Pyknometers (what hydrometers emulate) revisited!

[MashBag]

I think you are right. Ethanol has a density of 789 kg/m³ and Water has a density of 997 kg/m³
Source. Google. For example purposes only.

As the quantity of ethanol increases, the density of sample changes. Any suspended matter is also constant at the point of sample.

So for the levels of accuracy we need as brewers I think (so far) this ought to work.

[PeeBee]

I think you are right. Ethanol has a density of 789 kg/m³ ...

Ah, so you were talking "density". In which case Eric summarised it (and yeast suspension) very well earlier. "Specific Gravity" is linked to "density" in that SG is a ratio of two densities (one being, in a brewer's case, the density of water at 20°C). (That's a relief, I thought I was going to have to blag my way around viscosity!).

You have to be careful about your source of data. There are different "standards". Engineers seem to talk in kg/m³, Scientists in g/ml. And they are often differences other than magnitude! You've exampled water at 997kg/m³, I can find it at 0.9970g/ml @ 25°C. Why users of the kg/m³ figure seem to assume 25°C I have no idea. Confusing though.

As for "levels of accuracy": I'm always banging away at this one (though I know you're not suggesting the levels of accuracy are too fine, I'm just using that comment to take a more general swipe). There's forever criticism from other homebrewers of why fart about with levels of accuracy to three decimal places or better ... they'll say while reading figures from their hydrometers like 1.045 or so.

And on the subject of temperature calibration/compensation ... tbc!

[PeeBee]

Temperature Compensation - Part One:

Quick review 'cos this subject is forever creating conundrums in me 'ead (like ... "that can't be right", and "what have I done wrong here").

I'll work on getting all this in a Google "Sheets" compatible spreadsheet so there is no need to do the repetitive grind (or am I doing that just for me?).

Water is unique amongst liquids, made very easy to use through SI units, and even though you are brewing beer pure water plays a big role in monitoring your beer's progress. It attains its highest density while still liquid, which in SI units is 4°C (very slightly under that to be unnecessarily precise) when it reaches a density of 1g/ml (also very slightly under that to be unnecessarily precise). This means it can be used easily as a bridge between different units: E.g. I was using the weight of water to earlier determine the volume of a pyknometer (on the basis of 1g = 1ml). I've to repeat that stuff so (using my bottle as an example):

The Tare (dry) weight of my bottle is 35.72g.
The bottle's weight full of water @ 20°C is 135.21g.
The weight of water sample @ 20°C is 135.21 - 35.72 = 99.49g.
Density of water at 20°C is 0.9982g/ml
If the bottle and water was at 4°C, the sample would weigh (undo the applied density so density = 1.0000g/ml) 99.49 / 0.9982 = 99.67g
Therefore ... the pyknometer bottle's volume is 99.67ml

I could do the same for other temperatures of sample. I declared earlier I would shift to Fahrenheit for this, as the other common temperature compensations for hydrometers are 60 and 80°F, plus I was finding more reliable density data for the Fahrenheit scale: But I can now get reliable density data for the Celsius (Centigrade) scale and there won't be any benefit it using the Fahrenheit scale even to those that would use Fahrenheit (accuracy will not take on a significant change).

So, repeating the calculations for 15 and 25°C, water density at 15°C is 0.9991g/ml and at 25°C is 0.9970g/ml:
The weight of water sample @ 15°C is ((99.49 / 0.9982) x 0.9991) = 99.58g.
If the bottle and water was at 4°C, the sample would weigh (undo the applied density so density = 1.0000g/ml) 99.58 / 0.9991 = 99.67g
... and
The weight of water sample @ 25°C is ((99.49 / 0.9982) x 0.9970) = 99.37g.
If the bottle and water was at 4°C, the sample would weigh (undo the applied density so density = 1.0000g/ml) 99.37 / 0.9970 = 99.67g

No change! Which is what you'd expect, as a change in nett weight at 4°C would mean a change of volume of the pyknometer bottle, which isn't going to happen! All the temperature compensation will be down to the reference's density (the subject of the next post).

