the motor is not a resistive load, I think of it as a coil, instead of 'R', it's a combination of ohmic resistance and inductance. For inductance, I usually think of it as a bucket. The current flows in, filling it up, when the current is cut, the bucket is tipped over, pouring out its energy. High inductance = larger bucket.
When you increase the battery voltage, you increase the diameter of the hose, making filling faster without increasing heat loss in the ohmic part.
I was simplifying things for him, V=IZ is a better representation for an inductive load such as a motor where Z is the impedance of the winding.
You lost be with the plumbing analogy, I tend to work the other way around and equate water flow, height and restriction to electrical terms.
I've tweaked the link provided by sjpt (thanks sjpt) to compare motor characteristics using 48V LiFe battery with those from a 36V LiFe battery for example. Move the cursors to just before the point where the back EMF using the 36V motor comes into effect so that a fair comparison can be made (ie to a speed of 11.3km/h, I didn't play with the gearing, the indicated speed has no relevance to the discussion).
Our ebike motor simulator allows you to easily simulate the different performance characteristics of different ebike setups - with a wide selection of hub motors modeled, and the ability to add custom batteries and controllers and set a wide variety of vehicle parameters you'll be able to see...
www.ebikes.ca
look at the Mtr Amps (motor winding phase currents) and Batt Amps (current drawn from the battery) parameters. The battery amps is being current limited by the controller but the motor current is higher, as the link says "At low speeds when controller is PWM current limited, it is possible for the motor current to be several times greater than the current drawn from the pack."
With the cursors at this point:
1. The 36V system is more efficient
2. The 48V system is providing more current to the motor
3. The 48V system is providing more power