Is this question on the Navier-Stokes equations on topic?

Question

Two days ago, the question What is the physical interpretation of the second term in the viscous stress tensor in the Navier-Stokes equations? was asked. In essence, it asks about the "physical interpretation" of the term $\nabla \cdot \mu (\nabla\vec{u})^T$ in the Navier-Stokes equations, which are very important in fluid dynamics.

It's a good question - one of my favorites of the last few weeks - but I'd like to discuss whether or not it's on-topic. The only reason I ask is because the immediate application to engineering is not necessarily obvious - for example, it could be used for a numerical simulation of some natural process, which, it could be argued, is falls in the realm of the natural sciences, not engineering. There are other equations which fall even more into the grey area.

I write "could be argued". I think it could go either way - and we should keep in mind that it doesn't matter if it falls on-topic on some other Stack Exchange site. So long as it's on-topic on Engineering.SE, it should be warmly welcomed.

So is this question (and others like it) on-topic, or not?

Answer 1

Navier-Stokes is one of the fundamental equations in the field of hydraulics. From that fact alone we can be confident that:

• A significant portion of our target audience will find this question and its answer(s) useful and relevant to engineering problems.
• A significant number of our users will be uniquely qualified to answer this question because of their engineering background.

For me, that's enough to call the question on-topic. I don't think there is a "grey area" here or that we need to identify one specific engineering application to make that determination.

We can flip these points around to examine when a conceptual question might be off-topic as well. If we expect that a certain question and its answer(s) aren't useful in an engineering context or that our users wouldn't draw meaningfully on their engineering background in answering the question, then we can reasonably argue that the question's off-topic. I don't think this question meets either of those criteria.

Answer 2

the immediate application to engineering is not necessarily obvious

I would ask why there has to be an application. While it's true that a lot of engineering deals with taking concepts from other fields in math and science and applying them to solve real-world problems, not all engineering is about the application. Otherwise, what would be the point of a Ph.D. in engineering? The research conducted at universities around the world does not necessarily lead directly to new products; things may be developed from that research, but that research is about pushing the boundaries of our knowledge as a society.

To me, this is the side of engineering that this question is on. That's not to say that this is a research topic that will get someone $1,000,000. But it's about the theory behind engineering, and understanding an equation that is vital to a massively important branch of engineering. We could go back and forth all day long on whether Navier-Stokes is more physics or engineering, and what I'll say to that is that though I didn't take a lot of physics courses, I only ever saw it come up in any detail in engineering courses. But more important I think is the fact that engineering exists on both theoretical and applied levels, and we shouldn't limit ourselves here to answering questions about an actual project someone has in front of them.

Answer 3

I would like to add that although application of the Navier-Stokes equation may not be obvious, it is an equation with a lot of applications in engineering. It is a statement of the scientific principle that momentum should be conserved. In particular the NS equation shows how this conservation principle applies to a Newtonian fluid undergoing flow. The principle of momentum conservation is one of the cornerstone of many engineering calculations and of equations that engineers use every day. Examples include sizing of pumps, design of pipe runs, and calculation of forces due to an impinging fluid jet (to take the classic textbook examples). Granted most engineers will apply the principle behind NS without even noticing that they are using it.