Tuesday, July 26, 2011

The Moody diagram: notes

In my studies, I have learned today what I was meant to learn many years ago. I can't stop getting surprised by the fact of having a certain level of knowledge at hand for years and, even after dedicate myself to the topic for a while, not having the stamina or curiosity to dig into it. I looked today into the basics of a few topics of the fluid dynamics and, again, I don't understand how I have being without grasping a tenth of it for so many years.

Anyhow, I am studying deeply friction in pipes, you know. Today, I have read the original paper of Lewis Moody in Transactions of ASME,1944. It is such an interesting historical piece! I honestly had lots of fun and read it like watching an action movie.

The derivation and generalization of the Hagen-Poiseuille relation between pressure drop in small pipes (blood conducts) and the forth power of the flow rate (which is the linear part for laminar flow in the Moody diagram) is from 1860. Before that date, the problem was approached from an engineering point of view and empiricism was exerted within the practical purposes of hydraulic calculations (by, mainly, I guess, the French school) and the aim was, solely, to compute the head loss in, mainly, water circuits. It could not be more: Reynolds' famous experiment in the University of Manchester which set the studies of the transition between the laminar and turbulent regimes is from 1883.

From that year on and, foremost, after the summer of 1904 (when Prandtl presented in Heidelberg his theory of the Boundary Layer), the problem is approached in a more scientific rationale, albeit keeping engineering applications in mind. The struggle with the transition and turbulent areas in the diagram by Prandtl and some of his students, apart from others, is extremely interesting (Blasius, von Karman, Nikuradse, Colebrook, etc.).

As a matter of fact, Moody's paper in 1944 is quite illustrative (take a look at the year as well). The paper has a discussion at the end, and different authors bring up collateral topics of extreme interest. The case Rouse-Moody about the originality and best form of the diagram is so, so entertaining. I think it tells a lot about the personalities of both or, at least, one can guess, as well as being of great historical interest.

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