You'll need to know the rating  of your tyres.

 But look here at Firestones load and inflation tables..  http://www.firestoneag.com/tiredata/load_inflation_tables.asp

 and my guess is this might be what applies to your application..  

  http://www.firestoneag.com/tiredata/info/tables/table_b.asp

  The 1000 US galls of water will weigh approx 8,330 pounds, plus whatever the tare weight of the sprayer is.

I am asssuming it's a trailed sprayer, and you have two  single tyres to take the weight, so divide the total weight by 2, and see from the table what inflation pressure you need.   Your tractor drawbar will take some weight also, but that probably should be left as a safety margin.

My initial look-through suggests that your tyres are overloaded  seriously in that application.

But if you are talking an SP sprayer with 4 tyres, maybe not..