water volume help

[simo72]

Hi i am in the middle my first biab and have 14 litres of wort at a gravity of 1.078 the recipe states SG of 1.045 dies anyone know how much water to add to achieve this ?
Many thanks

 

[rpt]

14L at 1.078 = 15.092kg

xL at 1.045 = 15.092kg

So x = 15.092/1.045 = 14.442L

So you need to add 442ml of water.

 

[simo72]

That doesn't seem like much to me adding less than 1/2 ltr will not bring the gravity down from 1.078 to 1.045 but will try

 

[Dunfie]

I think the figure if closer to 10.3 litres.

Total wort at 1045 would be the actual gravity divided by the intended gravity multiplied by the amount of wort collected.

So ((78/45)°14)=24.27

As you already have 14l you just need to add the remainder.

 

[Dave1970]

there is a dilution calculator built into the Brewmate software, which as it's free you might as well try...I put your numbers in, it comes out as 10 litres to get to 1045

 

[rpt]

I have to confess I was surprised at such a low number. Where did my maths go wrong?

 

[Dunfie]

14L at 1.078 = 15.092kg

xL at 1.045 = 15.092kg

So x = 15.092/1.045 = 14.442L

So you need to add 442ml of water.

If you only use the last two digits of the gravity figure then your calc works.

14 x 78 = 1092

Therefore you can use the answer and substitute in the intended gravity.

Wort x 45 = 1092

Wort = 1092/45

= 24.26

 

[rpt]

OK, let's try again.

Currently volume is 14L
Mass is 14 x 1.078 = 15.092kg

Add xL of water
Volume is then 14 + x
Mass is 15.092 + x

Specific gravity is mass/volume = (15.092+x)/(14+x) = 1.045

So 15.092+x = 1.045 x (14+x) = 14.63 + 1.045x
15.092+x - 1.045x = 14.63
-0.045x = 14.63-15.092=-0.462

So x = 10.27L

Got it right this time!

Now I need to work out why the first calculation was wrong!

I did make the mistake of not allowing for the wort and the water having different specific gravities but that would not have been out by a factor of 20.

 

[Dunfie]

Yip that will do it :lol:

However its a lot easier if you just remove the constant gravity of water (and the fact that alcohol is lighter than water).

 

[simo72]

Thanks for the help everyone tho i only had 12 ltres and just diluted to 20 lts and checked gravity and was spot on 1.045 so well happy