Shell balance

About: Shell balance is a research topic. Over the lifetime, 154 publications have been published within this topic receiving 3691 citations.

Theoretical Study on Fluid Velocity for Viscous Fluid in a CircularCylindrical Shell

Abstract: A theoretical algorithm by united Lagrangian-Eulerian method for the problem in dealing with viscous fluid and a circular cylindrical shell is presented. In this approach, each material is described in its preferred reference frame. Fluid flows are given in Eulerian coordinates whereas the elastic circular cylindrical shell is treated in a Lagrangian framework. The fluid velocity in a two-dimensional uniform elastic circular cylindrical shell filled with viscous fluid is studied under the assumption of low Reynolds number. The coupling between the viscous fluid and the elastic circular cylindrical shell is kinematic conditions at the shell surface. Also, the radial velocity and axial velocity of the fluid are discussed with the help of graphs.

Chapter 2 – Fundamentals of Fluid Mechanics

Abstract: Publisher Summary This chapter focuses on the fundamentals of fluid mechanics. A fluid is defined as any material that deforms continually under the application of a shear stress, which is a stress directed tangentially to the surface of the material. Fluid mechanics is the study of fluids at rest and at motion and can be divided into two main categories, which are static fluid mechanics and dynamic fluid mechanics. In static fluid mechanics, the fluid is either at rest or is undergoing rigid-body motion. In dynamic fluid mechanics, the fluid may have an acceleration term and can undergo deformations. Five relationships are the most useful in fluid mechanics problems, which include kinematic, stresses, conservation, regulating, and constitutive. The analysis of fluid mechanics problems can be significantly altered depending on the choice of the system of interest and the volume of interest. Most fluids, under normal conditions can be considered Newtonian fluids. A Newtonian fluid is classified by a constant dynamic viscosity under any shear rate. Similar to a purely elastic material, these fluids have a linear relationship between shear stress and shear rate. However, many fluids do not exhibit Newtonian properties and, therefore, are termed “non-Newtonian” fluids. A fluid can undergo four general motions, which are useful in defining the position of fluid packets, the velocity, and the acceleration of the fluid. A two-phase flow consists of a fluid in both a gas and liquid phase, or two fluids with different viscosities within the same flow conditions. Fluid structure interaction modeling is also important if the fluid can affect and cause a deformation on the flow boundary. This is especially important in the cardiovascular system, in which the blood vessel wall is deformable and cellular matter can interact with the wall.

Fluid boundaries shaping using the method of kinetic balance

Abstract: Fluid flow in curved channels with various cross-sections, as a common problem in theoretical and applied fluid mechanics, is a very complex and quite undiscovered phenomenon. Defining the optimum shape of the fluid flow boundaries, which would ensure minimum undesirable phenomena, like "dead water" zones, unsteady fluid flow, etc., is one of the crucial hydraulic engineering’s task. Method of kinetic balance is described and used for this purpose, what is illustrated with few examples. .

Relativistic Axially Symmetric Flows of a Perfect Fluid

Abstract: fluid which is characterized by a general density-pressure relation ,u(p). It is shown that the meridional components of velocity can be derived from a stream-function, the trajectories of the fluid particles being spirals wound around torus-shaped surfaces. The moment of the velocity, and another dynamical variable, are conserved for fluid particles along their motion. However, the relativistic angular-momentum-density is convectively conserved only in a fluid in which the velocity of sound equals the velocity of light. We evaluate the total angular momentum L and the total energy E of a spherical vortex in such a fluid, based on a solution given previously. Putting L = h and E = Mc2, where m denotes the mass of the neutron, and letting the maximum value of the flow in the vortex equal c, we get a value of 1.2 x 10-13 cm for the radius of the vortex. 1. INTROD UCTION In nonrelativistic hydrodynamics, the assumption of incompressibility, which is made for mathematical convenience, provides a useful approximation to a wide class of naturally occurring flows of real fluids in which the effects of incompressibility are small. The notion of incompressibility is, however, alien to relativistic hydrodynamics because of the associated infinite value of the velocity of sound. The question therefore arises whether in relativistic hydrodynamics there exists a model which provides mathematical simplification in the manner in which the model of an incompressible fluid does in the non-relativistic case. Such a model was found to be (Pekeris I976) a fluid in which the velocity of sound u8 exactly equals the velocity of light c. The discussion was based on an assumed linear relationship between the density t and the pressure p