Actually, the bottle's volume will change minutely with temperature, just nowhere near enough to interfere with these calculations. Some pyknometer bottles are created from Borosilicate glass which is very stable dimensionally to changes of temperature, hence thar glass is difficult to break by thermal shocks. But such stability isn't really necessary as these pyknometers are unlikely to be used outside the 10-30°C range.

[EDIT: REMOVED ALL THE "+" 'COS THEY LOOK LIKE "+" SYMBOLS AND REPLACED WITH "/".]

[PeeBee]

Temperature Compensation - Part Two-A:

Do remember, this "mathematical" discussion is purely academic. To give anyone who's interested chance to go over my work to check I'm not doing anything "impossible". For anyone who isn't going to add anything that way and trusts the outcome, I will be scrawling it all into a spreadsheet so you can skip straight to the practical stuff and to hell with the egghead stuff! Though the "egghead stuff" does open your eyes to what a "hydrometer" tells you; or perhaps doesn't tell you!

"Part One" showed that temperature isn't a concern in the same way as a hydrometer. Pyknometers are only extracting the weight of a fixed volume. A hydrometer has no "fixed" volume and assumes a result based on a temperature it expects (usually 20°C), and if that isn't correct needs lookup tables to adjust the result (which hardly any homebrewers bother with). But it's not quite so "cut-and-dry" for pyknometers: Knowing the density of a liquid at an unspecified temperature isn't that useful, so "Relative Density" (Specific Gravity) was devised. The density of a liquid is shown "relative" to pure water (usually) at the same (unspecified) temperature. Hydrometers have this "relative" value built into the scale it uses, hence most hydrometer users aren't even aware that such a second temperature calibration exists. Pyknometer uses are aware! But the usual way to deal with it is to fill the pykmometer once with the sample, then with pure water at the same temperature and divide the result of the first with the second (two identical pyknometers isn't practical). What a phaff! Hence, I'm sticking with knowing the temperature of the sample and knowing the density of water at the sample's temperature.

So, what starts as a clear advantage for pyknometers, ends up with the same tie to temperature and the same dependence on lookup tables. That's what I'm trying to address in this thread! (Along with the inaccuracy of hydrometers, the difficulty reading the blasted things, and the impracticalities of handling those bits of fragile nonsense ... can you tell I hate hydrometers?). It's way easier to address the temperature issues with pyknometers (the subject of this post), whereas to achieve it with hydrometers will need multiple instruments or one instrument with multiple confusing scales (some will say they already have those!).

Continued as Part Two-B ...

[PeeBee]

Sorrieeeeee ...

Got ahead of myself a bit and I'm getting well bogged down with the maths trying to bring it back in line! I thought discussing temperature compensation before addressing the "make my pyknometer bottle 100.00ml in volume" made sense? It doesn't! It seems to make things ridiculously complicated.

So, I'll wind back a couple of posts and come back to "Temperature Compensation - Part Two-B" in a short while.

Next up: "Make my pyknometer bottle 100.00ml in volume"!

[PeeBee]

Right: Making your pyknometer bottle exactly 100.00ml in capacity. Using my bottle as an example:

Dry bottle weight = 35.72g
Full bottle weight (water @ 20C) = 135.21g
Sample weight @ 20C = 135.21-35.72 = 99.49g
Bottle Volume = 99.49/0.9982 = 99.67ml

So, despite being a supa-dupa, classy and expensive, pyknometer bottle, it's still all of (100 - 99.67)ml ... or 0.33ml ... under-volume. This can be "fixed" (i.e. "tricked") quite easily.

