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There are many widely-held errors of understanding and application in open channel hydraulics. This is a
catalogue of some of them, but as it is a website under development, some of
the criticisms have not been detailed at this stage, for which I apologise. They will be soon.
The Bernoulli equation 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
more intellectually honest and simpler to use conservation of energy, which is more
easily derived and is a more plausible model of most hydraulic problems.
Reference can be made to On
the energy and momentum principles in hydraulics or to the energy
conservation chapter of
A First Course in
Hydraulics On a similar note, the Coriolis "energy coefficient" as conventionally-defined
is not - it is an approximation to the real energy transmission coefficient, see On
the energy and momentum principles in hydraulics, which also shows that both the corrected Coriolis energy coefficient and the Boussinesq momentum
coefficient should be further corrected to allow for turbulence. When
correctly defined, they form a very useful simple method of simulating
turbulent flows. Incorporating them, even if their value is not exactly
known, gives a useful reminder that we are modelling a more complicated
situation and excessive accuracy is not to be expected. The derivation of the long wave equations using non-orthogonal
bottom-oriented co-ordinates is mathematically wrong, and curvature terms
should be added if those awkward and poorly-defined co-ordinates are used.
Fortunately this is simply obviated by using cartesian co-ordinates. This
allows for a simple derivation of the equations, and it is easily shown that,
contrary to popular belief, the long wave equations can be used on steep
slopes, provided a simple correction is made to the slope term. See
The long wave equations for
a derivation of the equations for a straight channel. The Gauckler-Manning-Strickler equation has been a huge mistake. There is
little basis in fluid mechanics, and the most common method of obtaining
resistance coefficients seems to be by looking at picture books, where the
important underlying roughness is not visible, or by ringing a friend to find
out what he/she used on a similar stream. Using the Darcy-Weisbach formulation
was recommended by the ASCE nearly 50 years ago, and I used this in
The long wave equations.
Here,
Calculating resistance to flow in open channels, an explicit formula for
resistance is obtained in terms of the relative roughness and the Reynolds
number. Such a formula was presented by Yen in 1991. It is surprising that it
has not been adopted. The traditional
fiction in hydraulics is that All Rivers Are Straight. They are not. In 1995
at the IAHR Congress in London, I presented a paper with Guinevere Nalder, a
student of mine, on this topic:
Long
wave equations for waterways curved in plan. It was later expanded
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 the separation of flow
around bends ... Using complicated implicit methods to solve problems, when explicit
methods are simpler to understand, to teach, to research, and to implement.
This applies to the solution of problems with one independent variable, such
as the routing of floods through reservoirs, where the modified Puls method
is an absurd way to solve a simple problem (Reservoir
routing), and similarly the calculation of
the steady surface profile in a stream by both "Direct" and
"Standard" Step methods. In both cases, any simple explicit
numerical scheme for the solution of a differential equation is preferable.
This criticism also applies to unsteady wave propagation problems, where
unnecessary and complicated implicit schemes obfuscate the intellectual
development and have led to the commercial centralisation of hydraulics in
few hands. 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. I calculate the criteria for
when it can be used:
Accuracy of Muskingum-Cunge methods False interpretations from the method of characteristics have led people
to a faulty understanding of the behaviour of waves in channels. Long waves
are actually dispersive and diffusive; they travel at speeds generally
dependent on their wavelength and generally show finite diffusion effects.
There is no such thing as a "long wave speed". I believe that the simplest possible numerical method for the long wave equations, using
explicit finite differences, forward in time and centred in space, is actually
quite stable, with a not un-generous limit on time step, and is not
unstable as asserted by Liggett & Cunge (1975). I think that when they left
terms out of their
stability analysis, that misleading results were obtained, leading them to call it the "Unstable Method". Ever
since the field has been hampered by unwieldy implicit methods and dominated by
large software houses. Another perfectly good cottage-industry becoming a victim
of the Industrial Revolution. Spatial integration methods used in hydrometry are clumsy and the
most-commonly used one is wrong (Numerical
methods and mathematics in hydrography). This applies not only to conventional stream-gauging
operations, but also to implementations of ultrasonic time-of-travel methods,
where the incorrect method has been implemented, and whose manufacturers make
claims for accuracy that are unjustified. Conventional scalings and non-dimensionalisations of the long wave
equations make a fundamental a priori error in assuming that all time
scales and length scales are connected by the mean fluid speed in the channel.
The time scale is actually imposed by the inputs to the system, and the length
scale emerges from the system. This means that the unsteady term in the momentum
equation does not scale like the square of the Froude number. This is being
developed in a work under preparation. Recent model equations for the long wave equations over an erodible bed
use an incorrect model of the solid-fluid interface. The results of Lyn (1987) and Lyn & Altinakar (2002) for waves over an erodible bed are wrong. They
assumed the friction slope was constant and as a result obtain much over-simplified results. Analyses of the effects on a stream due to obstacles and bridges can be
quite wrong, as the HEC-RAS manual shows. Like the Curate's Egg, parts of it are
excellent, but those parts where the loss of momentum due to an obstacle is
ignored and the long wave equations solved alongside as if it were just a
channel narrowing, are best left ignored. Momentum can be used quite well to
solve the problem. This paper, presented at the IAHR Congress at Thessaloniki in
2003 gives an explicit formula for the backwater due to an obstacle:
Effects of obstacles on surface levels and boundary resistance in open channels.
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