scholarly journals LONG WAVES IN CHANNELS Of ARBITRARY CROSS-SECTION

1968 ◽  
Vol 1 (11) ◽  
pp. 12
Author(s):  
D.H. Peregrine
Keyword(s):  
Cross Section ◽  
Gravity Waves ◽  
Reasonable Agreement ◽  
Arbitrary Constant ◽  
Arbitrary Cross Section ◽  
Cross Sectional ◽  
Curved Channels ◽  
Channel Curvature ◽  
M Channels ◽  
Theoretical Results

This warier summarises some recent work on lone gravity waves on still water m channels of arbitrary constant cross-section. Theoretical results have been obtained for both straight and curved channels. Some experimental work has been performed m straight trapezoidal channels and shows reasonable agreement with theory. For straight channels some details of the second approximation are given, and the cases where the approximation breaks down are indicated. For curved channels it is found that the effect of channel curvature is more pronounced when the cross-sectional shane of the channel is not symmetric with resnect to its centre-line.

Hydrodynamical Entrance Length Effects for Duct Flows With Arbitrary Inlet Velocity Profiles

1984 ◽  
Vol 51 (2) ◽  
pp. 239-243 ◽  
Author(s):  
J. P. Du Plessis ◽  
D. G. Kro¨ger
Keyword(s):  
Cross Section ◽  
Velocity Profiles ◽  
Arbitrary Cross Section ◽  
Tube Flow ◽  
Entrance Length ◽  
Cross Sectional ◽  
Inlet Velocity ◽  
Flow Divider ◽  
Laminar Tube Flow ◽  
Theoretical Results

An existing analytical method for predicting the entrance region pressure drop and relating effects in straight ducts of arbitrary cross section is generalized to include the application of arbitrary inlet velocity profiles. The only requirement for the use of the derived theoretical results is the availability of integrable (analytically or numerically) expressions for the inlet and the fully developed velocity profiles for the cross-sectional geometry under consideration. The derived results are applied to the case of the transition of fully developed laminar tube flow to fully developed circular-sectorial flow. The latter may be induced by the introduction of a flow divider into the tube. The numerical results are tabulated and also presented graphically.

Numerical Simulating Open-Channel Flows with Regular and Irregular Cross-Section Shapes Based on Finite Volume Godunov-Type Scheme

2020 ◽  
pp. 2050047
Author(s):  
Xiaokang Xin ◽  
Fengpeng Bai ◽  
Kefeng Li
Keyword(s):  
Finite Volume ◽  
Cross Section ◽  
Cross Sections ◽  
Open Channel ◽  
Arbitrary Cross Section ◽  
Second Order ◽  
Cross Sectional ◽  
Shallow Flows ◽  
Natural Streams ◽  
Saint Venant Equations

A numerical model based on the Saint-Venant equations (one-dimensional shallow water equations) is proposed to simulate shallow flows in an open channel with regular and irregular cross-section shapes. The Saint-Venant equations are solved by the finite-volume method based on Godunov-type framework with a modified Harten, Lax, and van Leer (HLL) approximate Riemann solver. Cross-sectional area is replaced by water surface level as one of primitive variables. Two numerical integral algorithms, compound trapezoidal and Gauss–Legendre integrations, are used to compute the hydrostatic pressure thrust term for natural streams with arbitrary and irregular cross-sections. The Monotonic Upstream-Centered Scheme for Conservation Laws (MUSCL) and second-order Runge–Kutta methods is adopted to achieve second-order accuracy in space and time, respectively. The performance of the resulting scheme is evaluated by application in rectangular channels, trapezoidal channels, and a natural mountain river. The results are compared with analytical solutions and experimental or measured data. It is demonstrated that the numerical scheme can simulate shallow flows with arbitrary cross-section shapes in practical conditions.

Estimation of Nusselt Number in Microchannels of Arbitrary Cross-Section With Constant Axial Heat Flux

2008 ◽  
Author(s):  
Ehsan Sadeghi ◽  
Majid Bahrami ◽  
Ned Djilali
Keyword(s):  
Heat Flux ◽  
Nusselt Number ◽  
Cross Section ◽  
Cross Sections ◽  
Numerical Solutions ◽  
Arbitrary Cross Section ◽  
Geometrical Parameters ◽  
Thermal Systems ◽  
Cross Sectional ◽  
Axial Heat

In many practical instances such as basic design, parametric study, and optimization analysis of thermal systems, it is often very convenient to have closed form relations to obtain the trends and a reasonable estimate of the Nusselt number. However, finding exact solutions for many practical singly-connected cross-sections, such as trapezoidal microchannels, is complex. In the present study, the square root of cross-sectional area is proposed as the characteristic length scale for Nusselt number. Using analytical solutions of rectangular, elliptical, and triangular ducts, a compact model for estimation of Nusselt number of fully-developed, laminar flow in microchannels of arbitrary cross-sections with “H1” boundary condition (constant axial wall heat flux with constant peripheral wall temperature) is developed. The proposed model is only a function of geometrical parameters of the cross-section, i.e., area, perimeter, and polar moment of inertia. The present model is verified against analytical and numerical solutions for a wide variety of cross-sections with a maximum difference on the order of 9%.

