Question
Building backyard "vanishing stream" Water running approx. 5 ft wide , 30 ft. long on slight incline , at slow pace. At starting point a 4 ft.  mound , with a small " water fall " . What size pump , holding tank . proper piping to create pressure , and allow a continuous flow. Live in minnesota. would probablly Not run in winter. Thank You P.S. DOING THIS ON A VERY LIMITED BUDGET . ANY  "FRUGEL IDEAS" HELPFULL.

Answer
I am no expert on fountains, but I think what you need is a submersible pump in the tank end (the bottom) of the stream that would then pump into a small pond at the head of the fountain that will fill the resivoir and create overflow for your waterfall.  You should find a good design somewhere, or an example, and follow that.  You problbly wont need a huge pump, just enough to move emough gallons per minute from the bottom to the top, and probably some 3/4" PVC.