weird question.
My question is why would you think you couldn't use a 10 gallon cooler to mash a 5 gallon batch?
I did the math
10 gallon Igloo Cooler can hold 20 lbs of grain & 6.5 gallon of strike water
With an additional 3.5 gallon Batch Sparge
The math is flawed. Grain takes up volume, so you can't have 20 lbs of grain along with 10 gallons of water(6.5 + 3.5) in a 10 gallon cooler.
BATCH sparge
add 6.5 gallons - stir
Drain - get 3.8 out due to absorption
add 3.25 gallons - stir
Drain - get about 7 gallon pre boil
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