The hydrodynamics of non-Newtonian fluids. II

1949 ◽  
Vol 45 (1) ◽  
pp. 88-91 ◽  
Author(s):  
R. S. Rivlin
Keyword(s):  
Normal Stress ◽  
Cross Section ◽  
Pressure Difference ◽  
Circular Cross Section ◽  
Newtonian Fluids ◽  
Hydrodynamic Theory ◽  
Stress Components ◽  
The Absolute

In this paper, the general hydrodynamic theory of visco-inelastic, incompressible, non-Newtonian fluids, developed in a previous paper (l), is applied to the problem of the flow of such a fluid through a tube of circular cross-section. It is found that the absolute values of the normal stress components are no longer uniform over a cross-section of the tube normal to its axis, as in the case of Newtonian fluids obeying the laws of classical hydrodynamics.However, the pressure difference, between points at equal radii on two planes normal to the axis, is independent of the position of these points on the planes.

scholarly journals CRITERIA EVALUATION OF THE LIMIT DEPTH OF HORIZONTAL PRODUCTION

2019 ◽  
Vol 7 (4) ◽  
pp. 41-48
Author(s):  
Oksana Bogomolova ◽  
Aleksandr Bogomolov
Keyword(s):  
Normal Stress ◽  
Cross Section ◽  
Host Rock ◽  
Qualitative Agreement ◽  
Circular Cross Section ◽  
Fracture Zones ◽  
Output Circuit ◽  
Underground Workings

The paper presents the results of a study to determine the technological contours of horizontal underground workings and the maximum safe depth of their laying. The criterion for determining the limiting depth can be the condition that there are no points on the output circuit at which the stresses the tangential normal stress exceeds the tensile and compressive strengths of the host rock. The results of solving the problem of finding fracture zones on a circular cross-section working circuit are in satisfactory qualitative agreement with the result obtained independently of the authors.

scholarly journals Analysis of beam elements of circular cross section using the absolute nodal coordinate formulation

2012 ◽  
Vol 59 (3) ◽  
pp. 283-296 ◽  
Author(s):  
Grzegorz Orzechowski
Keyword(s):  
Cross Section ◽  
Absolute Nodal Coordinate Formulation ◽  
Gaussian Quadrature ◽  
Circular Cross Section ◽  
Beam Cross Section ◽  
Element Analysis ◽  
Absolute Nodal Coordinate ◽  
Beam Elements ◽  
The Absolute ◽  
The Cross

Abstract The beam elements, which are widely used in the absolute nodal coordinate formulation (ANCF) can be treated as isoparametric elements, and by analogy to the classical finite element analysis (FEA) are integrated with standard, spatial Gauss- Legendre quadratures. For this reason, the shape of the ANCF beam cross section is restricted only to the shape of rectangle. In this paper, a distinct method of integration of ANCF elements based on continuum mechanics approach is presented. This method allows for efficient analysis of the ANCF beam elements with circular cross section. The integration of element vectors and matrices is performed by separation of the quadrature into the part that integrate along beam axis and the part that integrate in the beam cross section. Then, an alternative quadrature is used to integrate in the circular shape of the cross section. Since the number of integration points in the alternative quadrature corresponds to the number of points in the standard Gaussian quadrature the change in the shape of the cross section does not affects negatively the element efficiency. The presented method was verified using selected numerical tests. They show good relatively agreement with the reference results. Apart from the analysis of the beams with the circular cross section, a possibility of further modifications in the methods of the element integration is also discussed. Due to the fact that locking influence on the convergence of the element is also observed, the methods of locking elimination in the proposed elements are also considered in the paper.

SAF file: It's really three dimensional file

2018 ◽  
Vol 14 (1) ◽  
pp. 1
Author(s):  
Prof. Dr. Jamal Aziz Mehdi
Keyword(s):  
Cross Section ◽  
Root Canal ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Circular Motion ◽  
Root Canal Treatment ◽  
Metal Core ◽  
Rotating Blade

The biological objectives of root canal treatment have not changed over the recentdecades, but the methods to attain these goals have been greatly modified. Theintroduction of NiTi rotary files represents a major leap in the development ofendodontic instruments, with a wide variety of sophisticated instruments presentlyavailable (1, 2).Whatever their modification or improvement, all of these instruments have onething in common: they consist of a metal core with some type of rotating blade thatmachines the canal with a circular motion using flutes to carry the dentin chips anddebris coronally. Consequently, all rotary NiTi files will machine the root canal to acylindrical bore with a circular cross-section if the clinician applies them in a strictboring manner

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