API 2000 gives methods for sizing vents for atmospheric tanks. Basically the method involves two considerations:
1) Vent size must be able to pass input filling or output emptying of liquid at the same rate it flows in the tank or out of the tank and not exceed the tank design pressure which is usually very small on the order of inches of WC or less. Therefore if you take the expected maximum flow in or out of the tank say 1000 gpm and convert to cubic feet per second this is the volume of gas that it must pass in or out without exceeding the positive or vaccuum design pressure. In this case the gas in the tank will be air with saturated water vapor.
2) Since API was developed for oil and gas storage tanks there is also a component of vaporization of the volatile components in the tank. For instance gasoline is very volatile so as the tank is filling or emptying there are vapors generated by the liquid which also adds to the volume that needs to be included in the design flowrate through the vent. However with water in tank I don't think this vaporization amount will matter that much but check API if there are any allowances.
Correction to the above - for case 2 above the correct mechanism for flow out of the tank is when it may be raining and the vapor space cools down simultaneoulsy during withdrawl of liquid which causes additional air flow into the tank due to cooling down and shrinking of vapor above the tank - this will also apply to air with water vapor. Also there is thermal expansion of fluid in tank considerations for outbreathing.
Here is a sample calculation with explanation on the web:
For a typical municipal tank with a shop-fabricated vent, just size it as big as the largest inlet or outlet (or combined are if multiple), keep the open screen area similar to that, and it should be good. If you check sizing based on pressures and flow characteristics, it should show as considerably oversized.
For a manufactured vent or P/V vent, get flow curves or data from the manufacturer.
For shop-fabricated vents, ASHRAE has duct-flow data that covers screens, exhaust hoods, etc., and some of that can be applied.
Is this is a potable water tank or a fire water tank? If potable water, making the vent freeze proof for both pressure and vacuum is as important as being sized to relieve pressure and vacuum, and it must have fine mesh screening to exclude bugs and birds.
In addition to the advice above by JStephen, if possible, consider also not desired emptying, as having a discharge opening fully open to e.g to the surroundings. If not restricted by codes and beneficial for the tank roof design, you could consider dividing the required air access opening cross section over multiple vent openings.
