Energy in fluids

As everyone knows, water flows downhill. This happens because its gravitational energy is changed into other forms -- sound, swirly motions in the water, and finally thermal energy (that can be detected as a tiny increase in temperature). The energy is now in many forms, and shared with everything nearby. Once the energy is shared this way, the water cannot regain it -- having moved down, it stays down. To get the water back to the top of the hill, energy has to be added -- by a pump, or the sun, or some other external agent.

a pond with a wavy surface and a pond with a flat surface We can use the energy concept to explain why the surface of a pond is flat. Suppose there was a pond whose surface was not flat. Then the "hill" of water on one side can move into the "valley" on the other. Water has moved downwards, decreasing its potential energy. The surface is flat because this gets the water as low as possible.

Energy considerations also explain how fast water runs out of a container. water running out of a tank Consider a tall tank of water, and suppose we remove a small amount -- let us say 1 liter (a mass of 1 Kg) -- by an outlet at the bottom. Even though we removed the water at the bottom, there is not an empty space there -- water moved in from surrounding regions to fill it up. The volume of liquid in the tank is smaller by 1 liter, but to show this we have to look at the water level at the top of the tank, which is now slightly lower. The water that we removed seems to have come from the top of the tank, even though it came out at the bottom. Another way to accomplish the same thing would be to have the water flow out through an outlet near the top, and then fall to the bottom. The change in the gravitational energy is the same (because it depends only on how much water is where, and not on how it got there), and so the resulting kinetic energy of the water is the same, too.

A tank full of water (or a lake full of water, behind a dam) can be regarded as a source of energy (as well as a source of water itself). Because the energy remains in the tank until we start to drain it, this kind of energy is sometimes referred to as potential energy.
a bottle with holes in it

Here is a picture of a container with several holes at different heights. (You could make this device for yourself. All you need is a container and a large needle or a drill; it's a fun thing to do on a hot day.) Where the stream from the top hole passes the stream from the bottom hole, they are going the same speed, but in different directions. The stream from the top hole is going fast because it has fallen many centimeters since it left the bottle. The stream from the lower hole was already going fast when it came out of the bottle. The speed of the water as it comes out of the bottle is greater towards the bottom, and so the jet goes farther horizontally.

Another way to describe this effect is in terms of the concept of pressure. The pressure is higher at the bottom of the container, which pushes the water out faster. These two explanations sound different but actually are not: although pressure is usually stated in terms of force per unit area (pounds per square inch, for example), it determines how much the energy of the system will decrease when a unit volume of fluid leaves, and could be stated as energy per unit volume. It is the energy that is turned into kinetic energy when a volume of water leaves the tank. This energy is higher for water at the bottom of the tank because all the water above the hole gets to move down a little bit.

Water pressure increases as we descend into a tank of water. This can be explained in two equivalent ways:

  1. as we have just seen, removing a small amount of water from the bottom of the tank makes a big change in the energy, since all of the water in the tank gets to move down a little;
  2. a surface at the bottom has to hold up all of the water above it, giving an increasing force on its area.

Siphons