### Author Topic: Math help  (Read 1560 times)

#### DrewG

• Brewer
• Posts: 359
##### Math help
« on: April 01, 2012, 07:15:07 AM »
Not sure how to figure this one, so I thought I'd ask:

5 gallons of a 1.052 wort with 3 quarts water added = ? gravity

Thanks
"Well, the Mexicans got a saying - what cannot be remedied must be endured."

-Barbarosa

#### bonjour

• Senior Brewmaster
• Posts: 1791
• Troy, MI, 37mi, 60.9deg AR
##### Re: Math help
« Reply #1 on: April 01, 2012, 07:22:16 AM »
Not sure how to figure this one, so I thought I'd ask:

5 gallons of a 1.052 wort with 3 quarts water added = ? gravity

Thanks
Total Gravity points = (52*5) = 260

New Gravity points = (52*5)/5.75 gallons = 45.22

New SG = 1.045
Fred Bonjour
Co-Chair Mashing in Michigan 2014 AHA Conference in Grand Rapids, Michigan
AHA Governing Committee; AHA Conference, Club Support & Web Subcommittees

Everything under 1.100 is a 'session' beer

#### DrewG

• Brewer
• Posts: 359
##### Re: Math help
« Reply #2 on: April 01, 2012, 07:23:44 AM »
Ahh. thank you Sir. Simple enough equation too.
"Well, the Mexicans got a saying - what cannot be remedied must be endured."

-Barbarosa

#### bo

• Senior Brewmaster
• Posts: 1141
##### Re: Math help
« Reply #3 on: April 01, 2012, 09:06:52 AM »
Not sure how to figure this one, so I thought I'd ask:

5 gallons of a 1.052 wort with 3 quarts water added = ? gravity

Thanks

Promash

#### punatic

• Official Poobah of No Life.
• Posts: 4583
• Puna District, Hawaii Island (UTC -10)
##### Re: Math help
« Reply #4 on: April 01, 2012, 11:06:11 AM »
C1V1 = C2V2

manipulate the equation to isolate the unknown and solve

C2 = C1V1/V2

where
C = concentration
V = volume
There is only one success: to be able to spend your life in your own way.

AHA Life Member #33907

#### euge

• I must live here
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• Ego ceruisam ad bibere cervisiam
##### Re: Math help
« Reply #5 on: April 01, 2012, 11:19:05 AM »
C1V1 = C2V2

manipulate the equation to isolate the unknown and solve

C2 = C1V1/V2

where
C = concentration
V = volume

I get 7.033 when I do this. (1.052*20)/3
The first principle is that you must not fool yourself, and you are the easiest person to fool. -Richard P. Feynman

Laws are spider-webs, which catch the little flies, but cannot hold the big ones. -Anacharsis

#### punatic

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##### Re: Math help
« Reply #6 on: April 01, 2012, 11:27:16 AM »
C1V1 = C2V2

manipulate the equation to isolate the unknown and solve

C2 = C1V1/V2

where
C = concentration
V = volume

I get 7.033 when I do this. (1.052*20)/3

1.052 is a ratio.  it must be expressed as a concentration -> 52 points of gravity

(52*20)/3 =  346.67 points of gravity

1.347

if you take 20 gallons of beer with SG 1.052 and reduce the volume to three gallons the SG becomes 1.347

or conversly

if you take a concentrated wort boil of 3 gallons with SG 1.347 and dilute it to 20 gallons your OG would be 1.052
« Last Edit: April 01, 2012, 11:29:48 AM by punatic »
There is only one success: to be able to spend your life in your own way.

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#### bonjour

• Senior Brewmaster
• Posts: 1791
• Troy, MI, 37mi, 60.9deg AR
##### Re: Math help
« Reply #7 on: April 01, 2012, 11:29:20 AM »
C1V1 = C2V2

manipulate the equation to isolate the unknown and solve

C2 = C1V1/V2

where
C = concentration
V = volume

I get 7.033 when I do this. (1.052*20)/3

I get 45.2 when I do this. (52*20)/23

(You need to use a concentration measure (PPPPG) not SG

Plus you must account for the final volume of 23 qts
Fred Bonjour
Co-Chair Mashing in Michigan 2014 AHA Conference in Grand Rapids, Michigan
AHA Governing Committee; AHA Conference, Club Support & Web Subcommittees

Everything under 1.100 is a 'session' beer

#### punatic

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• Posts: 4583
• Puna District, Hawaii Island (UTC -10)
##### Re: Math help
« Reply #8 on: April 01, 2012, 11:32:40 AM »
Oh, I see what you did euge - you converted gallons to quarts.

1.052 is the weight of the wort divided by the weight of water (a ratio)
There is only one success: to be able to spend your life in your own way.

AHA Life Member #33907

#### euge

• I must live here
• Posts: 8022
• Ego ceruisam ad bibere cervisiam
##### Re: Math help
« Reply #9 on: April 01, 2012, 11:39:47 AM »
Oh, I see what you did euge - you converted gallons to quarts.

1.052 is the weight of the wort divided by the weight of water (a ratio)

And I did it wrong to C2 is 23 quarts? I see now drop the 1.0 from 1.052...
The first principle is that you must not fool yourself, and you are the easiest person to fool. -Richard P. Feynman

Laws are spider-webs, which catch the little flies, but cannot hold the big ones. -Anacharsis

#### punatic

• Official Poobah of No Life.
• Posts: 4583
• Puna District, Hawaii Island (UTC -10)
##### Re: Math help
« Reply #10 on: April 01, 2012, 11:56:07 AM »
Yes, C2 is the total volume not the change in volume
and use points of gravity not the ratio.

Also, I misspoke - 1.052 is the density (mass per unit volume) of wort divided by the density of water. (a ratio)
There is only one success: to be able to spend your life in your own way.

AHA Life Member #33907

#### firedog23

• Brewer
• Posts: 262
• Just taking it one brew at a time!
##### Re: Math help
« Reply #11 on: April 01, 2012, 12:01:03 PM »
Writing a 10-12 page paper on morality in war and then read this thread.

In the fermenter:

Up coming brews:
First boil in a bag

#### tubercle

• Senior Brewmaster
• Posts: 1639
• Sweet Caroline
##### Re: Math help
« Reply #12 on: April 01, 2012, 01:10:36 PM »
E=MC2

Where
E=Every Beer
M=Malt
C=Citrus Hops
Sweet Caroline where the Sun rises over the deep blue sea and sets somewhere beyond Tennessee

#### punatic

• Official Poobah of No Life.
• Posts: 4583
• Puna District, Hawaii Island (UTC -10)
##### Re: Math help
« Reply #13 on: April 01, 2012, 02:00:03 PM »
E=MC2

Where
E=Every Beer
M=Malt
C=Citrus Hops
There is only one success: to be able to spend your life in your own way.

AHA Life Member #33907

#### euge

• I must live here
• Posts: 8022
• Ego ceruisam ad bibere cervisiam
##### Re: Math help
« Reply #14 on: April 01, 2012, 02:41:06 PM »
The first principle is that you must not fool yourself, and you are the easiest person to fool. -Richard P. Feynman

Laws are spider-webs, which catch the little flies, but cannot hold the big ones. -Anacharsis