# Liquid vortices

The dynamics of an ideal fluid is enough thorough described in "Basic laws". The real fluid differs by the viscous friction forces and the surface tension, which shape the vortices of the constrained sizes and speeds. The Euler’s equation ("Continuum", 2) with an additional viscous friction of the incompressible fluid refers to the Navier-Stokes equations: $\rho\frac{\partial\mathbf{\overrightarrow{v}}}{\partial t}+\rho(\mathbf{\overrightarrow{v}}\cdot\nabla)\mathbf{\overrightarrow{v}}+grad(P+U)=\eta\Delta\mathbf{\overrightarrow{v}}=\nu\rho\Delta\mathbf{\overrightarrow{v}}\tag{1}$ where $$\eta$$ is a dynamic viscosity,
$$\nu$$ is a kinematic viscosity,
$$\Delta$$ is a Laplace operator.

An infinitely large volume of the incompressible viscous fluid can support the ideal laminar and vortical flows, when $$div \mathbf{\overrightarrow{v}}=\nabla\mathbf{\overrightarrow{v}}=\Delta\mathbf{\overrightarrow{v}}=0$$.

The transition probability from a laminar flow to a turbulent flow (to a chaos of the unstable vortices) is estimated by the Reynolds number, which is compared with its empirical critical values: $Re=\frac{VD_H}{\nu}\tag{2}$ where $$V$$ is a mean velocity of the flow,
$$D_H$$ is a hydraulic diameter.

glass pipe,          copper pipe,          Schauberger’s copper pipe,
bright and dashed curves are supposed,   black curves in the lower diagram are calculated theoretically.

An inventor V. Schauberger proposed to direct the fluid by its natural helical flow, so that it would no longer whirls. The helicoid is a patented helical pipe, in which the water flow is rotated around the axis. Professor Fr. Pöpel [1] in 1952 had researched this pipe and had plotted the diagram of friction vs. velocity. The friction in the helicoid at the certain velocities drops significantly up to the negative values. This cannot be explained by a helical flow only, which reduces the friction due to decrease in the flow speed from the pipe axis to its walls. This effect can be explained by the aetheric macrovortices.

The aetheric macrovortices in fluids have two main causes:

• Molecular dipoles produce an electromagnetic field (see details in "Macrovortices").
• Electrical conduction produces the eddy currents due to the different velocities of the opposite charge carriers, which are separated by a centrifugal separation. Examples:

The thermal action of the aetheric vortices in fluids has two ways:

• Stable macrovortices reduce the temperature and entropy of the environment.
• Unstable vortices are decaying and emiting the unlimited aetheric energy in a form of the heat. This phenomenon occurs in the generators of Shauberger, Clem and Potapov.

## References

1. Pöpel, Franz, Rapport över preliminära undersökningar av spiralrör med olika form, Institute of Ecological Technology, Sweden, 1986. (Originally published as, Bericht über die Voruntersuchnungen mit Wendelrohren mit verschniedener Wandform} Internal Report, Institut für Gesundheitstechnik, Institute of Technology in Stuttgart, 1952. Published in English in, The Energy Evolution, Viktor Schauberger & Callum Coats (ed.), p. 222-47, Gateway Books, Bath, 2000)