Are there sprinkler system timers that measure flow rate (e.g., in ft³/min. or gallons/min.) in addition to time? For example, I could tell it to deliver 100 ft³ of water, and it would automatically know how long to run it to deliver that quantity of water.
Typically non-agriculturally based irrigation (in the US) is measured in gallons per minute by controllers. The most common monitoring is for high / low flow on zones, though some controllers will also monitor for high flow mainline situations. The accuracy of the measurements depend on type of sensor and size of pipe. I'm curious to know more about your use.
If you know the total GPM for the zone, and the precipitation rate of the nozzles of the zone you can calculate how many inches of water you want to put down. From there, you can calculate how the frequency and length of time needed to put down a certain volume of water.
I can help with the math if you're interested.