Hopefully I can help solve your dilema as im a professional tile contractor. I'll be the 4th generation to do this so my advice is based on decades of experience. What it really depends on is how much you want to spend. If you want to do it right and not worry about it ever again, it'll cost you more. In my opinion, I would hire a contractor to come in and tile the whole thing. Most people think that running tile to the low hole will fix the problem, this is only partially true as the water that is collecting there, is running off the hills surrounding it. So one must ALSO tile the hill to cut off the water from ever reaching the hole. Water will still collect in the hole on heavy rains, so i would suggest 2 things, either install a french drain (trench backfilled with stone, going from the tile all the way to the top) or a T fitting put in the tile with a piece of tile coming up to the top. In your case if its your yard or just a field, i would rather go the french drain route, its cleaner looking and theres no open tile for trash to go in an plug up the system. A 4" tile has the capacity to drain roughly 4 acres, which is way more than what your plannin on draining.
Tile depth varies, and old time practice was to put tile in deep an wide, somewhere around 4' deep on about 50' spacing, farmers could drain more acres with less tile. But as time went by, we found out that on top of pulling the water table down too low (bad for crop root development) it also had a long response time (time it took for rain water to soak in an get to the tile). So tile is now put in at an average depth of 2.5-3.0ft depth, and around 40' spacing. Tile should also have a minimum grade of .2, thats 2 tenths of a foot, a rise of 2.4'' every 100', this will ensure self-cleanout.
for a rough pricing estimate, 4" tile costs around 30cents a foot, at most you have 2.5 acres to tile. on 40' spacing it takes 1089 feet of tile per acre, so your looking at around 2800' feet of tile, plus a lil extra maybe to run to an outlet, so 3,000' will probably be more than enough. what will really determine the price is a contractors installation price, around here in NW ohio the going rate is 20 cents a foot, anywhere else it ranges from 50 cents to over a dollar a foot. guessing the rate is 50 cents, you'll have an installation cost of around $1500, plus $900 for the tile, a couple ton of stone for the french drain, lets say 7 tons at $250 a ton, so another $1750 plus a few fittings, your looking at ROUGHLY $4300. may sound expensive to ya, may not, if its put in right even your grandkids wont have to worry about it. hope this helps and if you have any questions, please ask, i dont mind helpin others out.
