The falling water will feed the pump inlet. Just think of siphoning- the way it works is water is drawn to a point lower than where it is fed- say one bucket 1m high and another one on the ground. As soon as the water level is lower than the 1m bucket, gravity will assist in drawing the water out of the 1m bucket. This works even if the tube extends 10m in the air out of the 1m bucket and then goes to the bucket on the ground.
So, the falling water draws up the other water. A water level works much in the same way.
When you calculate a pump's head height, you must consider the absolute height of what it will be pumping to with 0 pressure on the inlet. A pump (considering everything is strong enough to sustain the pressure) attached to a long tube filled with water that is draped over the empire state building could pump water like it was 0' head pressure if the tube end matched the elevation of the pump (not taking friction into account). However, if you take the end of the tube and lift it over the max head pressure of the pump, it will not be able to pump the water.
In that same scenario, lts say you have a bucket on the roof that has 2 fittings on it. The setup is the same with the pump on the bottom and the other tube exits at the same level as the pump. This setup wont work because the falling water is no longer a variable in drawing up the water. The water can fall independently from the pump's actions, so the pump must pump the 1,300 so odd feet to the top of the building instead of the 0' of the previous setup.
It is difficult to describe, but it is the truth.
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