But you need to appreciate that all these things you're talking about are pipes with different diameters..
"At the washer" - I presume you mean that brass screw on top of the pressure pump?
Small hole; it'll blast out of it
Then you connect the pressure hose; large hole, it'll pour out of it
Then you connect the gun trigger handle; large hole, it'll pour again
Then you connect the lance with pressure jet tip, tiny hole, should blast out of it
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You can't look at the amount of water emerging from the pressure hose and say "it seems less/more pressure than X"
You need to be more scientific; collect the water in a bucket and time the period required to generate the volume.. Repeat for each component you connect; it will tell you where the restriction is coming as there will be less water delivered per the same time period after connecting that part
When liquid passes through a pipe, for a given pressure, the flow rate is the same (more or less). If you place a restriction in the pipe the water speeds up to get past it and keep the same volume flow rate (smaller pipe, faster water movement, same volume delivered)
Incidentally exactly the problem with roadworks closing 2 lanes of a 4 lane motorway; if the 4 lanes of cars doing 70mph did 140mph through the 2 lane roadworks there would be no tailbacks
Water doesn't tailback; you make the hole smaller and smaller, it blasts out faster and faster to keep up, but the pressure is the same