GrInGo04:
I will use a relay then.
Not only a relay! An Arduino can't drive that directly either. Then you need a transistor (and a diode and resistor) as well. That's why I said relay module, that has all that build onto it 
GrInGo04:
Isn't the step up voltage regulator job to deliver the power to the water pump?
But where is the step up getting it's power from then?
Power is not the same as voltage. P = U x I and for a Arduino pin that means 5V x 40mA = 200mW... And that's not even including the losses in the step up