Kansas soil is an odd thing. If you have ever seen the Kansas and Missouri rivers you understand that heavy sediments from this soil are part of it. Eventually that water with the consistency similar to chocolate milk winds up in the Mississippi and then on to the gulf of Mexico. In different soil like Ohio or Florida sediment is a non issue. Sometimes pictures say a thousand words On installation. Here is an example How agricultural drainage works
Never saw a system this big put in but I know the concept. In Kansas normally the Drainage pipes are not over 12" - 15". Pipe can be extremely expensive and the larger stuff is much more expensive. For a 15" stick of pipe 20 feet long it costs around $400 . Some used perforated pipe some prefer terraces to a location that collects in a small pond then drains through a pipe that’s perforated sitting verticle I have seen it both ways depending on the installer. Most systems are 4" to 6" for small areas like a yard. https://www.tractorsupply.com/tsc/product/culvert-hdpe-15-in-x-20-ft-hdpe-1520.
This is the small inexpensive system normally used at a house we here referred to as a French drain.
Water like what’s in my pond was ran through a rock filter so would be considered relatively clean for this area
https://growingfruit.org/t/ponds-are-a-great-investment/7033