Differential Equations Governing the Geometry of a Diamond Mesh Cod-end of a Trawl Net

1997 ◽  
Vol 64 (1) ◽  
pp. 7-14 ◽  
Author(s):  
F. G. O’Neill
Keyword(s):  
Differential Equations ◽  
Cross Section ◽  
Good Description ◽  
Circular Cross Section ◽  
Mesh Size ◽  
Force Balance ◽  
Special Cases ◽  
Theoretical Predictions ◽  
Predicted Values ◽  
Simple Points

A new surface, made up of an infinite number of infinitesimal meshes, is defined to approximate the cod-end. The force balance on a mesh element of this surface is considered in the limit as the mesh size tends to zero and the differential equations governing the geometry of a diamond meshed cod-end of circular cross section are derived in cartesian coordinates. The parametric form of the equations in terms of a, the distance along the cod-end profile, is then deduced and some special cases examined. In particular the case of a partially filled cod-end hanging under gravity is investigated and experimental measurements are compared with numerically obtained theoretical predictions. The numerical results are shown to provide a good description of the cod-end geometry except where the cod-end diameter is at its narrowest where there is a systematic departure of the predicted values from those measured. It is demonstrated that a probable explanation of this discrepancy is the assumption that the knots are simple points of intersection rather than finite well-defined structures.

Toroidal plasma configuration with non-planar magnetic axis

1984 ◽  
Vol 32 (2) ◽  
pp. 179-196
Author(s):  
Hussain M. Rizk
Keyword(s):  
Cross Section ◽  
Ohmic Heating ◽  
Circular Cross Section ◽  
Magnetic Axis ◽  
Toroidal Plasma ◽  
Mhd Equilibrium ◽  
Special Cases ◽  
Magnetic Surfaces ◽  
Plasma Configuration ◽  
The Ideal

The ideal MHD equilibrium, stability, classical diffusion, effective thermal conductivity, and Ohmic heating of a zero-shear toroidal plasma configuration with a single non-planar magnetic axis of variable torsion and curvature are investigated. The plasma has a circular cross-section through which a longitudinal current density with arbitrary profile flows. In this type of magnetic configuration, the magnetic surfaces arbitrarily rotate around the magnetic axis. This magnetic toroidal configuration is of a stellarator type with a non-planar magnetic axis. The present work also covers as special cases tokamak and a magnetic toroidal plasma configuration with a magnetic axis of arbitrarily modulated curvature.

Friction Factor Determination for Flow Through Finite Wire-Mesh Woven-Screen Matrices

1997 ◽  
Vol 119 (4) ◽  
pp. 847-851 ◽  
Author(s):  
J. R. Sodre´ ◽  
J. A. R. Parise
Keyword(s):  
Cross Section ◽  
Circular Cross Section ◽  
Mesh Size ◽  
Packed Bed ◽  
Reynolds Numbers ◽  
Wire Mesh ◽  
Hydraulic Radius ◽  
Fully Developed Flow ◽  
Flow Through ◽  
Screen Mesh

Experiments were carried out to determine the pressure drop through an annular conduit filled with a plain square wire-mesh woven-screen matrix. The tests involved turbulent fully developed flow of air at steady-state conditions, with the modified Reynolds number (M(1−ε)/Re), based on the hydraulic radius of the packed bed, ranging from 5 × 10−4 to 5 × 10−3. The test section was built according to the geometry of a Stirling engine, simulating an annular regenerator with a radius ratio of 1.369 and a screen of mesh size 10. A corrected Ergun equation was used to correlate the experimental data, considering the wall effects. Comparisons with results obtained by other authors extended the validation of the correlation obtained to a wider range of modified Reynolds numbers (1 × 10−4 ≤ M(1 − ε)/Re ≤ 1) and to different screen mesh sizes. The correlation has been found to work for annular and circular cross-section beds.

Free Vibration of a Simply Supported Bar With a Linearly Variable Height of Cross Section

1962 ◽  
Vol 29 (3) ◽  
pp. 497-501 ◽  
Author(s):  
E. Krynicki ◽  
Z. Mazurkiewicz
Keyword(s):  
Differential Equations ◽  
Free Vibration ◽  
Exact Solutions ◽  
Cross Section ◽  
Approximate Solutions ◽  
Variable Cross ◽  
Simply Supported ◽  
Special Cases ◽  
Formal Integration ◽  
Simple Integration

The problem of vibration of nonhomogeneous bars or bars of variable cross section1 leads to differential equations, which are generally unsolvable by formal integration. It is known that functional coefficients occur in these equations, which make it difficult, if not impossible, to obtain exact solutions by simple integration. Several exact solutions obtained for a few special cases and also some interesting approximate solutions are mentioned in the paper.