The normal way is to put the empty bottle on the weighing scales and press the "TARE" button. But drying the bottle is all but impossible and having the scales "zeroed" means the full bottle still weighs 99.49g (@ 20°C) like before. I've got nowhere. So, fabricate a weight weighing:

(35.72 - (100 - 99.49)) = (35.72 - 0.51) = 35.21g

Use this weight to TARE (zero) the scales, and the sample appears to weigh (135.21 - 35.21) ... or 100.00g (which can be translated as 1.0000 SG 20°C/20°C).

A filthy trick! How well does it hold up?

If the bottle holds a sample of 1.080 SG @ 20°C:
1.0800 x 0.9982 = 1.0781g/ml (multiply by density of water @ 20°C) <- This "undoes" the SG bit and leaves the density @ 20°C
1.0781 x 99.67 = 107.45g ("real" weight of sample in bottle)
107.45 + 35.72 = 143.17g (gross weight in "real" bottle)
whereas:
143.17 - 35.21 = 107.96g ("imagined" nett weight in "imaginary" 100ml bottle weighing 35.21g)
which can be translated as 1.0796 SG 20°C/20°C, or 0.4 of a "gravity unit" under reading.

Not bad, only 0.4 of a "gravity unit" error for a 1.080 SG wort. But that's only theoretical and doesn't allow for any error in the weighing scales measuring at 2DP. But we can do something about that! And remember, this is for a bottle only 0.33ml short of 100ml and presumes a temperature of 20°C. [EDIT: A "gravity unit" is 0.001 in SG terms (where water equals 1.000).]

So, measuring accurately at 1.0000 SG is a waste of time (we rarely measure that). Shift "zero error" to 1.020 SG 20°C/20°C? And perhaps set maximum SG limit for this TARE weight to be 1.080?

If the bottle holds a sample of 1.020 SG @ 20°C:
1.020 x 0.9982 = 1.0182g/ml (density of a 1.0200 SG sample @ 20°C)
1.0182 x 99.67 = 101.484g ("real" weight of sample in bottle)
101.484 + 35.72 = 137.204g (gross weight in the "real" bottle)
whereas:
"Imagined" nett weight of sample is 102.00g (to be read as 1.0200)
"Imagined" gross weight of sample is 102.00 + X = 137.20g where "X" is the new "TARE" weight
Therefore X = 137.20 - 102.00 = 35.20g where "X" is the adjusted "TARE" weight (0.01g lighter in this example).

Repeating the 1.0800 example:
143.17 - 35.20 = 107.97g ("imagined" nett weight in "imaginary" 100ml bottle weighing 35.20g)
which can be translated as 1.0797 SG 20°C/20°C, or 0.3 of a "gravity unit" under reading.

Not a startling improvement but an improve all the same.

Another weight could be created for the (nominal) 1.0800 to 1.1600 range. But would one really be necessary? For such rare occasions I'd go back to "manual mode" with no "tricks". Grist for the proposed spreadsheet.

This example was for a bottle 0.33ml under volume. As I've said before, I'd be happy with 0.5ml under capacity, perhaps 1.0ml. What of over-volume? The "TARE" weights will alter by very similar amounts except the "TARE" weight will be increasing in weight, not decreasing. But there is one significant difference: You can't make an under-volume bottle physically have increased capacity, but you can restrict the capacity of an over-sized bottle, perhaps even tune them to have exactly the physical volume required. This might even be an advantage of having "sub-prime" bottles! Anyway, that's a subject to return to; for now, I want to pick up that temperature compensation subject where I left off ...

[PeeBee]

A cross-check opportunity! Just casked an attempt at "Boddington's 1901 AK" dug up by Ron Pattinson.

Boddies1901AKii-END.JPG (40.02 KiB) Viewed 15931 times

Using the 100ml Pyknometer (long-hand - the most accurate) gravity at casking comes out as 1.0139. I rough out a 35.20 "TARE" weight, tare the scales to that weight and pop on the full pycnometer:

20220910_184912.jpg (51.57 KiB) Viewed 15931 times

Ah poo. I better figure that out! ... hang on, why is this "TARE" weight 35.70g? Seems I really did rough it out, relying on my "pin sharp" memory (which can muddle up how many fingers I have on one hand).

