Rocket taking off.

Hydrometry isn’t Rocket Science – It is Way Harder!

Every once in a while you do a Google search for one thing and can’t find it but discover something that is way better than what you were looking for. That happened to me today.

What I found is a Google book: A general formula for the uniform flow of water by E. Ganguillet and W.R. Kutter, 1889.

There are many reasons why I think every stream hydrographer should read this book but one thing that caught my attention was the anecdotes about false starts in the science of hydrometry. In particular, there is a story about how Galileo turned his attention from the sky to the flow of rivers.

Apparently, Galileo opposed a plan to straighten the Vicentio River and maintained the velocity of the water would be the same regardless of the length of the river given the same total fall. The engineer responsible for the project was unable to refute Galileo and when the project was not undertaken for other reasons came to the conclusion that “Galileo had the misfortune to accomplish his triumph of his opinion to the prejudice of the truth.”

In another quote Galileo “found less difficulty in the discovery of the motions of planets, in spite of their amazing distances, than in his investigations of the flow of water in rivers, which took place before his very eyes.”

A student of Galileo, Torricelli, “discovered that except for the resistance, the jets of water flowing from small openings was equal to that of bodies falling from space” and this discovery led to the deduction of the fundamental theory of hydraulics.

Guglielmini, at the end of the 17th century, developed the parabolic theory based on Torricelli’s theorem. The theory is expressed in the ν=√2gχ  where ν is velocity, χ is the distance from the surface and g is gravitational acceleration. One small problem with this theory as pointed out by Ganguillet and Kutter is that the velocity of flowing water must reach a maximum at the streambed and be zero at the stream surface. In 1732 Pitot was able to experimentally demonstrate the error in the parabolic theory using a device of his own invention.

The narrative continues on from there with a fairly comprehensive tour of the development of modern hydraulic theory. However, the formula being presented in this book did not stand the test of time and was just one of 7 formulas Robert Manning evaluated come up with his own formulation that is now in widespread use. Even though you may never have occasion to use the Ganguillet and Kutter formula this history of hydrometric science will give you a better understanding of our more familiar methods and techniques.

Hydraulic theory and the principles of space travel have much in common. Where they differ is that it took much longer to develop an understanding of the principles of flow in open channels.

Photo Credit: SpaceX | ORBCOMM | SpaceX’s Falcon 9 rocket launched the ORBCOMM OG2 Mission 1 on July 14, 2014 | License

  • Jaime Saldarriaga
    Posted at 11:40 am, September 21, 2012

    Stu: Thanks for this interesting historic note.

  • Alex Springall
    Posted at 6:12 pm, December 17, 2012

    That’s a most interesting article, Stu.
    May I add to your reading list “Della misura dell’acque correnti” (On the measurement of running water) by Dom Benedotto Castelli.
    Castelli was a student and later a colleague of Galileo. In his paper, published in 1628, is the first modern statement of the continuity equation Q=A1.V1 = A2.V2. If you can, you should try to get the facsimile edition with translation & commentary by Dean Blackman, ISBN 88 222 53353.

  • james okongo
    Posted at 1:26 am, July 1, 2013

    this is a good pieace. i am currently pursuing an msc degree in hydrology . i would like some help in choice of topic of research.

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