Final answer:
Water shot upwards in a fountain broadens because its velocity decreases under gravity, and thus its cross-sectional area increases. Conversely, water falling from a faucet narrows because its velocity increases, leading to a decrease in the cross-sectional area. Surface tension helps maintain the stream's shape but does not significantly alter these effects.
Step-by-step explanation:
The phenomenon where water shot upwards in a fountain broadens, but a stream falling from a faucet narrows, is mainly due to the principles of fluid dynamics, specifically the continuity equation. According to this principle, the product of the cross-sectional area and velocity of a fluid stream remains constant if the fluid's density does not change.
Hence, as the water in the fountain moves upwards, its velocity decreases due to gravity, so the cross-sectional area must increase, leading to a broadening of the stream.
On the other hand, a water stream falling from a faucet narrows because as it descends, the velocity increases under gravity. Thus, to conserve the product of area and velocity, the cross-sectional area must decrease. In terms of surface tension, it acts to keep the water together, but it's the change in velocity due to gravity that primarily dictates the stream's behavior in both cases.
Surface tension does play a role in maintaining the stream's shape but does not significantly change the overall effect.
Additionally, the Bernoulli effect can be cited to explain water pressure within a hose nozzle being less than atmospheric pressure.