Approximate Optimum Fin Design for Boiling Heat Transfer

1971 ◽  
Vol 93 (1) ◽  
pp. 19-23 ◽  
Author(s):  
D. R. Cash ◽  
G. J. Klein ◽  
J. W. Westwater
Keyword(s):  
Cross Section ◽  
Atmospheric Pressure ◽  
Design Method ◽  
Circular Cross Section ◽  
Film Boiling ◽  
Optimum Shape ◽  
Base Temperature ◽  
Extended Surfaces ◽  
Predicted Values ◽  
Fin Design

For extended surfaces used in boiling liquids, the specified fin-base temperature may be such as to result in simultaneous nucleate, transition, and film boiling at adjacent positions on the fins. If the fins are spines of circular cross section, the optimum shape to minimize the volume of metal resembles a turnip, as shown by Haley and Westwater. The object of the new study was to develop easy-to-machine shapes using cones and cylinders. It was shown mathematically that two cones, base-to-base, give an excellent approximation to the turnip shape. Three such fins were constructed of copper and tested in Freon-113 at atmospheric pressure. The measured, peak heat duties were 5 to 70 percent higher than the predicted values, proving that the design method is conservative.

Solving Large-Deflection Problem of Spatial Beam with Circular Cross-Section Using an Optimization-Based Runge–Kutta Method

2016 ◽  
Vol 17 (1) ◽  
pp. 65-76 ◽  
Author(s):  
Geng Li ◽  
Jianyuan Jia ◽  
Guimin Chen
Keyword(s):  
Finite Element ◽  
Differential Equations ◽  
Cross Section ◽  
Circular Cross Section ◽  
Nonlinear Finite Element ◽  
Kutta Method ◽  
Euler Beam ◽  
Runge Kutta Method ◽  
Spatial Beam ◽  
Runge Kutta

AbstractBased on the Bernoulli–Euler beam theory, the nonlinear governing differential equations (GDEs) for a spatially deflected beam with circular cross-section are formulated, which are then reduced to first-order differential equations to be compatible with Runge–Kutta method. With the boundary conditions of a spatial beam, the governing equations are treated as an initial value problem (IVP) of ordinary differential equations. A Runge–Kutta method combined with an unconstrained optimization algorithm (RKUO) is presented to solve the IVP. The approach for determining the orientation of the cross-section plane at any position on the deflected beam is also provided. Finally, the comparison between the RKUO results and those achieved using nonlinear finite element (NFE) analysis and spatial pseudo-rigid-body model validate the accuracy and effectiveness of RKUO. The results also demonstrated the unique capabilities of RKUO to solve large spatial deflection problems that are outside the range of nonlinear finite element model.

Routes to Chaos Exhibited by Closed Flexible Cylindrical Shells

2006 ◽  
Vol 2 (1) ◽  
pp. 1-9 ◽  
Author(s):  
J. Awrejcewicz ◽  
V. Krysko ◽  
N. Saveleva
Keyword(s):  
Cauchy Problem ◽  
Differential Equations ◽  
Cross Section ◽  
Cylindrical Shells ◽  
Circular Cross Section ◽  
Qualitative Theory ◽  
The Other ◽  
Chaotic Vibrations ◽  
Runge Kutta Method ◽  
The Cauchy Problem

Complex vibrations of closed cylindrical shells of circular cross section and finite length subjected to nonuniform sign-changeable external load in the frame of classical nonlinear theory are studied. A transition from partial differential equations to ordinary differential equations (Cauchy problem) is carried out using the higher order Bubnov–Galerkin’s approach and Fourier’s representation. On the other hand, the Cauchy problem is solved using the fourth-order Runge–Kutta method. Results are analyzed owing to the application of nonlinear dynamics and qualitative theory of differential equations. The present work is devoted to the analysis of influence of the system dynamics of the following parameters: length of pressure width φ0, relative linear shell dimension λ=L∕R, and frequency ωp and amplitude q0 of external transversal load. Some new scenarios of vibrations of closed cylindrical shells exhibiting a transition from harmonic to chaotic vibrations are illustrated and studied.

