The (Very) Basics of Fluid Dynamics

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Before we boldly set forth to discover new and exciting Science we need to ask ourselves what we want to study. What are fluids? Why is dividing the world into fluids and not-fluids a good idea? The name “fluid” is a label that we assign to certain materials that behave in a similar way when put under stress. This is not to say that scientists stand around shouting at cups of water for not meeting their deadlines. What I mean in this case is mechanical stress. A fluid is defined as anything that cannot help but be deformed when a stress that doesn’t change the volume of the fluid is applied. What the hell does that mean, I hear you ask.

Imagine you’re holding a hot mug of tea and blow across it. The fluid will deform, forming ripples and movement. In other words, fluids flow. Compare this to what would happen if you blew across a mug full of solid steel. Unless you have extremely strong lungs, there will be no deformation of the steel. So steel is not fluid, unless by blowing on it you have somehow raised it to melting point, in which case you should probably see a doctor.

There is a very important caveat to the whole “not withstanding stress” thing. The stress needs to keep the volume of  liquid the same. If we squeeze a balloon full of water equally on all sides, the water inside will only compress a very small amount, and for most purposes we can regard it as incompressible. In this situation water does withstand deformation, but we still regard water as a fluid because the stress we are exerting in this case would change the volume of the water. This provides our first way (of many) to tell the difference between two different fluids: if one is compressible and the other is not.

So, now that we have come to the deep understanding that fluids are things that flow, we have answered our question haven’t we? Well, yes and no. We still have to find out which things flow. We already know that tea does, and that steel (at room temperature) doesn’t. So what about things like gases? Well, they can’t withstand stresses without deforming, so they’re counted as fluids too. Some people are surprised by this, mainly because in common phrases like “Brake fluid” or “He stopped jogging to take on some fluid”, the implication is that the fluid is a liquid, but this is not necessarily the case. Even the plasma that makes up the sun and the stars is a fluid.

Then there are the grey areas. Is a collection of grains of rice, an example of a granular material, a fluid? It can’t help being deformed most of the time, but it can still get jammed in a funnel. And if you push down on it when it’s jammed, exerting a stress, then it doesn’t deform. So what about custard? This can withstand deformation from sharp impact, but if you gently put your hand into it, it will behave like a fluid and deform. What about cars on a road? You can measure their density, speed, and how they interact. And they seem to “flow” along the road. Does that mean they are a fluid?

At this point, it is useful to bear in mind that being called a fluid is only a label that we as scientists give to things. If we want to label rice, custard or cars as fluids, we can.  So why would we want to? Well, in a lot of situations these things do behave in similar ways to other fluids, and mathematical techniques that work for normal fluids can also work in these situations. Measuring densities and speeds of cars is often a useful way for (mathematically capable) town planners to make decisions about infrastructure.

In fact these happen to be some of the most engaging cases to study precisely because they don’t behave exactly as we expect, and often under these circumstances our physical intuition can be quite misleading. However, the usefulness of extending the idea of a fluid depends heavily on context. If we want to describe the dynamics of rice or cars at a microscopic level, for example, a fluid mechanical approach isn’t at all appropriate.

Do you know of any other interesting examples where the boundary between solid and fluid is unclear? Do you have anything to add about my definition of a fluid? Let me know in the comments.

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About owenjordan

I grew up in Wales, studied mathematics at Cambridge, and am in the process of moving to Imperial College for a 4-year Masters/PhD in Fluid Dynamics. Hopefully, I will teach you something interesting about fluids. In my spare time I'm a musician, part-time gardener, rugby player, welsh speaker, and computer geek.
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