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[Guido]

One evening, a husband and wife are working in their garden. While watering the grass, the wife holds the hose horizontally and the water flows from the end of the hose. She twists the nozzle of the hose to partially close it and suddenly the water shoots farther from the end of the hose. This seems odd to her husband, who wonders, " Why does the stream of water travel farther, since it appears that less water is flowing from the end of the hose?" Your challenge is to give a scientific explanation for this seemingly unnatural phenomenon.

(f) Choose some real numbers and show how this equation provides an answer to the husband's apparent problem. What does this equation suggest about the relationship between velocity and area?

(g) Write a detailed explanation of your solution to this Thought Project.

(h) Suggest some other situations in which the Continuity Equation would come into play.