Why water pressure is higher in the lower stories of a building when one can can open the faucet on the roof story and have the water free fall? Say a building comprises 7 stories. Imagine also that the upper story has a faucet that leads to the ground (level 0)
Now it is well known (alas for those on the upper stories) that water pressure is highest in the lower stories, where residents enjoy good water flow. But this seem conflicting with the physics I know: if one opens the faucet in the top story, and let the water flow towards level 0, then the water will gain kinetic energy equivalent to the head of the water in the ground story faucet.
So why would the first enjoy better flow?
 A: In a first-order approximation, flow is determined by two things: (1) The size of the opening that the water flows through, and (2) the difference in pressure between the two sides of the opening. For a faucet, that would be the difference between pressure in the supply pipe and atmospheric pressure. If two identical faucets are opened by exactly the same amount, the one that is supplied with greater pressure from the pipe (i.e., the one on the lower floor) will provide more flow.
A: The simplest model for this is the Bernoulli equation
It has 3 terms, each representing the 'specific energy' i.e. energy per unit volume.
The balance of these 3 terms changes as fluid flows or changes height
BUT the sum of them remains constant - i.e. the energy switches between the 3 'types', being Pressure, Kinetic and Potential.
With no flow:
The water at ground level has High pressure, low potential and zero Kinetic
The water at high level has Low pressure, high potential and zero Kinetic
When you open both the taps the potential energy does not change in either case, BUT the pressure is transferred to kinetic.
Since the lower floors have higher pressure if follows that the velocity (flow) is greater a level 0.
The water that flow UP the pipe to the upper floors is gaining potential energy but losing pressure, and hence, when it flows AT THS SAME level it achieves less Kinetic, i.e. slower flow.
A: If there is a vertical pipe of let's say 1/2" from the water tank to the first floor, the flow from that pipe will be the same as from a 1/2" pipe from the water tank to the upper floor. In reality it will be even a little smaller due to the friction with the pipe walls.
But that is not the way that the system is designed. There is a vertical pipe of 2" for example, and horizontal pipes of 1/2" deliver water to faucets on each floor. Now, if the faucet of the first floor is opened, the water on the 2" vertical pipe is not in free fall. Therefore, each small volume of water is under the weight of the water column above it (pressure). That pressure is greater on the first floor, so the flow will be higher there.
But opening 16 faucet of 1/2" at the same time we get a free fall situation, and no matter the floor, the flow would be the same (if we disregard friction).
