I have a small water pump with a brushed D.C. motor that is designed to operate off a 12 volt battery. With no load on the pump the current drawn from the battery is around 3 amperes. If the motor RPM continues to rise until the back-EMF nearly equals the supply voltage, why is the pump drawing such a large current? The mechanical losses are from brush and bearing friction and windage . I suppose that under no load the iron losses will greatly exceed the copper losses . It seems out-of-place for the power going to the motor to be ~36 watts. What is going on?
There is not enough information available to do more than guess at how the motor and pump are performing. The pump manual indicates the pump can pump at 20 gallons per minute with a 3.45 ft. (1 m) static head and 11.33 GPM with a 6.7 ft. (2 m) head. That is 12.6 watts and 14.3 watts actually used in lifting the water.
The motor is designed to cycle on and off frequently. Every 2.5 minutes the pump is supposed to run for a short time to detect the water level. When the motor is first turned on, the only thing limiting the current is the winding resistance. If the motor has a low winding resistance the current would be quite high and frequent starting would be hard on the commutator and brushes. It seems likely that the motor has a high winding resistance to limit the starting current. That means it is quite inefficient and doesn't draw much more current at maximum load than at minimum load.
Since there is probably some water in the pump most of the time, there will be some loss in stirring the water when there is no discharge. For all operating conditions, more than half of the input power is probably dissipated in the winding resistance.
DC motors have a commutator that switches the magnetizing current in one (or more) windings. Those windings (electromagnets) take current regardless of mechanical power draw, maximum current when the motor is stalled. When rotating, the motor takes less current, but you still need to remagnetize the iron parts in different polarities throughout the rotation cycle, and the iron parts will warm up as the commutator does so. Power draw can be minimized by controller trickery, but a bilge pump probably works most reliably when the design is kept simple.
Iron losses could be minimized by exotic materials, but when the pump has a real load, those losses wouldn't be important anyhow.