An experimental study of gas exchange in laminar oscillatory flow

1983 ◽  
Vol 133 ◽  
pp. 245-254 ◽  
Author(s):  
C. H. Joshi ◽  
R. D. Kamm ◽  
J. M. Drazen ◽  
A. S. Slutsky
Keyword(s):  
Experimental Study ◽  
Cross Section ◽  
Oscillatory Flow ◽  
Circular Cross Section ◽  
Effective Diffusivity ◽  
Constant Infusion ◽  
Tracer Gas ◽  
Theoretical Predictions ◽  
Induced Flow ◽  
Buoyancy Induced Flow

Experiments were conducted to determine the effective diffusivity for axial transport through a tube of circular cross-section of a contaminant gas in oscillatory flow. Results were compared with the theoretical predictions of Watson (1983) and found to be in excellent agreement. The experiments differ from the theoretical situation in that the oscillations are superimposed upon a steady flow due to a constant infusion of tracer gas, and a buoyancy-induced flow associated with spatial variations in gas density. The influence of both artifacts is found to be negligible.

Experiments to Investigate Flow Regime Transition for Steam and Subcooled Water From Stratified Flow to Slug Flow in Horizontal Pipe

2008 ◽  
Author(s):  
Hiral J. Kadakia ◽  
Brian G. Williams ◽  
Richard R. Schultz
Keyword(s):  
Flow Regime ◽  
Cross Section ◽  
Slug Flow ◽  
Good Description ◽  
Circular Cross Section ◽  
Water Hammer ◽  
Horizontal Pipe ◽  
Representative Data ◽  
Subcooled Water ◽  
Flow Regime Transition

Steam flowing over horizontally-stratified subcooled water in a circular-cross-section pipe may result in condensation-induced water hammer (CIWH). This subject has been studied by a number of researchers and representative data are given by Bjorge and Griffith 1986 who studied the conditions that lead to CIWH. Bjorge & Griffith give a good description of the phenomena including its precursors and characteristics.

Scattering from a helical coil of circular cross section in the Rayleigh–Debye theory

1980 ◽  
Vol 58 (9) ◽  
pp. 1375-1382 ◽  
Author(s):  
A. J. Patitsas
Keyword(s):  
Form Factor ◽  
Cross Section ◽  
Circular Cross Section ◽  
Graphical Form ◽  
Helical Coil ◽  
X Ray Diffraction ◽  
Debye Theory ◽  
X Ray ◽  
Special Cases ◽  
Sharp Minima

The scattering form factor (structure factor) for a helical coil of N turns and of arbitrary circular cross section is expressed in infinite series form by utilizing the approximate Rayleigh–Debye scattering theory. The effect of the finite cross section of the coil on the form factor and on the phase angle of the amplitude of the form factor is shown in graphical form for various directions of the incident and scattered waves and for various values of the pitch and the radius of the coil in the range of those encountered in the X-ray diffraction by DNA molecules. The very long coil and the ring are considered as special cases. In all cases it is found that the extrema of the form factor for the thick coil appear at almost the same angles as those of the thin coil. The major difference appears at about 90° from the direction of the incident wave where the plot for the thick coil has sharp minima totally absent in the plot for the thin coil.

The Line Contact Between Two Cylinders—Some Experiments and Theoretical Predictions

1988 ◽  
Vol 110 (2) ◽  
pp. 285-291 ◽  
Author(s):  
J. M. de Mul ◽  
H. van Engelenburg
Keyword(s):  
Half Space ◽  
Cross Section ◽  
Circular Cross Section ◽  
Infinite Cylinder ◽  
Space Model ◽  
Linear Elastic ◽  
Cylinder Model ◽  
Theoretical Predictions ◽  
Frictional Effects ◽  
Good Agreement

Experiments are presented in which various combinations of two (almost) straight cylinders with circular cross-section are pressed together while their axes remain basically parallel. Results are compared with theoretical predictions from a half space model; from this half space model extended with adjustments for the finite dimensions of the cylinders in contact; and from an infinite cylinder model from literature. Frictional effects are not considered and the material is assumed to be linear-elastic. Agreement in the approach of the center lines of the cylinders under load is found to exist more or less between the experimental results and the theoretical predictions by the models. The behaviour of the models is discussed, and reasonable to good agreement is demonstrated for the extended half space model using an integral depth adjustment of 3/4 of the diameter of each cylinder in contact. A possible way to further improve this model is indicated.

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