Sometimes flow is 10 liter/sec and sometimes 20 liter/sec and this is we can see on any gauge or meter.
I see you already have the instantaneous water flow reading.
So, it is only a matter of adding up every x period of time.
According to how much the reading varies over time , you could do this every second, 30 seconds, 1 minute etc.
For example :
You take readings every second . Instrument is telling you 10 liter/sec x 1 sec = 10 liter
Next second same thing , reading in [liter/sec] x time elapsed [ sec ] = liter , yo keep adding the result to a totalizer in liters.
That is it.
Should your readings vary to much you can program to fire the reading and time elapsed with a window of values , say 9 <= reading <= 11 liter/sec. applying average values
Hope this helps
If the instrument you are using has some kind of interfase you can probably do this calculation and adition in an Microcontroller or Pc.