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.

Answer: No, atmospheric pressure will not lift a column of water taller than 10 meters even if there is zero pressure above it.

Why: The surface water in the well is at atmospheric pressure. If you remove the air pressure from above part of that water, it will accelerate upward and begin to lift a column of heavy, dense water upward. By the time that column is 10 meters tall, it weighs as much as a similar column of the entire atmosphere. At that point, the atmospheric pressure well water will be unable to push the column of water any higher. It will not reach you and you will not get a drink.

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?

Answer: Atmospheric pressure.

Why: The surface water in your basin is in contact with the atmosphere and yet it is not accelerating. Therefore, its pressure is atmospheric. Because the basin and the basement plumbing are all at basically the same height, there are no gravity-induced changes in pressure in that plumbing and the pressure in the plumbing is all roughly atmospheric pressure.

3. When you turn on the basement shower, approximately no water comes out. Why not?

Answer: There is no pressure imbalance to make the water accelerate out of the shower head.

Why: With atmospheric pressure inside and outside the shower head, nothing is pushing on the water in the shower head. It is stationary everywhere and it experiences no accelerations.

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?

Answer: About 2 atmospheres (or about 200,000 pascals).

Why: The water in the basement is now supporting the weights of a column of water 10 meters high and a column of the earth's atmosphere. Both columns weigh roughly the same amount and require a pressure of 1 atmosphere each to support. The total pressure in the basement plumbing is therefore about 2 atmospheres (which is roughly 200,000 pascals of pressure, in SI units).

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?

Answer: Water will flow only out of the first and second floor showers, not the attic. The shower on the first floor will be weaker than in the basement, and the shower on the second floor will be weaker still.

Why: The lower the shower, the more gravitational potential energy that the water will be able to convert into kinetic energy as it travels down through the pipes and sprays out of the shower head. The attic shower is at the same height as the water basin, so it has no available energy to produce a fast spray. The second floor shower has a little energy available and the first floor shower has more. But the basement shower is still the best because it is the lowest and the water can release more gravitational potential energy on its way to the shower head.

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?

Answer: Energy is conserved and the water has only enough energy to return to its original height.

Why: The water starts motionless and at atmospheric pressure in the attic basin. When it sprays upward through the window and rises to its peak height, it is again motionless and at atmospheric pressure. Since energy is conserved and nothing is doing work on that water, its peak height can't be any higher than the attic basin's height. In fact, if energy is wasted en route as thermal energy, the water won't even reach that attic height.

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?

Answer: It was converted into thermal energy.

Why: As water moves through plumbing, it rubs and wastes some of its ordered energy as thermal energy. The faster the water moves through the plumbing, the harder it rubs and larger a fraction of its ordered energy its wastes. Thus when you turn the shower on fully, the faster moving water wastes more of its precious energy and the spray becomes weaker.

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.]

Answer: The pump transform electric energy into pressure potential energy (in the water). (As water rises in the plumbing and flows (slowly) into the basin,) this pressure potential energy becomes gravitational potential energy. (Because the water moves and rubs in the pipes,) some of the energy becomes thermal energy in the water.

Why: The pump starts with well water that has approximately no kinetic energy, no available pressure potential energy, and very low gravitational potential energy. To get that water to flow up the plumbing, it needs to boost the water's pressure potential energy. It can't very well boost the water's gravitational potential energy because that would require it to carry the water upward and it lives in the well. It can't very well boost the water's kinetic energy because that would require it to throw the water upward and the plumbing is not a good container for thrown water.

Once it is at high pressure and pressure potential energy, the water can lift itself upward through the plumbing until it reaches the attic. During that trip, it converts much of its pressure potential energy into gravitational potential energy. It enters the basin with most of its total energy in the form of gravitational potential energy. However, some amount of rubbing during the climb will have wasted a portion of its total energy as thermal energy. The water that arrives will have slightly less than the amount of total energy per liter given it by the pump and the missing total energy will take the form of thermal energy--the water will be slightly warmer than when it started in the well.