# How to measure the inner diameter of thin tube (0.5mm to 2mm)

Does anybody know what method or equipment could be used to measure the inner diameter of capillary tubes? They would be in the region of 0.5-2mm in diameter.

Edit: the tube is made of plastic and I have standard lab equipment available.

• If you are talking about metal capillary tubes, take a look at this article nvlpubs.nist.gov/nistpubs/jres/045/jresv45n4p283_A1b.pdf – J. Shupperd Aug 27 '16 at 15:44
• I have an idea, but for it to be a good one I need to know a few things: 1) What is the tube made of? 2) Would it be ok to get the tube wet? 3) How much length of tube do you have available? – DanielSank Aug 27 '16 at 20:26
• @Christian : That looks like an answer. Why haven't you posted it as such? – sammy gerbil Aug 28 '16 at 1:32
• It would be helpful if you could tell us what material the tubes are made of, what length of tube you have available, and what other equipment you have. Micrometer, balance, accurate scale, microscope, ... What do you have? Is the tube transparent or not? Can you assume constant diameter? Do you know the material properties? Can your experiment destroy the tube? – Floris Aug 28 '16 at 12:38

The simplest method is probably to use a travelling microscope to measure the wall thickness at the ends of the tube, and vernier calliper or micrometer to measure outer diameter at a few points along the tube. The drawback is that this does not give an average value for wall thickness.

This article entitled "The Exact Measurement of Capillary Holes" describes a method using hydraulic resistance applying Poiseuille's Formula. The apparatus is a little complicated but fairly basic, and could probably be further simplified. It claims an accuracy of at least an order of magnitude better than the microscope method.

(Item #3 on page 1 of a Google Search "measure diameter capillary tube". The article cited in J Shupperd's answer was #1 in the same search. Hence my down-vote for lack of research effort.)

• That fourth-power of $r$ thing sure help, doesn't it? – dmckee --- ex-moderator kitten Aug 27 '16 at 23:58
• @dmckee : I didn't think about that when I posted this answer. It sounds like a good reason. – sammy gerbil Aug 28 '16 at 1:30

An easily applied lab technique would be to measure a length of tubing, and find its outer diameter with a micrometer, then weigh it. Knowing the density of stainless steel or glass (or whatever) completes the equation.

mass = density * length * (D_outer **2 - D_inner **2)* pi/4

• This depends very much on knowing the exact density of the plastic used. – sammy gerbil Aug 28 '16 at 21:37
• Yeah, even using a micrometer on a (possibly soft) plastic would make for some error bars. On the other hand, plastic parts aren't usually precise; I'd wonder, too, if the inner diameter is different when wet. – Whit3rd Aug 29 '16 at 4:04
• Good points. I hadn't thought of those. – sammy gerbil Aug 29 '16 at 10:05

I'm not a physicist so what I'm saying may be senseless. Since you used the tag home-experiment I thought of something you could do at home. What if you fill with a syringe containing water the tube until it's full? By knowing how long the tube is and how much water the syringe had initially you could calculate the diameter (I think at least). To block the possible backdraught you could pierce first a pencil eraser(the built-in to the pencil). And yes, you can find syringe needle smaller than 0.5mm.

Some reasonable methods have already been proposed, but you might just measure the height of water column in the capillary (at least if the capillary is transparent) and calculate the diameter (https://en.wikipedia.org/wiki/Capillary_action#Height_of_a_meniscus)

• As long as you know the contact angle - which requires you to know the properties of the water and the surface VERY well. Also it is not stated whether these capillaries are transparent. – Floris Aug 28 '16 at 12:36
• @Floris: I agree with your comment. I would like just to note that I edited the answer to add the caveat on transparency (before you commented:-)) and that one can estimate the contact angle if the capillary is indeed transparent. – akhmeteli Aug 28 '16 at 12:48