Actually I believe Brettski is in error (sorry) in stating that the cut out section of the pipe in the picture above would minimize vortex formation. The engineers who have designed my dams use a hooded inlet on pipes, so that when the water level is above the top of the tube, a vortex cannot form. A vortex forming will swirl air down into the tube and reduce its capacity. The hood prevents this vortex, so the water flows in a more laminar motion into the tube inlet.
If the tube in the picture was rotated 180 degrees, this would be a hooded inlet, and that what the NRCS engineers I've worked with would do in this situation.
The other thing to be careful with when using dual walled pipes (which I would definitely use over singe walled), is that they are bouyant. The first few feet of the pipe are only covered by a few inches of soil, gradually working up to a couple of feet. In a heavy rain, the water can soften this soil, allowing the end of the tube to lift up. Althought the tubing is pretty rigid, I've had it bend in these situations up to 30-40 degrees. Thus I would recommend placing large, heavy rocks on both sides and around the top of the tube. This will weight it down, and also keep varmints like muskrats from burrowing along the outside of the tube. We learned this the hard way.
Bill