In physics, fluid dynamics is a sub-discipline of fluid mechanics that deals with fluid flow—the natural science of fluids (liquids and gases) in motion. It has several subdisciplines itself, including aerodynamics (the study of air and other gases in motion) and hydrodynamics (the study of liquids in motion). Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space and reportedly modeling fission weapon detonation. Some of its principles are even used in traffic engineering, where traffic is treated as a continuous fluid.

Fluid dynamics offers a systematic structure that underlies these practical disciplines, that embraces empirical and semi-empirical laws derived from flow measurement and used to solve practical problems. The solution to a fluid dynamics problem typically involves calculating various properties of the fluid, such as velocity, pressure, density, and temperature, as functions of space and time.

Historically, ''hydrodynamics'' meant something different than it does today. Before the twentieth century, hydrodynamics was synonymous with fluid dynamics. This is still reflected in names of some fluid dynamics topics, like magnetohydrodynamics and hydrodynamic stability—both also applicable in, as well as being applied to, gases.

Equations of fluid dynamics

The foundational axioms of fluid dynamics are the conservation laws, specifically, conservation of mass, conservation of linear momentum (also known as Newton's Second Law of Motion), and conservation of energy (also known as First Law of Thermodynamics). These are based on classical mechanics and are modified in quantum mechanics and general relativity. They are expressed using the Reynolds Transport Theorem.

In addition to the above, fluids are assumed to obey the ''continuum assumption''. Fluids are composed of molecules that collide with one another and solid objects. However, the continuum assumption considers fluids to be continuous, rather than discrete. Consequently, properties such as density, pressure, temperature, and velocity are taken to be well-defined at infinitesimally small points, and are assumed to vary continuously from one point to another. The fact that the fluid is made up of discrete molecules is ignored.

For fluids which are sufficiently dense to be a continuum, do not contain ionized species, and have velocities small in relation to the speed of light, the momentum equations for Newtonian fluids are the Navier-Stokes equations, which is a non-linear set of differential equations that describes the flow of a fluid whose stress depends linearly on velocity gradients and pressure. The unsimplified equations do not have a general closed-form solution, so they are primarily of use in Computational Fluid Dynamics. The equations can be simplified in a number of ways, all of which make them easier to solve. Some of them allow appropriate fluid dynamics problems to be solved in closed form.

In addition to the mass, momentum, and energy conservation equations, a thermodynamical equation of state giving the pressure as a function of other thermodynamic variables for the fluid is required to completely specify the problem. An example of this would be the perfect gas equation of state:

:$p=\; \backslash frac\{\backslash rho\; R\_u\; T\}\{M\}$

where $p$ is pressure, $\backslash rho$ is density, $R\_u$ is the gas constant, $M$ is the molar mass and $T$ is temperature.

Compressible vs incompressible flow

All fluids are compressible to some extent, that is changes in pressure or temperature will result in changes in density. However, in many situations the changes in pressure and temperature are sufficiently small that the changes in density are negligible. In this case the flow can be modeled as an incompressible flow. Otherwise the more general compressible flow equations must be used.

Mathematically, incompressibility is expressed by saying that the density $\backslash rho$ of a fluid parcel does not change as it moves in the flow field, i.e., : $\backslash frac\{\backslash mathrm\{D\}\; \backslash rho\}\{\backslash mathrm\{D\}t\}\; =\; 0\; \backslash ,\; ,$ where $\backslash mathrm\{D\}/\backslash mathrm\{D\}t$ is the substantial derivative, which is the sum of local and convective derivatives. This additional constraint simplifies the governing equations, especially in the case when the fluid has a uniform density.

For flow of gases, to determine whether to use compressible or incompressible fluid dynamics, the Mach number of the flow is to be evaluated. As a rough guide, compressible effects can be ignored at Mach numbers below approximately 0.3. For liquids, whether the incompressible assumption is valid depends on the fluid properties (specifically the critical pressure and temperature of the fluid) and the flow conditions (how close to the critical pressure the actual flow pressure becomes). Acoustic problems always require allowing compressibility, since sound waves are compression waves involving changes in pressure and density of the medium through which they propagate.

Viscous vs inviscid flow

Viscous problems are those in which fluid friction has significant effects on the fluid motion.