So, it should have displayed (100.80 + (35.70-35.20)) or 101.30. Still got something wrong (1.0130 isn't 1.0139), but nothing like as dramatic.

[PeeBee]

Ah ... to hell with this error, it'll come out when I put this stuff in a spreadsheet. This is only a record of my work should anyone want to trawl through it and tell me "You're wrong!". So, getting on with where I left off ...

Temperature Compensation - Part Two-B:

All the calculations so far have been based on the sample being 20°C, and the "reference" (water) also being 20°C. So, what if it's different?

The difference can also be absorbed by the TARE weights. But when does it become worthwhile? Summarising earlier posts (using my bottle as an example):
The Tare (dry) weight of my bottle is 35.72g.
The bottle's weight full of water @ 20°C is 135.21g.
The weight of water sample @ 20°C is 135.21 - 35.72 = 99.49g.
Rounding up to 100g requires the addition of 0.51g, this is the same as subtracting 0.51g from the TARE weight. Subtracting a further 0.01g from the TARE weight shifts "zero error" from 1.000 SG to 1.020 SG (errors due to "fitting a square peg in a round hole" ... using addition/subtraction for modifying the TARE weight because the weight is static and can't do on-the-fly multiplication!). So, the weight of water sample @ 20°C is 135.21 - 35.20 = 100.01g.

Slightly over-weight (0.1 "gravity units") 'cos I'm doing the "fitting a square peg in a round hole" trick! It's a very narrow square peg and a very wide hole so I can get away with doing this trick. But all these calculations have assumed the temperature is 20°C. Let me try 15°C:

The bottle's weight full of water @ 20°C is (as above) 135.21g.
The bottle's weight full of water @ 4°C is (density of water is 1.000g/ml, at 20°C it was 0.9982g/ml) (135.21 / 0.9982)g (there is no need to multiple by 1.000!).
The bottle's weight full of water @ 15°C is (density of water is 0.9991g/ml) ((135.21 / 0.9982) * 0.9991)g

So, a full pyknometer of pure water will weigh 135.45g @15°C (there's a conundrum brewing here, anything other than water isn't going to share the same properties as pure water so I need to tread carefully). The water sample will weigh 135.45 - 35.72 = 99.73g. Create a "customised" TARE weight of (35.72 - (100 - 99.73)) = (35.72 - 0.27) = 35.45g, less 0.01 to shift "zero error" to SG 1.020 (rather than 1.000, I'm not recalculating it because the tiny difference will be swallowed up by rounding to two decimal places) it will be 35.44g. With this TARE weight, the weight of water sample @ 15°C is 135.45 - 35.44 = 100.01g.

Doing the same for 25°C (water density 0.9970g/ml), the weight of water sample @ 25°C is 135.01 - 35.00 = 100.01g. TARE weight would be 35.00g.

Phew! That takes me a bit of following and I'm writing it! Gawd, what got me started on this mind-numbing caper? Anyhow, here I'm trying to prove whether it's worthwhile (or not) to have multiple "TARE" weights.

With the 20°C TARE weight and a 20°C 1.020 sample the weighing scales will display 102.00g (= no error).
With the 20°C TARE weight and a 15°C 1.020 sample the weighing scales will display 102.09g (= +0.0009 SG error).
With the 20°C TARE weight and a 25°C 1.020 sample the weighing scales will display 101.87g (= -0.0013 SG error).

Which is about the same as a hydrometer (SG 15.67°C, or SG 60°F, hydrometers read about 1 gravity unit different than a SG 20°C one). So, it's probably worth having these alternative TARE weights for the pyknometer (plus and minus 5°C seems fine, you might prefer something tighter or more relaxed), as the weights can be fabricated very quickly and cheaply (if using hydrometers, you'd use tables or buy a new instrument).

