Density — The Fundamental Equation

As we look deep into space, far from our Earth home, using the best tools science has developed — including the Hubbell telescope, which gives us today’s photo — we still see only two things: Matter and Energy. As far as we can tell, these are all there is to the Universe; these and only these.

Matter is the “stuff” of the Universe. It is defined as anything that has mass and occupies space.

But this definition leads to two more definitions. What is mass? Well, in one of the least satisfying definitions you are likely to encounter, mass is defined as the quantity of matter. It’s a bit of a circular definition, isn’t it? Matter has mass; mass is how much matter we have.

Perhaps a little physics will help. I bet that’s the first time you ever heard that! I say that because we all have a feel for what weight is. And weight and mass are related concepts. To a physicist, weight is a force, and force equals mass times acceleration. In the case of weight, the acceleration is that of gravity. This acceleration varies depending upon our place in the Universe. But as long as we confine ourselves to the surface of our planet, gravity doesn’t change. What this means for us is that weight and mass mean essentially the same thing — as long as we stay here on the surface of Earth.

Since we are concerned about water systems, this is a pretty safe assumption … although I have known a few Operators that I thought might be heading back to the Mother Ship soon.

So how about space? In this definition, space is not the region beyond Earth. Instead, it is a far more familiar concept. Think volume, instead.

So another way for us to define matter is anything that weighs something, and has some volume.

The weights and the volumes could be incredibly large — as in the galaxy shown — or incredibly small — if we are considering atoms or molecules. Or they could be “normal” sizes, like we encounter in water systems work.

Which brings us to today’s title of Density, The Fundamental Equation. Why fundamental? Because density equals mass divided by volume. (Or weight divided by volume, if we keep the discussion above in mind.) Density is the ratio of the only two terms that we use to define matter, which is all the stuff of the Universe.

Water has a pretty high density, especially for a liquid. If you’ve carried a bucket of water, you know this to be true. That relatively small volume weighs a lot! Its density is greater than that of crude oil, for example. And we can tell this because the oil floats on the water.

I came across a good illustration of the difference between weight and density: Which is more likely to sink in water, and elephant or a penny? After a slight pause to think about it, you would tell me that the penny will sink — despite its obviously lower weight. Floating and sinking have nothing to do with weight, and everything to do with density.

One expression of the density of water is 8.34 pounds per gallon. If we took 8.34pounds of water and heated it up, the weight would not change. However, the volume would expand slightly. When this occurs, the density decreases! This means warmer water will float on top of cooler water. And we see this all the time in the oceans and in deep lakes. In fact, we often see it in our distribution system storage tanks.

Density is truly a fundamental topic for Scientists to explore. But it’s also an essential concept for water system Operators. Check back with our May 8 blog to see how we use this equation for water systems math problems. And stay tuned for a few looks at how density impacts water quality in our distribution systems.

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