The Reynolds number, which is a ratio between inertial and viscous forces, can be used to evaluate whether viscous or inviscid equations are appropriate to the problem.

Stokes flow is flow at very low Reynolds numbers, ''Re''<<1, such that inertial forces can be neglected compared to viscous forces.

On the contrary, high Reynolds numbers indicate that the inertial forces are more significant than the viscous (friction) forces. Therefore, we may assume the flow to be an inviscid flow, an approximation in which we neglect viscosity completely, compared to inertial terms.

This idea can work fairly well when the Reynolds number is high. However, certain problems such as those involving solid boundaries, may require that the viscosity be included. Viscosity often cannot be neglected near solid boundaries because the no-slip condition can generate a thin region of large strain rate (known as Boundary layer) which enhances the effect of even a small amount of viscosity, and thus generating vorticity. Therefore, to calculate net forces on bodies (such as wings) we should use viscous flow equations. As illustrated by d'Alembert's paradox, a body in an inviscid fluid will experience no drag force. The standard equations of inviscid flow are the Euler equations. Another often used model, especially in computational fluid dynamics, is to use the Euler equations away from the body and the boundary layer equations, which incorporates viscosity, in a region close to the body.

The Euler equations can be integrated along a streamline to get Bernoulli's equation. When the flow is everywhere irrotational and inviscid, Bernoulli's equation can be used throughout the flow field. Such flows are called potential flows.

===Steady vs unsteady flow===

When all the time derivatives of a flow field vanish, the flow is considered to be a steady flow. Steady-state flow refers to the condition where the fluid properties at a point in the system do not change over time. Otherwise, flow is called unsteady. Whether a particular flow is steady or unsteady, can depend on the chosen frame of reference. For instance, laminar flow over a sphere is steady in the frame of reference that is stationary with respect to the sphere. In a frame of reference that is stationary with respect to a background flow, the flow is unsteady.

Turbulent flows are unsteady by definition. A turbulent flow can, however, be statistically stationary. According to Pope: This roughly means that all statistical properties are constant in time. Often, the mean field is the object of interest, and this is constant too in a statistically stationary flow.

Steady flows are often more tractable than otherwise similar unsteady flows. The governing equations of a steady problem have one dimension fewer (time) than the governing equations of the same problem without taking advantage of the steadiness of the flow field.

Laminar vs turbulent flow

Turbulence is flow characterized by recirculation, eddies, and apparent randomness. Flow in which turbulence is not exhibited is called laminar. It should be noted, however, that the presence of eddies or recirculation alone does not necessarily indicate turbulent flow—these phenomena may be present in laminar flow as well. Mathematically, turbulent flow is often represented via a Reynolds decomposition, in which the flow is broken down into the sum of an average component and a perturbation component.

It is believed that turbulent flows can be described well through the use of the Navier–Stokes equations. Direct numerical simulation (DNS), based on the Navier–Stokes equations, makes it possible to simulate turbulent flows at moderate Reynolds numbers. Restrictions depend on the power of the computer used and the efficiency of the solution algorithm. The results of DNS have been found to agree well with experimental data for some flows.

Most flows of interest have Reynolds numbers much too high for DNS to be a viable option, given the state of computational power for the next few decades. Any flight vehicle large enough to carry a human (L > 3 m), moving faster than 72 km/h (20 m/s) is well beyond the limit of DNS simulation (Re = 4 million). Transport aircraft wings (such as on an Airbus A300 or Boeing 747) have Reynolds numbers of 40 million (based on the wing chord). In order to solve these real-life flow problems, turbulence models will be a necessity for the foreseeable future. Reynolds-averaged Navier–Stokes equations (RANS) combined with turbulence modeling provides a model of the effects of the turbulent flow. Such a modeling mainly provides the additional momentum transfer by the Reynolds stresses, although the turbulence also enhances the heat and mass transfer. Another promising methodology is large eddy simulation (LES), especially in the guise of detached eddy simulation (DES)—which is a combination of RANS turbulence modeling and large eddy simulation.

Newtonian vs non-Newtonian fluids

Sir Isaac Newton showed how stress and the rate of strain are very close to linearly related for many familiar fluids, such as water and air. These Newtonian fluids are modeled by a coefficient called viscosity, which depends on the specific fluid.

