Like the others have said, there are too many variables in your question. Some of the things that will affect the amount of water that you will drain are the types of surface that you have, how long the grass is, how many trees there are and the slope of the land. Steeper land with short grass will move allot of water very quickly. Flat land with lots of trees will hold the water and you will get very little runoff compared to the short grass.
Then there is the design of the ditch. If it's just narrow, it will create more erosion, but take up less land. If it's wide, the water will move slower and you will have less erosion.
I try to make my ditches as wide as possilbe. I want to be able to mow them without risking my life on a steep slope. From a distance, my ditches should look natural and blend in with the surround landscape. That means moving more dirt then a narrow ditch.
Usually I start out digging the ditch as shallow as I think I can get away with and then I see what happens after it rains. It usually takes me a few times to get it right by taking a little away until I get it right.
Eddie