Liquid Volume at Temperature

[frankieboy]

Hello! Bit of a technical/maths based question for you!

So I did my 4th all grain brew today (Son of Punkie from MM) and was pondering the amount of water I am using.

I use the calculator at Sparge Water Calculator | MoreBeer to work out my sparge water. It says on there that theres an accepted difference on 4% volume between boiling wort and 'room temperature' wort (20C).

Does anyone know if this is linear, so for example will wort at 60C have 2% more volume than wort at 20C?

I stopped measuring using jugs as it was tedious and so use a cylindrical volume calculator and a steel ruler to fill my kettle and take readings (Cylinder Volume Calculator in Metres and Centimetres), but I can't figure out if this method is subject to inaccuracy based on the different volume at different temperature - or perhaps, for example, the 'pre-wort volume' on that morebeer calculator is already taking into account the fact that pre-boil wort is likely to be 60-70C.

This also poses the question of calculating my boil off rate, because if I start with 20L and boil for 1 hr, then measure it as 15L, if I take that measurement pretty much straight away then presumably by the time that liquid is back to its starting temperature of 20C then it has lost another 4% volume, which is another 600ml so is my boil off rate 5L per hour or 5.6L per hour?

Or whether any of this even matters!

Thanks

(Sorry for making you read all that haha!)

 

[strange-steve]

I got a little lost reading that I'm afraid, but I'll try to answer some of your questions if I've understood them correctly.

No it's not linear (although from 20-100° it's not a million miles away). At 20° water has a density of ~1.002 l/kg, at 60° it's 1.017, and at 100° it's 1.043. That means that a mass of water at 60° will take up ~1.5% more volume than at 20°, and water at 100° will take up 4.1% more volume than at 20°. (I know we're talking about a sugar solution rather than water but I don't think it makes a big difference at typical wort density.)

To calculate boil-off rate you'll take the first measurement at the start of the boil, ie when it reaches 100°, and the second measurement at the end of the boil while it's still at 100°, so you don't need to account for temperature.

 

[strange-steve]

If you're trying to figure out water volumes then it's pretty straightforward:

Mash water = g * r
Sparge water = (f + t) / 0.96 + b + a - m + d

g= grain bill in kg
r= mash ratio in l/kg
f= fermenter volume
t= boiler trub
b= boil off volume
a= grain absorption, ~1l/kg
m= mash water
d= mash tun dead space

 

[frankieboy]

This is exactly the answer I was after, thank you!

 

[Clint]

I get this conundrum when adding oil to a pan to make curry as...Indian restaurant curry style uses lots of oil..but when you heat it it always "looks" more....but I'm only taking tablespoons...perhaps I should cook earlier....