Question On Water Level Calibration

[bouncingcastle]

Hi guys and girls,

Just a quick question on calibrating volumes in brewery vessels.

I've always calibrated with cold water, which has got me thinking. With liquid expansion under heat, how does that play with the numbers?

This might sound stupid, but If I move 30 litres of 70*C water from my HLT (calibrated cold) is that still 30 litres?

Does beersmith compensate for this expansion with the numbers it crunches??

Hmmmm.

Chris

 

[jonocarroll]

Yaay a physics question! My time to shine (I hope). B)

The thermal expansion of a volume of liquid changes the volume by

deltaV = beta x V0 x deltaT

deltaV; change in volume
beta; thermal coefficient (= 3 x alpha)
V0; original volume
deltaT; change in temperature (Celcius or Kelvin)

30L of water (beta = 0.000207) expanding from 25C to 70C will expand by 0.28L.

I have no idea whether or not beersmith takes this into account, but it's really not much.


Hope that helps.

 

[buttersd70]

Beersmith kinda sorta allows for loss to cooling, but only does so as a simple percentage of loss to cooling (with a default value of 4%, but this can be changed.) The effect this has is in the calculation of water required for the boil, when you have it set to work out the boil volume for you, based on losses and final batch size.

As qb said, the difference in water is minimal, but it would still be best to calabrate the HLT hot. You won't eliminate any error completely (because the temps needed will change, depending on what you're mashing, and lets face it, hb equipment is hardly that accurate) but it will help reduce any error. My 2c is that, whilst in the end it may be a small amount that hardly has any effect, if you can simply and easily reduce that error, you may as well do so.

 

[bouncingcastle]

Thanks guys

Those were exactly the two answers I was after!

I'll calibrate my HLT at 70* - as you have both said, it isn't much... BUT.... If I'm going to do it, I may as well do it right

Cheers,

Chris

 

[Thirsty Boy]

A litre is still a litre - no matter what.

I calibrated my brewery with cold water because that way I wouldn't burn myself. The measurements are still the same.

However - I do all my brewday calculations as though the water is hot - that way I only have to do one compensatory calculation at the end. I will have around 4% less volume in my fermentor at pitching temps than I drained to my cube - so into my cube goes 21L of wort and out of it comes 20L of wort.

It sort of seems logical that you would get density differences as well... the wort reduces volume by 4%, so the density must go up right??? except you need to remember that you will have cooled your samples (or use an auto correcting refractometer) before measuring your density... so its a pure volume thing. 21L of wort that you measure at 1.050 will magically turn into 20L of 1.050 wort

TB

 

[newguy]

The increase in volume of the liquid would be partially/completely/or over-compensated by the increase in size of the vessel due to its temperature increasing. As the vessel undergoes heat expansion, its volume will increase which means that your volume measurements/markings made at a lower temperature will be out.

As others have said, do your volume measurements with hot water and allow the vessel sufficient time to heat up as well.

 

[katzke]

Do not want to steel the thread, but does it really matter?

If I fill with cold water and chill to end up with cooled wort does it make any real difference to the recipe or anything?

I bet I spill, miscalculate boil off and trub loose enough to change the final brew somehow.

 

[jonocarroll]

The increase in volume of the liquid would be partially/completely/or over-compensated by the increase in size of the vessel due to its temperature increasing. As the vessel undergoes heat expansion, its volume will increase which means that your volume measurements/markings made at a lower temperature will be out.

As others have said, do your volume measurements with hot water and allow the vessel sufficient time to heat up as well.

I did indeed neglect that, but I can show that it's valid to do so;

The equation for linear thermal expansion is deltaL = alpha x L0 x deltaT
For area thermal expansion it's deltaA = 2 x alpha x A0 x deltaT

deltaL; change in linear length
deltaA; change in area
alpha; coefficient of linear thermal expansion
L0; original length
A0; original area
deltaT; change in temperature

I don't have my vessels here to measure, so I'm going to assume a cylinder with base radius 0.15m and height 0.6m. This gives a total volume of about 42.4L, or similar to a converted keg.

Assume the vessel has a flat base. Stainless steel has alpha = 0.0000173 (Aluminium has alpha = 0.000023). If the base has a radius of 0.15m, heating from 25C to 70C will change the base area by 0.00011m^2 (0.00015m^2). A non-flat base will make this less.

Assume the vessel has straight walls. Just working with the walls, the thermal expansion of 0.6m makes the vessel grow by 0.00047m (0.00062m). Accounting for the expansion in the base and the walls, the new volume is larger by about 0.1L (0.13L). Non-straight walls will make this less.

BUT! It doesn't matter how tall the vessel is - the calibration doesn't change if we make the vessel taller, but it will change if the base gets wider, so we only need to take into account the change in the base, so the increased volume is just 0.066L (0.09L).

... I think you'll be fine. If you want to be really fussy we could include the contribution from the increase in water vapour pressure inside the vessel and capilliary action inside the sight glass. Perhaps not.

@katzke - the question is not so much how much will I end up with, it's how much am I adding to the mash to begin with. According to these calculations, the calibration of the sight glass on the HLT will be off by about 0.3L (you end up adding 0.3L less than you thought). If it was a significant volume, it could affect the mash.

 

[newguy]

I did indeed neglect that, but I can show that it's valid to do so;

Nice calcs! Now I know for certain that the thermal expansion of the pot is nothing to worry about.

PS. Put down your beer now. You don't want to piss off MADD - Mathematicians Against Drunk Deriving. If you derive, don't drink. If you drink, don't derive.

 

[jonocarroll]

Nice calcs!

<sniffle> It's so nice to hear that for once :beer:

 

[newguy]

<sniffle> It's so nice to hear that for once :beer:

Lemme guess, you're in grad school and your supervisor keeps pointing out.....issues.....with your work? Been there, buddy. Been there. It's a rite of passage.

 

[jonocarroll]

Lemme guess, you're in grad school and your supervisor keeps pointing out.....issues.....with your work? Been there, buddy. Been there. It's a rite of passage.

Counting down 3 or 4 months till I finish my PhD. JUST TODAY my final calculation decided to start working!!!!!! There's light at the end of the tunnel. This should be enough to convince me that it's time to work out a 'graduation ale' recipe.

 

[bouncingcastle]

Best thread ever

Thanks boys - as qb has stated, the only reason for my thoughts on this particular subject were adding water to mash and then sparging volume.

That being said... Sounds like bugger all, but worth doing... I think. All those greek math symbols have put my head into a spin

I think I'm going to have another beer to sort it all out.