However, some of the other materials, such as emulsions and slurries and some visco-elastic materials (e.g. blood, some polymers), have more complicated ''non-Newtonian'' stress-strain behaviours. These materials include ''sticky liquids'' such as latex, honey, and lubricants which are studied in the sub-discipline of rheology.

Subsonic vs transonic, supersonic and hypersonic flows

While many terrestrial flows (e.g. flow of water through a pipe) occur at low mach numbers, many flows of practical interest (e.g. in aerodynamics) occur at high fractions of the Mach Number M=1 or in excess of it (supersonic flows). New phenomena occur at these Mach number regimes (e.g. shock waves for supersonic flow, transonic instability in a regime of flows with M nearly equal to 1, non-equilibrium chemical behavior due to ionization in hypersonic flows) and it is necessary to treat each of these flow regimes separately.

Magnetohydrodynamics

Magnetohydrodynamics is the multi-disciplinary study of the flow of electrically conducting fluids in electromagnetic fields. Examples of such fluids include plasmas, liquid metals, and salt water. The fluid flow equations are solved simultaneously with Maxwell's equations of electromagnetism.

Other approximations

There are a large number of other possible approximations to fluid dynamic problems. Some of the more commonly used are listed below.

The Boussinesq approximation neglects variations in density except to calculate buoyancy forces. It is often used in free convection problems where density changes are small.

Lubrication theory and Hele-Shaw flow exploits the large aspect ratio of the domain to show that certain terms in the equations are small and so can be neglected.

Slender-body theory is a methodology used in Stokes flow problems to estimate the force on, or flow field around, a long slender object in a viscous fluid.

The shallow-water equations can be used to describe a layer of relatively inviscid fluid with a free surface, in which surface gradients are small.

The Boussinesq equations are applicable to surface waves on thicker layers of fluid and with steeper surface slopes.

Darcy's law is used for flow in porous media, and works with variables averaged over several pore-widths.

In rotating systems, the quasi-geostrophic approximation assumes an almost perfect balance between pressure gradients and the Coriolis force. It is useful in the study of atmospheric dynamics.

Terminology in fluid dynamics

The concept of pressure is central to the study of both fluid statics and fluid dynamics. A pressure can be identified for every point in a body of fluid, regardless of whether the fluid is in motion or not. Pressure can be measured using an aneroid, Bourdon tube, mercury column, or various other methods.

Some of the terminology that is necessary in the study of fluid dynamics is not found in other similar areas of study. In particular, some of the terminology used in fluid dynamics is not used in fluid statics.

Terminology in incompressible fluid dynamics

The concepts of total pressure and dynamic pressure arise from Bernoulli's equation and are significant in the study of all fluid flows. (These two pressures are not pressures in the usual sense—they cannot be measured using an aneroid, Bourdon tube or mercury column.) To avoid potential ambiguity when referring to pressure in fluid dynamics, many authors use the term static pressure to distinguish it from total pressure and dynamic pressure. Static pressure is identical to pressure and can be identified for every point in a fluid flow field.

In ''Aerodynamics'', L.J. Clancy writes: ''To distinguish it from the total and dynamic pressures, the actual pressure of the fluid, which is associated not with its motion but with its state, is often referred to as the static pressure, but where the term pressure alone is used it refers to this static pressure.''

A point in a fluid flow where the flow has come to rest (i.e. speed is equal to zero adjacent to some solid body immersed in the fluid flow) is of special significance. It is of such importance that it is given a special name—a stagnation point. The static pressure at the stagnation point is of special significance and is given its own name—stagnation pressure. In incompressible flows, the stagnation pressure at a stagnation point is equal to the total pressure throughout the flow field.

Terminology in compressible fluid dynamics

In a compressible fluid, such as air, the temperature and density are essential when determining the state of the fluid. In addition to the concept of total pressure (also known as stagnation pressure), the concepts of total (or stagnation) temperature and total (or stagnation) density are also essential in any study of compressible fluid flows. To avoid potential ambiguity when referring to temperature and density, many authors use the terms static temperature and static density. Static temperature is identical to temperature; and static density is identical to density; and both can be identified for every point in a fluid flow field.

The temperature and density at a stagnation point are called stagnation temperature and stagnation density.

