Final answer:
The given details pertain to fluid dynamics in physics, focusing on gauge pressure and fluid flow. Specific calculations involve using Bernoulli's equation and principles related to pressure, fluid velocity, and density.
Step-by-step explanation:
The initial question about an air gap in plumbing does not match the subsequent detailed physics questions that follow it related to fluid dynamics and gauge pressure. However, regarding the provided information about a tapered pipe, gauge pressure at the water main, and an airtight dispenser, these all pertain to the principles of fluid dynamics, Bernoulli's equation, and static fluid pressure. For example, to calculate the gauge pressure needed for water to emerge from the tapered pipe with a specific speed, Bernoulli's equation would be used, factoring in the difference in height between the two ends of the pipe and the velocity of the water at the smaller end. When considering the water main pressure problem, one would apply principles of fluid flow and continuity to relate pressure drops to flow rate changes. Each of these problems requires understanding of pressure, fluid velocity, density, the effect of gravity in fluid motion, and the conservation of energy in fluid flow. These concepts fall under the broader umbrella of physics, specifically fluid mechanics, which is typically studied during college-level physics courses.