Real-world problems are ugly, and simplifications and assumptions need to be made to make the problem solvable. The researchers tend to gloss over these assumptions—if they mention them at all. I think many researchers may not even realize that they are making them. Most researchers are graduate students and their advisors, who have never worked on real-world problems. As a starting point for their work, they rely on prior research papers that contain assumptions that the prior authors did not mention. As a result, real-world complications are often lost in legacy papers.

Last fall, I did a hydraulics quiz and readers seemed to enjoy it. So, here’s another one. See how you do and feel free to share. Answers are at the end, but don’t peek.

In my work in water and wastewater hydraulics, the two that show up most of the time are the Reynolds number and Froude number. A small Reynolds number indicates that viscous forces dominate, while a large value says that inertial forces dominate. A large Froude number indicates rapid flow, while a small number points to tranquil flow.

There are several reasons. First, the pressure is so high and constant in water systems in most developed countries that the effects of pressure on flow is negligible.

The most common question in pump selection these days is whether to use variable or constant-speed pumps.

One of the most fundamental decisions made in wastewater collection system design is choosing between a gravity or pressure sewer system. (Yes, there are other options such as septic tanks, vacuum systems, and onsite treatment, but once you decide on a central system of any significant size, gravity and pressure are usually the primary options.)

In a pipe network, all elements are connected such that changing anything at any location impacts the entire network. Adding a pipe in the far northwest part of the system affects flow in the far southeast part (minimally in many cases). The right way to model any pipe network is to include all elements that affect the behavior of the network.

They are nonlinear, partial differential equations which are about the worst kinds of equations to solve. About the only things that can make them worse are changes in state (e.g. steam condensing) or non-Newtonian fluids (e.g. mudflows). Numerous researchers have shown that it is impossible to arrive at a closed-form, analytical solution in the form v(r, φ, z) =… When people work with these equations these days, they almost always use numerical solutions. I heard a story once that Albert Einstein started his research in solving the Navier-Stokes equations but gave up because it was too difficult. He moved on to easy topics like quantum physics and relativity. I haven’t been able to verify this, but it makes for a good story.