Water typically comes in at around 15 degree Celsius, so it needs to be heated by around 25 degrees to feel warm.
A regular high flow shower head flows up to 20 liters per minute (that’s 5.3 gpm in American). That’s 500 kcal/min of energy that needs to be added, which is 35 kW, or a total of almost 150A at 240V.
Indeed.
I guess you could also use an oversized heat pump in theory. With a setup like this, recirculation and/or wastewater heat recuperation would also need to be looked into. Either would significantly reduce the cost of running this.
But purely resistive heating without any form of recuperation would need impractical amounts of power.