My 2ps worth:
Under static conditions, the pressure will be the same whether it is a 1mm2 pipe or 1m2 pipe.
ie You will get the same water pressure out of a shower nozzle connected to either sized pipe.

Pressure = force per area

However, due to friction, once the flow has started, the pressure will drop off with the narrower pipe = less flow rate.

I'm no plumber, but the trick maybe was to make the h/w system closed - ie at mains pressure. ie nothing to do with pipe size.