See Photo- analyze my sump pump outlet

Help me ID parts of this sump pump drain system outside my house. (If I did this right, you should be able to click on below and see photo) And why it works.. or doesn't work the way it does...
http://photos12.flickr.com/15456715_6ea7a29b0d.jpg
It is the sump pump drain/setup outside my home (1970's cheaply built subdivision home in upper midwest)
Ignore wiring you see, it is TV cable & AC power and not related to drain system.
On top is the outlet from the basement, black corregated pipe connected to the outlet from the house. It runs into top of 4" pipe which comes up out of ground. The 2" "T" coming off to the right is where the water has always come out, since I have owned the house (7 years) Under that is a makeshift PVC drain that I fashioned last year, it goes underground and drains out on lawn 20 feet from house. I did that as a temp measure to get water from the base of house until I came up with better plan.
When I looked down the 4" pipe that goes into the ground, I saw it went down maybe 18" and then seemed to have an elbow and seemed to lead away from the house foundation.
My question is this: Why does the water come out the top "T", I assume the pipe leading into the ground was at one time a way for water to be carried from the home... but perhaps it is plugged or something, which causes the water to come out the top "T", which I am guessing could have been a relif type outlet in the event the main drain is clogged. Is that right? Is there any other reason for that pipe to exist? I have never found any kind of outlet for that pipe out on the lawn.
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The fact that it's a 4" pipe that the sump goes into would suggest that it's possible it was tied into the sanitary sewer system, perhaps through a clean out fitting. That is not allowed in most areas. However the fact that water won't go in it argues against that. What's on the other side of the basement wall? Does the sewer exit through that wall in that location? If not, then it's probably not tied into the sewer. Could be just a whacko hook up to an underground drywell that failed, though it's unusual to use 4" pipe for that.
But probably doesn't matter. If you have a good discharge spot 20 ft away, I'd just permanently use that.
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It actually my be a 3" pipe now that I think about it, not sure that is relevant.
On the other side of the basement wall is just the 2" PVC pipe that comes up the wall from the sump pump, then trough to the outside. The sewer connection is about 15 feet away, into the basement floor, which I assume is routine.
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Sump pumps are not rocket science. You run a pipe to a place where it can drain away from the house to a ditch, low area or whatever. If it drains to an area that the water will pool over the outlet, install an air relief at the high point to prevent syphoning water back into your sump when the pump shuts off.
I would re-pipe the whole thing with new pipe -- get rid of the corrugated section, it is probably ready to fail. Keep the pipe minimum 1 1/4" to 1 1/2" diameter. Run underground where practical. Also dig down and find out where that old pipe is running. If it is a sewer line it should be terminated properly.

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