Proof (yawn!):

Fabricated "TARE" weight for my bottle @ 20°C is 35.20g.

If the bottle holds a sample of 1.020 SG @ 15°C:
1.020 x 0.9991 = 1.0191g/ml (density of a 1.0200 SG sample @ 15°C) <- As before, this "undoes" the SG bit and leaves the density in g/ml @ 15°C
1.0191 x 99.67 = 101.574g ("real" weight of sample in bottle)
101.574 + 35.72 = 137.294g (gross weight in the "real" bottle)
whereas:
"Imagined" nett weight of sample is 137.29 - 35.20 = 102.09 or reading will be +0.9 gravity units out.
or, if a custom TARE weight of 35.29g is created for 15°C:
"Imagined" nett weight of sample is 137.29 - 35.29 = 102.00
For a 1.080 sample:
1.080 x 0.9991 = 1.0790g/ml ... 1.0790 x 99.67 = 107.544g ... 107.544 + 35.72 = 143.264g
And "Imagined" nett weight of a 1.080 sample is 143.26 - 35.29 = 107.97 or reading will be -0.3 gravity units out.

If the bottle holds a sample of 1.020 SG @ 25°C:
1.020 x 0.9970 = 1.0169g/ml (density of a 1.0200 SG sample @ 25°C)
1.0169 x 99.67 = 101.354g ("real" weight of sample in bottle)
101.354 + 35.72 = 137.074g (gross weight in the "real" bottle)
whereas:
"Imagined" nett weight of sample is 137.07 - 35.20 = 101.87g or reading will be -1.3 gravity units out.
or, if a custom TARE weight of 35.07g is created for 15°C:
"Imagined" nett weight of sample is 137.07 - 35.07 = 102.00

The eagle-eyed may notice a 1.020 liquid isn't water! Have I slipped into the afore-mentioned conundrum? Well, no. I'm trying to be careful and leave water properties (like water's density) out of it except when working with the "reference".


That'll do for now, my 'ead is well and truly mashed. And anyone left still reading this has fallen asleep. I'll set about some practical stuff and see if all this head scratching has produced something useable.

[PeeBee]

... So, it should have displayed (100.80 + (35.70-35.20)) or 101.30. Still got something wrong (1.0130 isn't 1.0139), but nothing like as dramatic.

Told you the error would come out in the translation to spreadsheet. And it did! Highly technical miscalculation that would have taken forever to find ...

I entered the bottle's volume as 99.57ml instead of 99.67ml.

It's kind of embarrassing, and at the same time a relief (I don't need the planned head-scratching checking all the elaborate faults I'd invented and might have introduced). So, 1.0130 SG was expected, 1.0129 I got. The"TiltPRO" had gone the other side at 1.0128. I'd have gloated at the achievement (only 0.1 of a density unit discrepancy) except I did an even more spectacular job of shooting meself in the foot.

[EDIT: Another silly mistake; I wave the Tilt's reading as "confirmation", but the picture clearly shows the temperature is wildly different for useful comparison. I keep doing that!]

[PeeBee]

... The bottle's weight full of water @ 20°C is (as above) 135.21g.
The bottle's weight full of water @ 4°C is (density of water is 1.000g/ml, at 20°C it was 0.9982g/ml) (135.21 / 0.9982)g (there is no need to multiple by 1.000!).
The bottle's weight full of water @ 15°C is (density of water is 0.9991g/ml) ((135.21 / 0.9982) * 0.9991)g. ...

Hey, I thought I'd post all this "mathematical" drivel 'cos I thought there's bound to be someone daft enough to check my work. Is no-one here daft enough?

Okay. So, I switched from the water sample weight to using the full bottle weight. Like I think the "density of water" applies to glass as well. Fortunately, the spreadsheet program knows it is dealing with a twerp and starts generating fantasy results. Little harm done, it only applied to Tare weights for temperatures above and below "normal". Correcting the above posts directly while I still can.

