Approximately 0.5Bar pressure drop over 10m of 10mm table x copper tube at a flow rate of 6l/min. This would give a velocity of around 1.7m/s though. This is based on a water temperature of 10°C.
You seem confident that you'll be able to install 10m of 10mm without any fittings. Certainly doable though, I'm not saying it's impossible. Plus I'd have never thought that 10mm would be so workable.
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