To fill a bucket of water

If we can choose the height(within the range of bucket) which the water is pumped into the bucket,
we could choose to pump the water at the highest point of the bucket, the middle point between the highest and the bottom of the bucket and the lowest point of the bucket. Which is the most energy efficient way to pump the water?

You don’t have to study three years of fluid dynamic to realize that pumping the water at the lowest point would consume the largest amount of kinetic energy just to fight off the weight of water pumped to the bucket; lesser if we choose the middle. And we virtually waste no energy (except against liquid-air friction) if we choose the pump at the height of the bucket.

To illustrate it, we just need to look the amount of pressure required to pump out the water at various instant. Naturally, when we choose the bottom of bucket to begin with, the pump would have to continually spare a part of kinetic energy to prevent water already pumped to the bucket going back to the pump. There will be less when the pump is the middle, and there will be none if the pump is positioned at the height of bucket.

The curious part is: The result are all the same, but the amount of energy spent is different. Where does the extra energy gone to?

waterbucket1

Morale of the story: In order to save electrical energy from the water pump, it is best to fill the water bucket from the highest position.