Simulation of liquid movement in cylindrical shells

Abstract

The motion of a viscous incompressible fluid with constant coefficients in case of the Hagen-Poiseuille  flow is considered in this paper. The equation of motion of the elastic shell in the absence of external perturbations is obtained on the basis of the Ostrogradsky-Hamilton principle. Assuming the Hagen-Poiseuille  flow, the expression for the kinetic energy of a moving fluid in a nanotube is obtained, and the equations to determine oscillation frequencies of a tube with a fluid are constructed, that allows investigating the stability of motion.  Using the Poiseuille formula it is possible to effectively determine the movement of fluid in tubes. According to the Bernoulli's equation, when the fluid is stationary along a rectilinear horizontal tube of a constant cross-section, the fluid pressure must be the same along the entire length of a tube.

In recent years, a new trend associated with nanotechnology has been developing in hydromechanics. The relevance of modeling fluid flow through micro- and nanotubes is confirmed by the results of many experiments conducted over two decades. A nanotube can be represented as a graphite plane rolled into a cylinder (hollow tube), which is a set of regular hexagons with carbon atoms in the vertices, and having the diameter of several nanometers. The fluid flow through micro and nanotubes is a common phenomenon in various biological and technical devices and systems and therefore is of great importance. Consequently, flows in nanometer-sized channels are being studied intensively. The numerical values of the oscillation frequencies of the elastic cylindrical shell for the cases of absence of fluid and the presence of fluid with different pressure values have been obtained.