# Fluid Dynamics without partial derivatives

### From the author

Many years ago a mathematics student specializing in fluid dynamics visited a laboratory developing hydraulically-driven centrifuges. The engineers showed him an experimental facility where centrifuges were tested. They asked whether he could help with the issue of the pressure drop across the centrifuge. His careful answer was that if the Reynolds number of the flow is not too high then, given enough time and computing resources, he could write a computer code and calculate the pressure drop. The engineers laughed uproariously, and one said:  “Press that button (to switch on the facility) and read (the pressure drop) from that gauge!” They explained that they were interested in why the pressure drop and other flow features behaved in the way they behaved. Experiments and numerical calculations were not enough for that.  Understanding fluid flows intuitively would allow them to invent better centrifuges, and inventing things is what the cream of engineers does.

This incident started a long process which led to these pages. An experienced fluid dynamicist can often tell what the flow will be like in a particular situation without doing calculations or experiments. After many years of trying I developed such ability myself. It was not easy because I, as all others, had to gain this ability the hard way. These pages are aimed at helping others in gaining it easier.

Intuitive understanding of most common fluid flows comes from three sources:

1. Understanding the vorticity dynamics – the way to think about fluid flows.
2. Understanding boundary layers – the most important concept in fluid dynamics.
3. Knowing many representative cases of fluid flows – the facts one needs to know.

Fluid dynamics is heavily mathematical. Fortunately, these three sources can all be understood intuitively without mathematics. To convert the understanding to the estimates of the forces the fluid exerts on the immersed objects one also needs to know the control volume approach, which involves only simple formulae. These pages will take the reader step by step through fluid dynamics explained at an intuitive level, and to a great depth. As an active researcher, a university teacher, and an administrator, I do not have much time, but additions will appear when possible. To get notified about new pages, subscribe to the mailing list. What topic to write about next will often be determined by the questions of the readers and users of Flow Illustrator – just ask.

Sergei Chernyshenko

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