...if a house has one shower satisfactorily operating on mains water pressure, what happens if add another shower? Will the performance of my original shower improve or get worse?
I have regularly designed and built this sort of arrangement (albeit without the <3KW facility) simply with CT switches and contactors.
The first was a temporary botch on site to prevent 2 sump pumps running simultaneously as the common outflow was too small and the back pressure stopped either pumping.
I stripped the windings from a couple of 4 pole relays and replaced with a few turns of thicker enamelled wire to make current operated relays, then used the N.C. contacts to disable the other pump.
It was in use for several months while some building works were being done and then went into a site hut to stop the kettle being used at the same time as a fan heater. It may still be laying around.
IIRC the old box I used had a couple of hours run meters and wired those in too.
Edit: That does look like a nice solution to what is becoming a regular problem.
Edit 2: correct from N.O. To N.C. contact and it has also been used camping to prevent kettle being used at the same time as the toaster and microwave.
IIRC, when we've tried to design something using interlocked contactors it looked like you could get problems with how it behaved on restoration of power.
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