Cold water tanks are commonplace in commercial breweries because they are handy reservoirs of cooling potential and help to spread the cooling load on refrigeration systems associated with wort cooling from as few as 30 minutes up to 3 hours or more, depending on the brewing interval of the brewery. Some breweries also use devices known as ice banks to provide cold “brine” (glycol or salt solutions) from refrigeration systems to wort coolers; warm brine flows back to the ice bank, melts ice, cools down, and is pumped back to the wort chiller in a loop.
Both devices spread the cooling load from wort cooling over a longer time range; the difference is that the cold water from cold water tanks is converted to hot water and captured for future brews, where the cold brine from ice banks flows back to the ice bank. When breweries use ice banks, ground water is always used to take the heavy hit and to produce high-temperature brewing water. Cold water tanks are sometimes sized to handle the full cooling load and other times are used in conjunction with ambient water. The takeaway is that your question makes total sense.
Let’s jump into the nuts and bolts of your question. You know that 7.5 gallons (28.4 liters) of water at 40 °F (4 °C) works in your system to chill 5 gallons (19 L) of wort to about 52 °F (11 °C). And you want to prepare this volume of cold water to use for wort cooling by mixing 80 °F (27 °C) water with ice. I am assuming you are pumping the water through your counterflow, but if you don’t have a pump, you can elevate your cold water reservoir and siphon through your cooler.
I am also going to slightly over-estimate the amount of ice required for this problem by assuming the ice temperature is 20 °F (-7 °C), warmer than the setting on most freezers. Skipping the energy balance math, 4 parts of water at 80 °F (27 °C) plus 1 part 20 °F (-7 °C) ice will give you with water at 39 °F (4 °C). Simply mix 6 gallons (22.7 liters) of 80 °F (27 °C) water with 12.5 pounds (1.5 gallons or 5.7 kg) of 20 °F (-7 °C) ice in a cooler, allow the ice to completely melt, and the resulting temperature should be a bit under 40 °F (4 °C) and provide the cooling needed for your system.
There are free online calculators that you can use to calculate different scenarios; check out this link as an example: www.onlineconversion.com/mixing_water.htm
I do want to point out that quick cooling of your homebrewed wort is not required to brew great beer. The quick cooling rule, like many homebrewing rules, came out of commercial brewing where large batch sizes make some sort of heat exchanger, whether a coolship, Baudelot cooler, or plate heat exchanger, a necessity. Homebrew batches cool quickly enough when wort in an uninsulated fermenter is simply allowed to chill out, no pun intended, until cooler than about 80 °F (27 °C).
Efficiency, a question you did not ask about, is a totally different topic, but a very inviting rabbit hole for me to hop into. Each cooling scenario depends upon how much energy is transferred from the cooling or heating medium to the product. In the case of wort cooling at home, we are typically looking at energy transfer from cool water to hot wort. You have empirically found that 7.5 gallons (28.4 liters) of 40 °F (4 °C) water cools 5 gallons (19 L) of your wort to about 52 °F (11 °C). How can the practical brewer reduce the volume of cooling water without changing water temperature?
One way to improve cooling performance is to change the cooling surface area by increasing the length of the cooling coil. This works until the water temperature leaving the chiller is nearly the same as the wort temperature entering the chiller. Another option is to increase liquid turbulence and the associated Reynolds Number (let’s save this discussion for another day) by changing the surface of the cooling area and/or increasing the flow rate of wort, cooling water, or both.
Simply denting a cooling coil increases turbulence when water-like liquids flow through the tube. And as turbulence as measured by the Reynolds Number increases, so does the overall heat transfer coefficient. Plate heat exchangers are another example of how turbulence increases heat flow. The real upside with turbulence is a decrease in cooling area to provide the same coiling duty. Changing the heat transfer surface from stainless steel to copper and reducing material thickness are other design details used to improve cooling efficiency. Hope this information is useful, stay chill, and enjoy those old-school lagers!