Calculating Water Usage
Because it typically comprises more than 90% of beer both by weight and by volume, it can be argued that no brewing ingredient is more important than water. In the May-June 2005 issue of BYO, this column examined water quality, specifically the mineral content of brewing water, the chemistry involved and its effect on the mash and the resulting beer. Just as important — and extraordinarily practical — is the quantity of water used. Such questions as how much water to use for mashing and sparging the grain, and boiling the wort are of great interest to brewers.
If you are using water that is filtered or adjusted for mineral content, you will want to know the total volume needed for a brewing session. The volume of water also impacts brewing equipment and system design because it is a major factor in determining the capacity of the vessels required. By keeping several concepts in mind — and using a few handy formulas —you should be able to calculate accurately the volumes of water needed, both overall and during each step of the brewing process.
All of the good comprehensive brewing software packages available have a brewing session water volume calculator that performs this task for you. It is also possible to construct a spreadsheet using the various formulas involved. However, even if you rely on the computer to do the routine calculations, an understanding of the underlying principles will make you a more knowledgeable brewer and might even improve your beer.
Beginning at the end
When calculating water quantity, it is helpful to begin by considering the final volume of beer you intend to brew. Recipes are usually expressed in round numbers, for example, 5.0 gallons (19 liters), and often they reflect the volume that is bottled or kegged. During fermentation, racking to other vessels and the bottling or kegging process, some beer is absorbed by hops or yeast, while an additional volume is evaporated or left behind in the equipment. After some experience, brewers come to know approximately how much wort is necessary in the fermenter in order to end up with a given volume of beer. I call this the “fermenter volume,” and to my mind, this is the real volume of a recipe. For 5.0–10 gallon (19–38 L) batches, typically this will be 1.0–4.0 quarts (0.9–3.8 L) larger than the published volume of the recipe.
Once experience has taught you the desired fermenter volume, you can work backwards to determine the total water volume needed, subtracting the various losses that occur during the brewing process. In reverse order, these will include many of the following:
• Wort left in lines and equipment, such as a chiller or pump, between the brewing kettle and the fermenter
• Wort absorbed by hop residue and protein break material in the kettle at the end of the boil
• Evaporation losses during boiling of the wort in the kettle
• Liquid left in lines and equipment between the mash tun and the kettle
• Mash “dead space,” that is, liquid that is left in mashing and sparging vessels due to their design and geometry
• Sparge water dead space, that is, water similarly left in the hot liquor tank or other sparge water vessel
• Water absorbed by the grain in the mash tun
Of course these losses are offset by water additions, which typically will include at least some of the following, listed in order of earliest to latest:
• Strike water, that is, the water initially mixed with the grain at the beginning of mashing
• Any additional water infusions during mashing
• Sparge water added to the mash in order to extract the sugars converted from the starches in the grain
• Any water added to the kettle to achieve the target pre-boil wort volume
• Any water added after the boil, either to the kettle or the fermenter, to achieve the target post-boil and fermenter volumes
Some of these values can be calculated from the recipe and brewing method, while a number of them are derived from the relationships among values, and still others are measured empirically based on the specifics of the equipment and brewing system. The last group includes the volume of liquid left in the various vessels, lines, chiller, pump, etc. Those values that depend on relationships are the boiling losses and any “top-off” water added to the kettle or fermenter. The remaining values, the volumes of strike water, water absorbed by the grain, any additional mash infusions and the sparge water, can be calculated from the recipe. I’ll provide those formulas shortly.
Trial and no error
Once you have extensive experience with a single brewing system, you should be able to estimate equipment losses (liquid left in vessels, lines, etc.) with a fair degree of accuracy. Even if you have a new system, however, or if you desire maximum accuracy, you can conduct a trial using ordinary water and measure the various volumes. The water should be at about the same temperature as is used during each stage of the brewing process, because at temperatures above 38 °F (4 °C), the volume of water or wort increases with the temperature — approximately 4% between 68 °F and 212 °F (20 °C and 100 °C).
For mashing and sparging purposes, it is very helpful to know the useful capacity of the mash tun and hot liquor tanks. Often this is not the same as the total capacity of a vessel. Dead space and other geometric considerations such as the space above the lid must be subtracted. The best way to determine the useful capacity is to measure the volume of water required to fill the vessel and then measure the volume of water drained.
Boiling losses depend on the heat source, the geometry of the kettle and the environmental conditions (mainly the temperature and any wind) during the boil. The value is typically expressed in terms of gallons (or quarts or liters) per hour. Again this can be measured during an actual brewing session, or you may wish to do a test boil with water. Measure and divide the actual volume loss by the total boil time in hours to calculate the value for a specific brewing session.
More difficult to measure is the liquid absorbed by hops and protein break material during the boil, but an estimated average value for all the recipes you brew is normally accurate enough for these purposes.
The volume of strike water for the mash is a function of the amount of grain and the desired mash thickness. The mash thickness can vary with the recipe, the mash tun configuration, the volume of any additional mash water infusions, the sparge water volume and individual brewer preferences, but a value in the range of 1.0–1.5 quarts of water per pound of grain (2.1–3.1 liters per kilogram) is typical for homebrewers.
Therefore the formula for calculating the strike water volume is:
Strike water volume = weight of grain * desired mash thickness
For example, for a mash thickness of 1.25 qts./lb. (2.6 L/kg) and a grain bill calling for 10 lbs. (4.5 kg) of grain, the calculated strike water volume is 12.5 quarts (11.8 liters).
