Sean
work out the evaporation rate (probably about 5mm a day in summer). Some days are more extreme (can be double) but other days are less.
Deduct any rainfall if reliable.
Multiply the daily mm by the green area to be covered, and you have a rough budget for the water.
For the surrounds, you might need two-thirds of the evaporation rate.
So, a 400 sq metre green (20 metres by 20 metres) needing 5mm a day for 5 months needs 400 sq metres x 0.005 metre x 150 days = 300 sq metres of water = 300 tonnes of water = 300 kilo litres for the summer.
If you use a drought-resistant grass eg couch, then less water. Benet is middle of the road, poa might need more than 100% of evaporation, especially when a hot drought is hitting you.
Hope this helps
James B