i’m just wondering how fluid & heat transfer works, if you mix water that is 20 or 30 degrees apart in temperature does the hot or cold have an advantage or does it meet in the middle and equalize?
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The formula for the heat capacity of an object (a bucket of water or a solid object) is mass times temperature.
So if you have 10 pounds of water at 50 degrees (irrelevant of Celcius, Fahrenheit or Kelvin) and 10 pounds of water at 80 degrees, the first one has a heat capacity of 10×50 = 500 and the second has a heat capacity of 10×80 = 800. Add them together (500+800 = 1300) and divide them by the new mass (10+10 = 20) and you end up with 65 degrees.
Now your question was in gallons of water, then you have to realize that objects which are hotter have a higher volume than objects which are colder[*] and as such the 10 gallons at 80 degrees will be lighter than 10 gallons at 50 degrees. At the volumes and temperature differences you work with, this is negligible, but if you are moving liquids around in a big tanker behind your truck in a hot day, then it’s important to remember this and take the volume/temperature difference into account.
But for you, working in theoretical and ideal situations, yes it will be 65 degrees Fahrenheit. Initially it will be colder/hotter on the outsides where the two liquids don’t touch, but overtime the energy of the liquid with the higher temperature will flow into the colder liquid and then everything will be the same.
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