A similar approach is also taken with the thermodynamic properties of compressible fluids. Many authors use the terms total (or stagnation) enthalpy and total (or stagnation) entropy. The terms static enthalpy and static entropy appear to be less common, but where they are used they mean nothing more than enthalpy and entropy respectively, and the prefix "static" is being used to avoid ambiguity with their 'total' or 'stagnation' counterparts. Because the 'total' flow conditions are defined by isentropically bringing the fluid to rest, the total (or stagnation) entropy is by definition always equal to the "static" entropy.

See also

Fields of study

Mathematical equations and concepts

Types of fluid flow

Fluid properties

Fluid phenomena

Applications

Miscellaneous

References

Originally published in 1879, the 6th extended edition appeared first in 1932. Originally published in 1938.

Notes

External links

eFluids, containing several galleries of fluid motion

National Committee for Fluid Mechanics Films (NCFMF), containing films on several subjects in fluid dynamics (in realmedia format)

List of Fluid Dynamics books

Fluid Mechanics, A short course for physicists

Category:Aerodynamics Category:Chemical engineering Category:Continuum mechanics Category:Piping

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Viktor Schauberger (30 June 1885 – 25 September 1958) was an Austrian forester/forest warden, naturalist, philosopher, inventor and Biomimicry experimenter.

The inventor of what he called "implosion technology", Schauberger developed his own theories based on fluidic vortices and movement in nature. He built actuators for airplanes, ships, silent turbines, self-cleaning pipes and equipment for cleaning and so-called "refinement" of water to create spring water, which he used as a remedy.

Schauberger's theories appear not to have received acceptance in the mainstream western scientific community, as replication proves either too difficult or results vary from previously published data. However, Schauberger's work remains an inspiration to many people in the Green movement for his own observations of nature.

Biography

Early years

Viktor Schauberger was born in Holzschlag, Austria, to a long line of Austrian foresters that could be traced back to early Germanic tribes, with views on and concepts of nature entirely different than the ones known to us currently. Creek and river flow fascinated him during his youth. He went on to develop a basic theory that contains a twofold movement principle for such phenomena.

His first concepts were brought on by studying trout in its natural environment. He was quoted as saying:

''How was it possible for this fish to stand so motionlessly, only steering itself with slight movements of its tail-fins, in this wildly torrential flow, which made my staff shake so much that I could hardly hang onto it?'' ''What forces enabled the trout to overcome its own body-weight so effortlessly and quickly, and, at the same time, overcome the specific weight of the heavy water flowing against it?''

These questions inspired further investigation to study the force that allowed such effortless natural motion. Schaubergers conclusion led to his theory of natural vortices.

Schauberger's second major theory was in the structure of water. He believed that water is at its densest when cold (at +4C water anomaly point) (and at the time of a full moon), and that there are many layers in the structure of flowing water. He claimed that nature creates vortices to create equilibria. He further claimed that our current form of energy production/consumption scatters matter into disequilibrium. His studies were not approved by science at the time, even when his ideas were put into practice.

In 1922 for Adolf I, Prince of Schaumburg-Lippe, Schauberger designed and had built several log flumes which reduced the timber transport costs to one tenth the previous cost and allowed transport of denser than water woods such as beech and fir. In 1924, Viktor Schauberger became a Public Council consultant for the log flumes for the Austrian state. He started construction of three large plants in Austria. In 1926, he undertook research at a timber flotation installation in Neuberg an der Mürz in Styria. In 1929 Schauberger submitted his first applications for patents in the fields of water engineering and turbine construction. He conducted research on how to artificially generate centripetal movement in various types of machines. He proposed a means of utilising hydroelectric power by a jet turbine. The log flumes used for timber flotation allegedly disregarded the Archimedes' principle, i.e., Schauberger was allegedly able to transport heavier-than-water objects by creating a centripetal movement (making the timber spin around its own axis, by special guiding-vanes which caused the water to spiral). Professor Philipp Forchheimer was sent to study the log flumes. Professor Forchheimer in 1930-1931 later published with Schauberger a series of articles in "Die Wasserwirtschaft", the Austrian Journal of Hydrology.

World War II

In 1934 Viktor met with Hitler, and had discussions about fundamental principles of agriculture, forestry and water engineering. Schauberger is believed to have lent his ideas in order to aid the German Reich. Although whether this was under duress or willingly is still a matter of debate; it appears that his aim was to see this theories put to the test (he had offered his log flume designs to several countries). There is no indication that he supported Nazism, and his private feelings about the Nazis seem to have been disdainful. At any rate, his later (post-1941) work for the regime was enforced by the threat of execution, Schauberger being a KZ prisoner at that time.

