# Measuring liquid density using upthrust

1. Apr 1, 2013

### Larsoo

Hi, I brew beer and part of the process is measuring the specific gravity of the fermenting liquid. This is done visually using a hydrometer. Digital hydrometers are available and very expensive. I'm trying to come up with a way to measure the liquid specific gravity electronically. Typical gravity readings are in the range 1.008 to 1.080, the lower number being an indication that fermentation has completed and the higher number being the SG or starting Gravity.
I need to understand how upward force of a floating device relates to gravity.
My idea is that using the transducer from one of those high precision scales(heres one for 12stg that weighs from 0.001 to 10 grams- http://www.ebay.ie/itm/0-001g-10g-M..._Measurement_Equipment_ET&hash=item5d3acdcbaf), I could have a floating 'device' pushing up against the transducer and I could use the measured force to determine the gravity?
Does this make sense or are there any obvious flaws?
Obviously the device would need calibration and I would need to source the transducer. Also I would intend that the floating ball/device drive a rod upwards that applies pressure to the transducer from which I take my reading. Can anyone tell me what sort of readings I would get on such a transducer? Would it be sensitive enough for my purposes?

Thanks

L

2. Apr 1, 2013

### sophiecentaur

There are a million ways of skinning a cat. Whatever method is used, you need to bear in mind that there are some very small forces involved if you want to be accurate. Friction could be relevant.
I might suggest measuring the capacity between a floating (glass) cylinder with a fixed (metal) plate on top and the liquid surface - to give you the distance that the hydrometer has sunk. OR you could do the same and measure the resonant frequency between plate and the water surface. I remember a guy who was designing a liquid level measurement, based on Time Domain Reflectometry - but that required some fancy ps time resolution. The advantage of all three above is that friction / stiction is minimal and it's all done at RF and a frequency of choice.

3. Apr 1, 2013

### Staff: Mentor

Something heavier than water sounds easier to measure, but it really depends on your setup.

An object with a mass of 100g and a density of 1.1g/cm^3 would lead to a downwards force equivalent to 2g (0.02N) to 8.4g (0.084N) , using your upper and lower density values.

4. Apr 1, 2013

### Larsoo

Thanks for the responses guys. During fermentation, a thick creamy yeast head forms on the surface of the liquid(called Wort, pre fermentation and Beer post fermentation) so its difficult to measure anything from the surface. Also, the liquid gives off CO2 as the fermentation occurs in varying quantities so I was thinking that multiple samples averaged over time could be used to calculate an average to get the most accurate result. Because of this and the need for sanitisation(a high level of sanitisation is required to avoid infecting the beer) I was thinking of a setup that has very little in physical contact with the liquid surface.
Rather than measuring the weight of the object. I thought it would be better to use an object thats less dense than my lowest measured density. This could be forced below the surface of the liquid by a rod and the upward force on the rod used to press against my pressure transducer of the type in the precision scales. Depending on the buoyancy of the object the upward force against the transducer would change and I could measure this and determine the density as it changes of the liquid. Am I making sense?
For the type of numbers I'm talking about, bearing in mind the scales I linked to has a 0.001gram resolution would you expect it is a realistic expectation to be able to measure changes in liquid density with a resolution of 1 gravity point(1.008 and 1.009) using this type of setup, or would a change in liquid density of 1 gravity point provide nothing like the sort of upward force I need to measure it?
Apologies if its a bit longwinded but I hope I'm being clear.

Thanks

L
MFB, how do you calculate those values for upward force in the case of my proposed setup?

Last edited: Apr 1, 2013
5. Apr 1, 2013

### Staff: Mentor

Pressure is problematic, as it always depends on the angles in your setup, you need some mechanism to keep the rod vertical and so on. Tension is easier, it aligns itself. Your proposed setup uses the surface, too, where is the advantage?
I don't think you can use this. That would probably require an isolated, closed box, as even air flow can influence the measurements.

The difference between 1.008g/cm^3 and 1.009g/cm^3 is 0.001g/cm^3. If your measured volume is 1cm^3, this corresponds to a difference of 0.001g. If it is more, the difference is larger.

$F=mg-V\rho g$ with the test mass m, its volume V and the water density ρ. With the density ρ' for the test mass, this can be written as $F=mg\left(1-\frac{\rho}{\rho'}\right)$.

6. Apr 1, 2013

### Larsoo

Thanks MFB, its important that I have as little as possible under the liquid as it must be in food grade enclosures. I thought it would be simple to have, maybe a ball pushing a rod upwards through a pipe. Also, it being a wet environment everything will need to be enclosed anyway.
Also, I figured the rod could be as thin as a pin meaning the krausen(foam) wouldnt impede flotation/surface tension with something sitting on the liquid surface. I also figured that being able to choose the depth it sits at would allow me more scope for setting the range of upward pressures.
Maybe all these things can be addressed in another way. Thats why I'm here picking your brains:)
w.r.t the difference that means I could get much better accuracy with something as small as 2cm^3?
The reason I'm keen on the contents of the scales is because its a 12Euro scales so the components must be cheap. Do you know if tension measuring devices can be purchased reasonably cheaply? or what I should look for, what theyre called exactly?
Thanks!

