John Fenton's Homepage


Cristina and John, May 2010


Home in Vienna


Collected papers - with links to PDF files

List of papers


Smoothing of data

Two programs for the smoothing of data in a file: Description of programs and their use, Download the programs.


Lectures in hydraulics, numerics, and maritime engineering

Introductory page

A First Course in Hydraulics

This is an introduction to hydraulics. True energy conservation is presented, and Bernoulli's equation is left to a subsidiary (and occasionally useful) role. It is an integrated momentum equation which is valid along a streamline and whose "constant" varies across streamlines. It is absurd to expect to apply it in fully-turbulent three-dimensional situations - for example the flow from a reservoir to a tap in a house. It is much more intellectually honest simply to use conservation of energy, which is more easily derived and is a more plausible model of most hydraulic problems.

Coastal and Ocean Engineering

A final year elective subject, dealing with elementary oceanography, water wave theory, tsunami, and coastal engineering

River Engineering

An introduction to waves and disturbances in channels, measurement, and structures

Computations and Open Channel Hydraulics

An introduction to numerical methods, presenting theory and applications largely using the optimisation package in Microsoft Excel. 



Home address

St-Ulrichs-Platz 2/4
1070 Vienna

Home +43 1 522 7467
John +43 664 7313 1035
Cristina +43 650 762 2417

Family History

John's mother spent many years researching the Family History

Recent research

Alternative-Hydraulics is where I publish my research these days, without having to bother about incompetent and self-interested referees seeking to deny me that publication. I think it was Heisenberg (but I can't find the quote) who said "any paper I have ever written, its importance was directly proportional to the difficulty I had getting it published".

Long waves in open channels - their nature, equations, approximations, and numerical simulation

This is a paper I presented to the 19th Congress of the Asia-Pacific Division of the IAHR in September 2014, Ha Noi, Viet Nam.

Several results are obtained that contradict current understanding and practice.

The long wave equations for a straight channel

It is surprising that derivations and presentations of the long wave equations have usually stopped short of presenting them in useable form. In this paper they are derived using the integral mass and momentum conservation equations. The derivation attempts to be a true hydraulic one, where quantities are modelled as simply as possible. It contains certain innovations.

Long wave equations for a channel curved in plan

The traditional fiction in hydraulics is that All Rivers Are Straight. They are not. This corrects the long wave equations, to allow for channel curvature in the horizontal plane, as exhibited by most rivers!

In 1995 at the IAHR Congress in London, I presented a paper with Guinevere Nalder, a student of mine, on this topic. It was later expanded considerably and submitted to the Journal of Hydraulic Research, where it was rejected.  One referee observed that we had not allowed for the separation of flow around bends. He presumably believed that the usual straight-channel approximation does allow for that. This is the theory based on that paper.

Calculating resistance to flow in open channels

The Darcy-Weisbach formulation of flow resistance has advantages over the Gauckler-Manning-Strickler form. It is more fundamental, and research results for it should be able to be used in practice. In this paper, available results for the limiting cases of smooth flow and fully rough flow are considered, and a general formula is obtained for calculating resistance as a function of relative roughness and Reynolds number. The result is similar to one found by Yen in 1991.

Accuracy of Muskingum-Cunge flood routing

Muskingum-Cunge flood routing has mathematical diffusion. It and its progeny are not accurate for streams with gentle slopes and where time variation is more rapid, and should generally be avoided. 

Coastal and Ocean Engineering - Steady water waves

One wave of a steady wave train,
                showing dimensions, co-ordinates and velocities

A computer program ("Fourier") that solves the problem of steadily-progressing waves over a flat bottom is described and made available here: Fourier

Programs that implement Stokes and cnoidal theories are also available. The instructions file for all is Instructions.pdf., which is also included in The latest changes are shown as highlighted comments.

The three wave programs are

  1. A Fourier approximation method whose only approximation lies in truncating the number of terms in the approximating series: - current version, 23 July 2015.
  2. An implementation of cnoidal theory, which is based on series expansions in shallowness, requiring that the waves be long relative to the water depth : - current version, 20 March 2015 (to be unpacked in a sub-directory of the Fourier one). This is an approximation, and not as applicable to higher waves as the Fourier method. It can be used as a check on that method - for long waves that are not high, both should give the same results.
  3. An implementation of Stokes theory, requiring that the waves be not too long relative to the water depth: - current version 20 March 2015 (to be unpacked in a sub-directory of the Fourier one). This is also an approximation, and not as applicable to higher waves as the Fourier method. It can be used as a check on that method - for waves that are not high or long, both should give the same results.

Maintained and authorised by John Fenton; Last modified: Thursday 23 July 2015