Hi Ben, and welcome to permies. Diameter of hose or pipe is critical to pumping efficiency because of friction with the walls of the pipe. As the diameter gets smaller, the cross sectional area of fluid that travels more or less unimpeded (laminar flow) decreases relative to the edge where there's lots of turbulence. The thickness of the turbulence stays roughly constant for a given speed of fluid movement, so as you shrink the hose, at some point you lose the laminar flow entirely. This really cuts the flow and puts back pressure on the pump.
Length matters as well. A trash pump will be rated for a given length of hose (across level ground) that's the same diameter as its outlet. Longer (or uphill) runs have more friction loss, so you won't be able to pump as far. To make the whole thing work, the best bet is to use the biggest hose you can to get the river water to the inlet of the pressure washer, since it's designed to push into small hose at high pressure.
Here are some examples from my Ace Hardware pocket reference tables on friction loss per 100 feet of pipe:
Pipe diameter | 2" | 1" | 3/4" | 1/2" |
1 GPM | 0 | 0.5 | 2.2 | 15.9 |
2 GPM | 0.1 | 2 | 7.9 | 57.2 |
5 GPM | 0.4 | 10.7 | 43.3 | * |
10 GPM | 1.3 | 38.4 | * | * |
20 GPM | 4.7 | * | * | * |
* don't bother - you'll blow up your pump
The values in the table get multiplied by a constant for the assumed friction of the interior surface of the hose or pipe and the result is how much static head is lost. New, clean hose might have a value of 120, and after a lot of use this would be around 100.