It is true according the Beananimal's site; the action of the pump moving water generates heat/energy in an amount equal to the wattage that the pump consumes.
Q: How much heat does my submersible pump add to the aquarium?
A:For our purposes, almost 100% of the energy consumed by a submersible pump (mag-drive, powerhead, etc.) is converted to heat in the tank! The simple fact is that if you were to take a heater that consumed exactly 100W and a powerhead that consumed exactly 100W and placed them each in a 5 gallon bucket with a lid, both buckets would reach the same temperature in the same amount of time! Why? Much of the energy consumed by the pump is directly shed as heat into the water. What is left does work and that work (moving water) causes friction (water moving against the objects and walls of the tank), most of which is converted to heat in the tank. When attempting to calculate the heat load on your tank, you should add up the total wattage of all submersible pumps in the system!
Source:
http://www.beananimal.com/articles/thermodynamics-for-the-aquarist.aspx
With all due respect, your equation is flawed.
You shouldn't add all the wattage of your heaters since they only come on for a small portion of the time whereas your pumps are running 24-7. Just because you have a 2,000 watt heater doesn't mean it's using 2,000 watts all the time. Pumps on the other hand are using energy all the time.
For example, during the coldest times of the winter, my heaters (1,800W) come on only about 20% of the time (5 hours per every 24 hour period) so that's the equivalent of 360 watts running 24-7. In other words, my tank requires the equivalent of a continuous 360 Watts of energy from my heaters to maintain 76F in the winter time. So it is more accurate to say that they are using 360 watts (not 1,800) when comparing them to what your pump draws, since the pumps are always using power, whereas heaters only draw power when the thermostat calls for heat.
There is no way that running more efficient pumps and relying on heaters to regulate your tanks temperature will increase your power bill, but you will likely see a reduction in your power bill if you run the most efficient pumps possible and rely on heaters to serve their function of regulating temps.
Your setup seems to work well for you, but to say that higher wattage pumps will reduce the total energy required to heat your tank is an incorrect statement.
The only reason I bring this up is because I have seen people on here say they chose a power hog of a pump because it will reduce their power bill in that their tank will require less energy to heat. This is false and during the warmer parts of the year can cause real problems with their tank overheating.
The amount of energy required to maintain any given temperature will require the same amount of energy, regardless of whether or not the energy comes from your pump or heater.
I’m pretty sure David was agreeing with me, at least if he knows anything about the laws of thermodynamics.