Problem Set #5
Goal of Problem Set #5: This assignment is meant to help you understand:
  1. pressure in fluids,
  2. pressure potential energy, gravitational potential energy, and kinetic energy,
  3. energy conservation in fluids,
  4. viscosity
A hurricane has toppled trees in your rural neighborhood and you are without electric power. How unusual! But as inconvenient as it is to be in the dark, a rural power outage has an added challenge: you are also without water! With no electricity to operate the pump in your well, this power outage is going to be really unpleasant.
1. You're getting thirsty. You lift the cover off the well and peer into it with the aid of a flashlight. 50 feet (15.2 meters) below you is water. You lower a long plastic tube into the well, so that the bottom end is in the water, and you try to suck the water up this giant "drinking straw." Can you succeed in drinking water this way? Explain briefly why or why not.
After a day or two, you're ready for a shower, even if it's cold water. Using a rope, you lower a bucket into the well and lift up some water. You carry that water into the house and pour it into a large basin in the basement. With repeated effort, you manage to fill the basin with water. You then use a piece of plastic tubing to connect the basin's water to a faucet in the basement, turn on the faucet, and thereby convert the basin into an open water tank. That tank can freely exchange water with the house's plumbing. Most importantly, water can flow into the plumbing from that tank.
2. The basement water tank is open to the atmosphere, so what is the approximate water pressure in your home's plumbing at the basement level?
3. When you turn on the basement shower, approximately no water comes out. Why not?
4. In a flash of insight, you realize how to remedy the situation. You first turn off the basement faucet and shower. You then carry the basin of water up to the attic and connect it to a faucet up there. As before, you connect the basin to a faucet that's turned on and convert the basin into an open water tank. The attic in your house is 33 feet (10 meters) above the basement. What is the approximate water pressure in your home's plumbing at the basement level now?
5. When you turn on the basement shower this time, water comes out. It's not a particularly intense spray, but it's usable. However, just to be sure that you're not missing something, you check the showers on the other floors of your home: the ground floor, the second floor, and the attic. Will water flow out of these three showers and, if so, how will the spray at each location compare with the spray in the basement shower?
6. The plastic tube is still connected to the basement faucet, so you turn on that faucet and use the tube to spray a little water up into the air through the basement window. You notice that the water won't go any higher than the attic of your home. There is a good physics reason for why the water won't travel any higher than the attic. What is that reason?
7. After turning off the basement faucet, you return to the basement shower and turn it on again. You discover that the more water you allow to flow out of the shower head, the slower that water travels as it emerges from the head. There is still plenty of water up in the attic basin, so that's not the problem. Somehow when you allow lots of water to flow through the plumbing, that water loses its ability to spray hard out of the shower in the basement. What is happening to some of the water's energy when you turn the shower on fully?
8. You're done with your shower and you turn it off. A few hours later, the electric power is suddenly restored and the well pump turns on. The attic basin immediately starts to refill with water. Beginning with electric energy, briefly follow the flow of energy as it goes from the power company to its final forms in the water in the attic basin. Be sure to consider the effects of viscosity. [Note: You can neglect the details of energy flow in the pump itself and simply let the energy flow directly into the water instead.]