In 1941, an intrigue caused by the Viennese Association of Engineers resulted in Schauberger's enforced confinement in a mental hospital in Mauer-Öhling, under continuous observation by the SS. In Augsburg, Schauberger worked with Messerschmitt on engine cooling systems and was in correspondence with designer Heinkel about aircraft engines.

In 1944, Schauberger continued to develop his Repulsine machine at the Technical College of Engineering at Rosenhügel in Vienna. By May 1945 a prototype had been constructed.

In 1945 Schauberger started to work on his "Klimator". The function of the Klimator is to cool and warm the air in living spaces.

At the end of the war Schauberger was apprehended by US intelligence agents, and kept in custody for 9 months. They confiscated all his documents and prototypes, and interrogated him to determine his activities during the war.

After the war Schauberger continued his work, leading to water-based power generation through vortex action in a closed cycle, the "Spiral Plough", an "Apparatus for soil cultivation made of copper" and tests with "spiral pipes".

Later years

In 1952, at Stuttgart Technical University, Schauberger claimed that tests were carried out by Prof. Franz Popel, on behalf of the West German government, to determine the validity of his ideas on water movement. Tests were performed on Schauberger's specially designed copper pipes, which had a conical, spiral, rifled shape, with apparent success confirming Schauberger's idea.

In 1958 Schauberger was approached by Karl Gerchsheimer and Robert Donner, with an invitation to come to the US to further develop his inventions.

Schauberger spent several months in the US writing articles and drawing sketches, then returned to Austria. He died in Linz, Austria, on September 25, 1958, 5 days after having returned to Linz.

Controversy

Schauberger and his works have become part of an internet-based conspiracy theory claiming that Schauberger invented free energy/perpetual motion devices and that this was "covered up" by the US government. Schauberger never claimed to have invented perpetual motion machines, but instead stated that he used the Earth's natural power.

Due to issues with translation from German to English, a number of papers and publications are in broken English. In ''Implosion'' magazine, a magazine released by Schauberger's family, he said that aeronautical and marine engineers had incorrectly designed the propeller. He stated:

“As best demonstrated by Nature in the case of the aerofoil maple-seed, today’s propeller is a pressure-screw and therefore a braking screw, whose purpose is to allow the heavy maple-seed to fall parachute-like slowly towards the ground and to be carried away sideways by the wind in the process. No bird has such a whirling thing on its head, nor a fish on its tail. Only man made use of this natural brake-screw for forward propulsion. As the propeller rotates, so does the resistance rise by the square of the rotational velocity. This is also a sign that this supposed propulsive device is unnaturally constructed and therefore out of place.”

Whilst the notion of a propeller being natural or unnatural is subjective, the maximum efficiency of the propeller can be considered. As a comparison, the fastest propeller-driven aircraft ever to fly, the Tupolev Tu-114 had a top-speed of 541 miles per hour, but a jet engine using suction and internal compressive forces can break the sound barrier.

Not everything that undergoes air or water resistance experiences an increase in drag with the square of velocity. Some insect wings rely on turbulence created by a previous wing beat to increase the efficiency of the stroke, and hence decrease the acting drag which uses less energy.

He has also been quoted as making the claim:

"Water is a living substance!"

and some of his language using scientific terms has been translated in incorrect ways. In another edition of ''Implosion Magazine'', he says:

"In contrast, all 'technical' machines, i.e. all dynamos, turbines, pressure pumps, propellers, explosion and steam driven engines, all furnaces, gas and electric heating appliances, all soil-tilling and harvesting machinery, etc. provide a developmentally harmful ex-pulse to initiate motion. Because of this and without exception, the atom lattice thus moved ruptures, resulting in the disintegration of the molecular (bacteriophagous) formations in suspension. In unnaturally moved air or water decadent stresses appear, causing the decay of the decisive energy-concentrates. This leads to the build-up of decadent potential and the decomposition of the blood of the Earth, and thus to a total economic collapse along the whole course of development."

