After re-reading your post I realize that I didn? really answer it. Here it goes again. The rotating impeller causes the liquid that enters the pump to increase in velocity. As I said we are taking input power from the driver and converting it to kinetic energy in the fluid. Kinetic energy is a function of mass and velocity. You are right, the amount of velocity we add to the fluid is fairly constant, but as more mass goes through the pump, it takes more energy from the driver, to continue to add the same velocity. The amount of mass pushed through the pump is dependent on efficiency and head. The fluid velocity exiting the pump is not constant, because in the diffuser the kinetic energy (or energy due to velocity increase) is converted to pressure. As a result the velocity of the fluid exiting the pump is lower than the velocity of the fluid at the tip of the impeller, and will be dependent on how much kinetic energy is converted to pressure in the diffuser.
I think I got it this time!