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The larger the height difference between a point in a liquid and its surface (AKA the deeper it is), the more the pressure exerted at that point.

To make it easy to visualize, imagine you are in a swimming pool. You get a feeling of being squeezed when you are under the water. The deeper you get (that is, the further you are from the surface), the stronger that squeeze is. That squeeze you feel is pressure.

Whatever your setup is, whether you take the water from the city main pipeline or you have your own water tank or water pump, the idea is the same. The downstairs tap is "deeper" than the upstairs tap, i.e. it experiences more pressure. Since the larger pressure means a larger force, the water in the downstairs tap experiences a larger force, so more water can come out of that tap.

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Q: Why filling a bucket from downstairs tap fills faster?
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