Drinking fountains are such simple devices, yet they're incredibly likely to misbehave. About half the fountains you encounter deliver so little water that it barely dribbles out of their nozzles and the other fountains typically spray water up into your eyes like fire hoses.
1. Water enters a typical drinking fountain through a large pipe at almost zero velocity and a pressure that's about 6 times atmospheric pressure (normal atmospheric pressure plus an additional 5 atmospheres). The water then passes through a nozzle and sprays up into the air. If the drinking fountain did nothing to alter the water's total energy as it flows, how high would the water jet rise above the nozzle before coming to a stop and then descending? (Assume that the nozzle and water jet are vertical, and neglect air resistance.)
2. Once the water in this full-energy jet has left the nozzle, it's surrounded only by air at atmospheric pressure. What is the water pressure in this freely moving jet at a height of 10 centimeters above the nozzle?
3. You lean your head over into this full-energy water jet and place your mouth 10 centimeters above the nozzle. What is the approximate pressure of the water as it hits your teeth and comes abruptly to a complete stop?
4. To prevent you from losing teeth or fillings, the people who built the drinking fountain included a pressure regulator that causes water in the free jet to stop rising only 10 cm above the nozzle. What fraction of its original energy does the water retain after passing through this pressure regulator and what probably becomes of that missing energy?
Your internship at the Supreme Court is on hold after the justice you were planning to work for broke a leg hang-gliding. So you decide to use your intellect working at another job: night chef at the local Krispy Kreme donut shop. You are in charge of the whole donut production system. This system begins with the machine that squeezes narrow rings of dough out onto a little conveyor belt. The dough rings rise as they travel along the conveyor for roughly half an hour. The now large rings of dough drop into a river of hot oil and cook. And after being flipped and then lifted up onto a drying belt, a river of liquid glaze covers each donut with a sugary coating. When no one is looking, it's all you can do not to sit at the end of the glazing station with tongs, a bib, and a smile on your face.
5. During the rising process, yeast in the dough converts some of the dough's sugar molecules into simpler molecules that include carbon dioxide gas. These gas molecules accumulate in the dough. In terms of density, pressure, and force, explain why these gas molecules cause the dough to rise, even against the force of gravity and the inward elastic forces of the dough itself.
6. The moment a ring of dough falls into the hot oil, it begins to swell up significantly. Explain this sudden swelling of the donut.
7. The glazing station uses a pump to recirculate the thick, hot, liquid glaze. Glaze accumulates in a pan below the donuts and is pumped up to a spigot above the donuts. It pours from that spigot as a smooth curtainlike sheet of glaze through which the donuts must pass on their way to the sales counter. The pipes carrying the glaze from pan to pump to spigot are surprisingly wide, despite the fact that they don't carry all that much glaze each second. In terms of viscosity and pressure, why does the glazing station need such large-diameter pipes for handling the glaze?
8. The thick glaze pours as a smooth curtain over the donuts and leaves each of them with a smooth shiny layer of glaze. If watery glaze were used instead of thick glaze, it would splatter all over and leave the donuts looking like they'd been sprinkled with droplets. Why does the glaze's thick character cause it to flow so smoothly and form such a smooth layer on the donuts?