The claim that a bacteriophage can exist in an atomic lattice is inaccurate, notably because a bacteriophage is approximately 1 thousand times larger than the gaps in a crystal structure. However it is evident that he had used the term atom generically to refer to particles, commonplace for his era, which contextually for his comment about bacteriophage in soil holds to be true as soil particles indeed host between them bacteria the disturbance of which breaks their bonds to surrounding material and organisms, thereby depleting soil's vitality.

''Implosion Magazine''

''Implosion'' is a quarterly magazine founded in 1958 by Aloys Kokaly at the bequest of Viktor and Walter Schauberger. It is still published quarterly or semi-annually by Klaus Rauber. It is the only known repository of Viktor Schauberger's writing (in German), and has been the source of substantial portions of the Eco-Technology series.

Films

Three documentaries in English dealing with the life and works of Viktor Schauberger are in existence:

"Nature Was My Teacher" - Borderland Science Research Foundation - narrated by Tom Brown (1993)

"Sacred Living Geometries" - narrated by Callum Coats (1995)

"Extraordinary Nature of Water" - narrated by Callum Coats (2000)

See also

Biomimicry

Bionics

Forester

Fluid dynamics

Hydrodynamics

Pseudoscience

Spiral: Golden spiral, Golden ratio, Fibonacci sequence

Vortex

Notes

Further reading

Kronberger Hans & Lattacher Siegbert, "On the Track of Water's Secret - from Victor Schauberger to Johann Grander", Uranus 1995; ISBN 3-901626-03-4

Jane Cobbald, ''Viktor Schauberger - a Life of Learning from Nature'' (2006) ISBN 0-86315-569-3

Olof Alexandersson, ''Living Water — Viktor Schauberger and the Secrets of Natural Energy''

(1982) ISBN 0-85500-112-7

(1990) ISBN 0-946551-57-X

(2002) ISBN 0-7171-3390-7

Alick Bartholomew, ''Hidden Nature — The Startling Insights of Viktor Schauberger'' (2003) ISBN 0-86315-432-8

Brian Desborough, ''A Blueprint for A Better World'' (2002) ISBN 0-9742018-0-4

Viktor Schauberger and Callum Coats, ''The Schauberger Companion'' (1994) ISBN 1-85860-011-1

''Eco-Technology'' (1994) ISBN 1-85860-011-1

''Living Energies'' (1995) ISBN 0-7171-3307-9 {UK edition has more ill.}

''Living Energies — Viktor Schauberger's brilliant work with Natural Energies Explained'' (2002) ISBN 0-7171-3307-9

''The Water Wizard: The Extraordinary Properties of Natural Water'', Eco-Technology no.1, (1997) ISBN 1-85860-048-0

''Nature As Teacher: New principles in the Working of Nature'', Eco-Technology no.2, (1998) ISBN 1-85860-056-1

''The Fertile Earth: Nature's Energies in Agriculture, Soil Fertilisation and Forestry'', Eco-Technology no.3,(2000) ISBN 1-85860-060-X

''Energy Evolution: Harnessing Free Energy from Nature'', Eco-Technology no.4, (2001) ISBN 1-85860-061-8

External links

Viktor Schauberger(Russian\English)

Pythagoras Kepler System, non-profit promoting Viktor's work, started by son Walter Schauberger, currently run by grandson Jörg Schauberger.

''Implosion Magazine'', Verein für Implosionsforschung und Anwendung e.V.

Ovesen, Morten, "''Life and work''". Malmö group.

"''Who was Viktor Schauberger?''"

"''Viktor Schauberger''". (30.6.1885 - 25.9.1958)

"''Viktor Schauberger, The Water-wizard from Austria.''".

Naudin, J., "''The Schauberger's Flying Saucer''".

"''Qualitatives Torkado-Modell (Hypothesen und Studien zu freien 3D-Schwingungen)''". (German)

"''Viktor Schauberger (30.6.1885 - 25.9.1958)''".

"''Viktor Schauberger The Water-wizard from Austria''

Viktor Schauberger''".

''Modern Energy Research Library"''.

Category:1885 births Category:1958 deaths Category:Austrian naturalists Category:Austrian philosophers Category:Austrian inventors Category:Bionics Category:Foresters Category:Austrian foresters Category:People from Rohrbach District

de:Viktor Schauberger es:Viktor Schauberger fr:Viktor Schauberger pl:Wiktor Schauberger ru:Шаубергер, Виктор uk:Віктор Шаубергер