There will be a spreadsheet! Still working on it.

[PeeBee]

... Correcting the above posts directly while I still can.

Where upon the forum site has a "disk space" tantrum, and in the time to fix I lost the chance to edit the defective post! So, the defects remain (I erroneously applied some calculations to the total bottle weight instead of just the sample weight excluding the bottle). I'll repost a corrected version when I get around to it.

Meanwhile the spreadsheet is coming on fine. And proving to be very "illuminating". For example: I'm finding "Relative Density" (aka. Specific Gravity) has nothing to do with hydrometers: Hydrometers only use the SG scale to continue a habit that developed before hydrometers came into use. SG only has relevance to weight driven mechanisms like pyknometers (and perhaps the Lbs extract per barrel arrangement) to act as a "temperature compensator". Hydrometers are "calibrated" for a specific temperature, and you need lookup tables to compensate for any difference in actual temperature. Weight-driven mechanisms (like pyknometers) using SG don't need to know the temperature at all.

[PeeBee]

I've gone as far as I'm probably going with this spreadsheet for the time being, so I'll get it posted. A Microsoft Excel spreadsheet. It has not been tested on "Google Sheets" but probably works?

It's been fascinating creating it. I knew hydrometers were only a convenient (in days past) way of extracting the density of liquids, but I never expected them to be a quite alien tool for doing the job. Density is mass (weight) times volume: For which you must know the weight and volume of the sample being tested. You can't get either of those parameters from a hydrometer, the hydrometer measures buoyancy and displays the result in an alien (for a hydrometer) units. Relative Density (Specific Gravity) was an adaption to the density scale to provide the results relative to another substance, water being the common one, and provided temperature compensation. Specific gravity was never designed for hydrometers which must rely on correction tables for temperature correction. And the scale hydrometers "borrow" is suspiciously dodgy. But I guess they do for beverage brewing.

Hardly surprising the Lab-rays have left their old hydrometers to gather dust.

I also learnt why "Fahrenheit" is such a mind-numbingly useless temperature scale. The spreadsheet doesn't support it as it stands!


But the purpose of this thread wasn't for me to learn how bad SG and hydrometers are, it was to make refractometers a worthy alternative that anyone who wants to can use now (I haven't much choice, I cannot handle "hydrometers"). Something that has become possible in very recent years with access to cheap weighing scales.

To do this I've borrowed a few "advantages" of hydrometers but in doing so rely on tricks to replace much of the temperature compensations built-in to pyknometer use, but the compensations are much simpler than for hydrometers.

The spreadsheet needs three bits of information to "calibrate" the bottle: The ambient temperature, the bottle's "dry" weight, and the bottle's weight when full of water. As a fourth bit of info enter the intended "calibration" temperature for the bottle (usually 20°C). This page is then static for the life of the bottle (and paired stopper). Information for configuring "Taring weights" is also provided on this page.

The second page takes the weight of the bottle loaded with the beer/wort sample and displays the Relative Density (SG), assuming the sample is at the calibrated temperature. The page also has a "simulator" section which allows temperature to be altered from "calibration": It does use a lookup table to correct the density of water used as the "reference" for the reading. It also shows the gravity reading should the "reference" not be corrected for temperature for those curious to see it. This page works with any sized sample, although it cannot be recommended to use bottles smaller than 25ml (unless you have extraordinary weighing scales).

Pyknometer Calculations.JPG (24.22 KiB) Viewed 15808 times

The third page is for 100ml bottles only! And was the purpose of this thread. It is only a "simulator" and has no parameters to alter. It displays the Relative Density (SG) as can be read directly from the weighing scales using the appropriate "Taring weight". The simulation uses the weight entered un the "manual" page as an example. For the purpose of curiosity, the simulator parameters (sample weight and temperature) can be altered in a "simulator" section.

