1. Since you love orange juice, you install plumbing from the orange juice container in the kitchen refrigerator to the breakfast area nearby. The spigot that delivers this orange juice is at exactly the same height as the orange juice container. If the container and spigot were connected only by a simple pipe, no orange juice would flow when you opened the spigot. Using the concept of pressure, briefly explain (A) why the juice wouldn't flow and (B) what is required to start the orange juice flowing.

2. You have a small pump installed in the orange juice container and now juice flows when you open the spigot. Assuming the pump uses its electric power perfectly efficiently, how is the total amount of energy consumed by the pump related to the total amount of juice that flows out of the spigot?

3. You also plumb the orange juice over to the guest apartment in another wing of the house. The spigot there is also at the same height as the orange juice container in the main refrigerator. When you open the spigot in the guest apartment, the juice flows much more slowly than it does from the spigot in the main kitchen. The pipes and spigots in both cases are identical, except that the guest apartment is much farther from the refrigerator and the pipe leading there is necessarily much longer. Explain briefly why that longer pipe slows the flow of juice.

4. You also plumb orange juice down to the bar area in the basement. Although this juice passes through the same pump that provides juice to the two spigots discussed above, the juice rushes out of this basement spigot at a much greater speed. It actually sprays into a glass, rather than pouring gently. This dramatic increase in the juice's kinetic energy appears to violate conservation of energy. From where does this kinetic energy come?

5. On the wall beside your bed, you have installed a narrow waterfall. Italian mineral water flows from a pipe at the top of this waterfall and is collected in a basin at the bottom. The soothing sound of the falling water helps you fall asleep and whenever you are thirsty, you can simply place a cup in the falling stream and get a drink. You notice that the lower the cup is in this stream, the faster the water is moving when it enters the cup. Explain this observation in terms of the various forms of energy that water in a streamline can have.

6. When water in the waterfall strikes the bottom of your cup, it essentially stops and its kinetic energy drops to nearly zero. What becomes of that energy?

7. You plumb shampoo and conditioner into the shower stall. To avoid having to install a pump, you simply put the storage containers in the attic above the shower and allow gravity to propel the fluids through the pipes. But you sensibly select very wide pipes for these two fluids. Why is a large pipe diameter so important in this case?

8. When you close the shampoo tap, the pressure inside the tap is large. There is a bottle of the same shampoo on a shelf to the right of the tap and its pressure is atmospheric. Since both the shampoo in the tap and the shampoo in the bottle are motionless and at the same height, how can one be at high pressure and the other be at low pressure? Doesn't that violate Bernoulli's equation?