SEE CALCULATION SUMMARY ABOVE
The following formula is used to calculate the power of heating element needed to heat a specific volume of water by a given temperature rise in 1 hour. Its from https://elementsofheating.wordpress.com/2012/09/26/how-to-calculate-the-kw-required-to-heat-a-volume-of-water-in-a-particular-time/
volume in litres x 4 x temperature rise in degrees centigrade / 3412
(4 being a factor and 3412 being a given constant)
for example 100 litres of water, to be heated from 10ºC to 42ºC, giving a temperature rise of 32ºC would give –
100 x 4 x 32 / 3412 = 3.75 meaning that the water would be heated in 1 hour by 3.75kW of applied heat.
For instantaneous water heaters the speed at which water can be heated (litres per minute), is the relevant measure. The temperature of 42ºC is my favourite shower temperature. The temperature of 10ºC is chosen as a typical mains water temperatures which in summer may be higher, and lower in the winter. You will get more flow in the summer , less in the winter, and the hotter the water you get, the lower the output.
3.75 KW Heats 100 litres/hr = 100 / 60 = 1.66 litres per minute (10ºC to 42ºC), 2.7 KW Heats 100 litres/hr = 100 / 60 = 1.66 litres per minute (15ºC to 38ºC)
The pro rata outputs for a 3KW and 7KW water heater is:-
3.00 KW gives 1.32 litres a minute (10ºC to 42ºC), 1.83 litres a minute (15ºC to 38ºC) 7.00 KW gives 3.08 litres a minute (10ºC to 42ºC), 4.27 litres a minute (15ºC to 38ºC),