The water absorbed by the grain will vary with the specifics of the grain bill, the type of malt and adjuncts and their moisture content, but an average value of 0.50 quarts per pound (1.04 L/kg) has proven to be a very reasonable assumption in most cases. In the hypothetical recipe above (10 lbs. or 4.5 kg of grain), the volume of water absorbed is 5.0 quarts (4.7 L).
In order to ensure adequate capacity of vessels for mashing and sparging, it is useful to know the total volume of the mash. The following simple formula should be rather obvious:
Total mash volume = volume of water + volume of grain
Of course first it is necessary to know the volume that the grain displaces when mashed (which is different from its dry volume). Once again this depends on the specifics of the grain bill, but a value of 0.32 quarts per pound (0.67 L/kg) is a reasonable average. Therefore, in the example above, the mash volume is 12.5 + 3.2 = 15.7 quarts (14.8 L).
Calculating the correct volume of sparge water is of particular importance because it greatly determines the wort pre-boil volume, which is critical to achieving the target original specific gravity. An old very general rule of thumb is to use approximately two quarts of sparge water per pound of grain (4.2 L/kg), but other factors such as the mash thickness and any additional water infusions can change this considerably.
It is becoming increasingly popular for homebrewers to batch sparge, that is, to add the sparge water in one or more batches, followed by stirring the mash, allowing it to settle and briefly recirculating the runoff until it clears before draining it into the boiling kettle. This can simplify and shorten the brewing session somewhat.
A useful value to know is the volume of first runnings that are drained from the mash tun prior to adding the sparge water. This is calculated using the following formula: Volume of first runnings = Strike water volume + volume of any other water added to the mash - volume of water absorbed by the grain - volume of liquid remaining in the bottom of the mash tun - volume of liquid remaining in lines or pump
In our example from the section on mashing earlier, and also using values of 1.0 quarts (0.9 L) for the liquid remaining in the mash tun and 0.25 quarts (0.2 L) for line losses, the calculated volume of the first runnings is 12.5 + 0 - 5.0 - 1.0 - 0.2 = 6.3 quarts (11.8 + 0 - 4.7 - 0.9 - 0.2 = 6.0 L).
Whether you employ continuous sparging or batch sparging, the total volume of sparge water is calculated from the target pre-boil volume by subtracting the volume of the first runnings. Therefore the formula is:
Total volume of sparge water = Target pre-boil volume - volume of first runnings
In our example, the target pre-boil volume may be 28.0 quarts (26.5 L) and the volume of first runnings is 6.3 quarts (6.0 L). Therefore the total volume of sparge water is 28.0 - 6.3 = 21.7 quarts (26.5 - 6.0 = 20.5 L). For the purposes of providing an adequate volume of sparge water, add to the calculated value the volume of any dead space in the hot liquor tank or sparge water vessel.
How many times?
If you batch sparge, in many cases the mash tun is not large enough for the entire volume of sparge water to be added in a single batch. Often more than one sparge water batch is required. The usual procedure is to divide the total sparge water required into equal batches based on the vessel’s useful capacity and the volume of the mash after the first runnings are drained. The formula for calculating the number of batches required is:
Number of sparge water batches = (Volume of sparge water - volume of sparge vessel dead space) / (sparge vessel useful capacity - volume of grain - volume of water absorbed by the grain)
Then round the result up to the next whole number.
In our example, we will assume a mash tun useful capacity of 24 quarts (22.7 L). Therefore the calculations are:
(21.7 - 1.0) / (24.0 - 3.2 - 5.0) = 1.3
or (20.5 - 0.9) / (22.7 - 3.0 - 4.7) = 1.3
Rounded up to the next whole number, the result is two sparge batches.
The formula for the volume of sparge water per batch is simply the volume of sparge water divided by the number of sparge batches, in our example 21.7 / 2 = 10.9 quarts (20.5 / 2 = 10.3 L).
Putting it all together
Armed with all this information, we are able to calculate the total volume of water required for a brewing session. Reviewing the list earlier in this article, we recall that the total water needed consists of the sum of the volumes of the strike water, any additional mash water infusions, the sparge water (including any sparge water vessel dead space), any water added to the kettle prior to the boil, and any water added to the kettle or fermenter after the boil. Expressed as a formula, it is:
Total volume of water needed = Volume of strike water + volume of any additional mash water infusions + volume of sparge water (including any sparge water vessel dead space) + any water added to the kettle pre-boil + any water added to the kettle or fermenter post-boil
Our hypothetical example had no additional mash water infusions, sparge water dead space, or water added to the kettle or fermenter either prior to or after the boil. This results in the calculation of the total water volume for the brew session as the simple addition of the strike water and the sparge water, or:
12.5 + 6.2 = 18.7 quarts
(11.8 + 6.0 = 17.8 L)
While the hypothetical calculations above have been expressed to a precision of 0.1 quart or liter, in real-world homebrewing situations you may find it necessary only to measure the volume of the actual water additions to the nearest whole unit. For the 5–10 gallon (19–38 L) batches of many homebrewers, this represents an accuracy of about 5% or less and is likely to produce meaningful and useful results.
Of course, many homebrewers detrmine their water needs by simple trial and error. The benefit of knowing how calculate water usage comes when you upgrade or modify your brewery, or buy or build a new one.
Bill Pierce’s water quality article appeared in the May-June 2005 issue of Brew Your Own.