Changes, other than required entries, are locked. But the password to remove locking is not set!

Have fun! Tell me of any errors encountered. I'll continue to tweak the spreadsheet, and write up how I'm creating "Tare weights".

(This forum only allows a limited number of file types. Download* the Pyknometer Calculations.xls from my Google drive. *It'll open in Google Sheets but I'm sure there's a way to download the XLS file? I'll have to figure that out. If it doesn't work I'll have to try something else.).

[EDIT: In Google Sheets type "download" in the "search the menus" box and select "Download as Microsoft Excel (.xls) file".]

[PeeBee]

...
The bottle's weight full of water @ 20°C is (as above) 135.21g.
The bottle's weight full of water @ 4°C is (density of water is 1.000g/ml, at 20°C it was 0.9982g/ml) (135.21 / 0.9982)g (there is no need to multiple by 1.000!).
The bottle's weight full of water @ 15°C is (density of water is 0.9991g/ml) ((135.21 / 0.9982) * 0.9991)g

So, a full pycnometer of pure water will weigh 135.45g @15°C ...

Best deal with this blatant codswallop first:

The bottle holds a sample of water at 20°C weighing 99.49g.
At 4°C the sample weighs (density of water is 1.000g/ml, at 20°C it was 0.9982g/ml) (99.49 / 0.9982)g (there is no need to multiple by "1"!).
Whereas at 15°C the sample weighs (where density of water is 0.9991g/ml) ((99.49 / 0.9982) * 0.9991)g

So, the sample of pure water in the pyknometer will weigh 99.58g @15°C ...

That's better! So, continuing with this corrected calculation: Create a "customised" TARE weight of (35.72 - (100 - 99.58)) = (35.72 - 0.42) = 35.30g ...

The spreadsheet can do the rest (it was created after my mathematical mishap) like alternative "sample temperatures", "zero error", predicted error ranges, blah, blah, blah.


Now, what next? The spreadsheet sort of supports Fahrenheit now, a few other minor changes, and I need to update the download ... but that won't happen today 'cos I need to get these pizzas on ...

[PeeBee]

Spreadsheet updated. Some minor changes and a bit more Fahrenheit support (displays the equivalent but does not use for calculations). There is a transformed lookup table for Fahrenheit, but I'm not using it.

I have mentioned that the "Specific Gravity" scale might be dodgy. But I've been through it and any "dodginess" is in the prediction areas ("For curiosity only!") and well documented that the "assumptions" could be out-of-order. There are two points where "assumptions" have been used and they are coloured dark red for emphasis (both labelled "Adapted full bottle weight"). The rest (and all the "real" operational stuff) is free of such "assumptions". You'd be hard pushed to ever see errors arising from the assumptions anyway.

[PeeBee]

Putting some flesh on these spreadsheet blathering:

I start by collecting the bits for a once off (per bottle) "calibration". Calibrated weighing scales (calibration weights to make sure), measuring cylinder full of tap water (use distilled/deionised if you must, but there is nowt much in my tap water anyway ... apart from the sheep pee), a good thermometer to take the temperature, and the pycnometer bottle to be tested (I've got two here; a 25ml one and a 100ml one).

20220927_152740_WEB.jpg (60.12 KiB) Viewed 15751 times

Then get the weight of a filled bottle.

20220927_153359_WEB.jpg (58.83 KiB) Viewed 15751 times

Stick the results into the calibration page of the spreadsheet. I'd already recorded the weight of the empty and dry bottle (18.28g). I worked really hard at judging the temperature of the sample; a bit more than 18.5, not quite 19.0, and what difference does it make ... zilch!:

20220927_153359_RESULTS.JPG (53.24 KiB) Viewed 15751 times

The important bit is the volume: 26.38ml. As I've been using this bottle for a few months, I had already figured it out at 26.37ml. 0.01 of a millilitre ... consistent enough for me!

Now to check out the 100ml bottle ...