L

7. Apr 1, 2013

### sophiecentaur

I, also, have had to spend ages, faffing about to determine what exact level the alcohol hydrometer has reached whilst brewing, with the grot and bubbles that float on top. Therefore, I can see that any automatic measurement with no moving parts of SG would be attractive. It could be worth while investigating the possibility of measuring the speed of sound in the water / ethanol solutions for different values of SG. There is a significant difference in speed for the two liquids (around 1100 vs 1400 m/s) You could set up a standing wave in a tube of, say 20cm and find the resonant frequency or even just measure delay time. Frequency / time are easy quantities to measure accurately and the temperature dependence could be factored out easily, too. Any equipment you made could be easy to sterilise, too. It's worth a thought.

8. Apr 1, 2013

### Larsoo

Sophiecentaur, you have me interested. However, my background is electronics rather than physics. Could you elaborate a little on the type of sensors/transducers would be used to achive that. Also, I'm not familiar with what a standing wave is. I wonder is the solution homogenous enough for a measurement concentrating on the ethanol level, and could that be converted to a gravity value which is the real indicator of completion?

9. Apr 1, 2013

### sophiecentaur

I was thinking of a loudspeaker and a microphone, for instance - or you could investigate ultrasonic transducers and pulses, to measure transit times. I don't think the transducers would be an issue - they are available for body scanning which involves resolutions of a very few mm.
Do the sums to see what the transit times would be and relate this to the pulse width and time resolution needed. Scan the on-line catalogues for devices. If you are into electronics then you can read data sheets, I guess. You'd need that if you can contemplate an electronics project. Give it a try and come back with some figures of bandwidths, frequencies etc..

10. Apr 1, 2013

### Staff: Mentor

Shipping is probably the most expensive part.

The speed of sound is an interesting approach. It could even work completely non-invasive: Attach the speaker to one side of the container and the microphone to the other. Measure the delay. I'm not sure how to do this as cheap as possible, and without significant programming effort, but the result could be very nice.

11. Apr 1, 2013

### sophiecentaur

It would be the practicalities of construction and the computer interface that would be the problem - I can't think the programming would be that hard. What about an Arduino Board as the basis for it?

12. Apr 1, 2013

### Staff: Mentor

You can get away without much programming, but then you have to buy some existing hardware. I don't think it is possible to avoid both.

13. Apr 1, 2013

### Larsoo

The programming doesnt bother me. However, I cant see the speed of sound approach working as the liquid is a lot more than just ethanol and water. Dependant on reipe/process there will be varying amounts of unfermentable sugars, proteins, break material and yeast in suspension. Measuring gravity by buoyancy is the traditional method usign a hydrometer so I would like to adapt soemthing along those lines as I believe it would be most likely to work. Whatever solution I go for I intend using a pic micro for the harware processing side. I think measurign tension/force/weight on a buoyant object is the best approach. Can anyone tell me what i should be looking for in terms of transducers/strain gauges etc??

14. Apr 1, 2013

### sophiecentaur

You may not be able to 'predict' the speed for the various concentrations but an intelligent system for processing the data could be devised after a calibration against a manual measurement. I realise that the traditional method is to use 'floating' technology but I have a feeling that the odd surface effects and things like bubble adhesion to any automatic / continuous floating hydrometer technique could actually be quite problematical. The trouble is that you're only looking for a fairly small change in SG - as you know - and the result would probably need some qualitative assessment (expertise) in any case, whatever method you use.
Have you any ideas about how it's done in commercial brewing?

15. Apr 1, 2013

### Bobbywhy

According to the Wikipedia entry for Specific gravity there are at least six types of fluid density measuring techniques. http://en.wikipedia.org/wiki/Specific_gravity

Also see: http://en.wikipedia.org/wiki/Relative_density

As mentioned by others above, ultrasonic spectroscopy can measure the absolute frequency dependent velocity and attenuation of pure and or mixed liquids over a wide range of frequencies, and from that determine the density. http://www.itoms.com/node/555 [Broken]

Here is an “off-the-shelf” unit already being used by some brewers:
“The submersible probe head contains a mathematically characterized spring-float system. When the head is immersed vertically in the liquid, the float moves vertically and the position of the float controls the position of a permanent magnet whose displacement is sensed by a concentric array of Hall-effect linear displacement sensors. The output signals of the sensors are mixed in a dedicated electronics module that provides a single output voltage which the magnitude is a direct linear measure of the quantity to be measured.”
http://www.gardco.com/pages/density/electric_hydrometer.cfm

For an alternate method you might consider using a common hydrometer and with a camera and radio downlink. Using this setup you could read the specific gravity directly but from a remote location.

Bobbywhy

Last edited by a moderator: May 6, 2017
16. Apr 2, 2013

### Larsoo

Thanks guys for your inputs. All food for thought. I'm going to have a think about it and see how best to approach it. I'm not completely off the speed of sound idea either, just need to figure out which is most likely to work for me.

Thanks

L