts.

Three views:

Top, showing the bubble base looks like an ellipse:

The side view is less satisfactory:

 

 

 

Dave

 

[FulmenParticipant @fulmen]

Nah, the Coriolis effect doesn’t work on small scales.

[Martin KyteParticipant @martinkyte99762]

What an interesting question. My only contribution would be to ascertain the contact angle for the liquid/glass which can be done by experiment or hopefully by looking it up. For water/glass it’s between 47 and 55 degrees. Levels usually use alcohol or acetone I believe. The other comment would be to consider a very long large bore straight tube partially filled first so edge effects can be ignored. In such a case I feel that top surface of the liquid should be a flat line along the length of the tube. The contact angles are known. A calculation of the pressure in the bubble is needed. I should think that it would be possible to model the surface shape as a stretchable  sheet using finite elements (not by me I hasten to add).

A close approximation, as a guess, I would suggest a parabolic curve lengthwise and crosswise of parameters that fit the contact angle.

I probably haven’t helped much but that’s all I can offer.

regards Martin

[Nicholas FarrParticipant @nicholasfarr14254]

Hi, for anyone who wants a photo of a bubble from above, below is the same bubble as the one in my previous post.

Regards Nick.

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