Question

The water supply for a city is often provided from reservoirs built on high ground. Water flows from the reservoir, through pipes, and into your home when you turn the tap on your faucet. Why does water flow more rapidly out of a faucet on the first floor of a building than in an apartment on a higher floor?

Short answer

The flow of water depends upon the difference in pressure between the pressure in the pipe and the air pressure outside the pipe.

Step-by-step solution

Pascal’s law

The pressure in a fluid at rest varies with depth h in the fluid according to the expression:

$P=P_0+\rho gh$

Where $P_0$is the pressure at $h=5$and $\rho$is the density of the fluid, assumed uniform. Pascal’s law states that when pressure is applied to an enclosed fluid, the pressure is transmitted undiminished to every point in the fluid and to every point on the walls of the container.

Explain the reasoning

At lower elevation the water pressure is greater because pressure increases with increasing depth below the water surface in the reservoir (or water tower). The penthouse apartment is not so far below the water surface.

The pressure behind a closed faucet is weaker there and the flow weaker from an open faucet. Your fire department likely has a record of the precise elevation of every fire hydrant.