Long waves in a uniform channel of arbitrary cross-section

1968 ◽  
Vol 32 (2) ◽  
pp. 353-365 ◽  
Author(s):  
D. H. Peregrine
Keyword(s):  
Solitary Wave ◽  
Cross Section ◽  
Gravity Waves ◽  
Equations Of Motion ◽  
Rectangular Channel ◽  
Arbitrary Cross Section ◽  
Long Waves ◽  
Order Of Approximation ◽  
Two Dimensional ◽  
Uniform Channel

Equations of motion are derived for long gravity waves in a straight uniform channel. The cross-section of the channel may be of any shape provided that it does not have gently sloping banks and it is not very wide compared with its depth. The equations may be reduced to those for two-dimensional motion such as occurs in a rectangular channel. The order of approximation in these equations is sufficient to give the solitary wave as a solution.

Cross-Section Deformation Effects in the Vibration of Thin-Walled Beams of Arc Section

1965 ◽  
Vol 7 (3) ◽  
pp. 292-299 ◽  
Author(s):  
S. A. Hasan ◽  
A. D. S. Barr
Keyword(s):  
Cross Section ◽  
Reasonable Agreement ◽  
Natural Frequencies ◽  
Characteristic Functions ◽  
Curved Beam ◽  
Cross Sectional ◽  
Frequency Spectra ◽  
Circular Arc ◽  
Beam Geometry ◽  
Thin Walled

Differential equations describing the coupling of ordinary bending motion with cross-sectional distortion are obtained for thin-walled beams of circular-arc cross-section using Hamilton's principle. In deriving the theory the cross-sectional deformation is assumed to take the form of the characteristic functions of a curved beam of the shape of the section. The variation with wavelength of the frequency spectra which result from the coupling is obtained. Experimental results showing the effects of the variation of the parameters of the beam geometry on the natural frequencies are in reasonable agreement with the theory.

Slip-Flow Pressure Drop in Microchannels of General Cross Section

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
M. Bahrami ◽  
A. Tamayol ◽  
P. Taheri
Keyword(s):  
Boundary Condition ◽  
Pressure Drop ◽  
Cross Section ◽  
Slip Flow ◽  
Homogeneous Boundary Condition ◽  
Slip Boundary Condition ◽  
Arbitrary Cross Section ◽  
Geometrical Parameters ◽  
Cross Sectional ◽  
Slip Boundary

In the present study, a compact analytical model is developed to determine the pressure drop of fully-developed, incompressible, and constant properties slip-flow through arbitrary cross section microchannels. An averaged first-order Maxwell slip boundary condition is considered. Introducing a relative velocity, the difference between the bulk flow and the boundary velocities, the axial momentum reduces to Poisson’s equation with homogeneous boundary condition. Square root of area is selected as the characteristic length scale. The model of Bahrami et al. (2006, “Pressure Drop of Laminar, Fully Developed Flow in Microchannels of Arbitrary Cross Section,” ASME J. Fluids Eng., 128, pp. 1036–1044), which was developed for no-slip boundary condition, is extended to cover the slip-flow regime in this study. The proposed model for pressure drop is a function of geometrical parameters of the channel: cross sectional area, perimeter, polar moment of inertia, and the Knudsen number. The model is successfully validated against existing numerical and experimental data collected from different sources in literature for several shapes, including circular, rectangular, trapezoidal, and double-trapezoidal cross sections and a variety of gases such as nitrogen, argon, and helium.

Influence of Cross-Section Distortion on the Bending Vibration of Thin-Walled Beams of H Section

1964 ◽  
Vol 6 (3) ◽  
pp. 211-218 ◽  
Author(s):  
A. D. S. Barr ◽  
T. Duthie
Keyword(s):  
Differential Equations ◽  
Cross Section ◽  
Reasonable Agreement ◽  
Experimental Results ◽  
Hamilton’S Principle ◽  
Hamilton's Principle ◽  
Bending Vibration ◽  
Cross Sectional ◽  
Thin Walled ◽  
The Cross

Approximate differential equations describing the bending vibration of beams of thin-walled H section, in which the distortion of the cross-section in its own plane is taken into account, are derived from Hamilton's principle using an assumed form for the cross-section deformation. Only the simplest of the cross-sectional deformation configurations which will couple with ordinary bending is considered. The variation with wavelength of the two spectra of frequencies which result from this coupling of the bending and cross-sectional motions is shown for several section geometries. Theoretical curves show reasonable agreement with experimental results from free beams.

Vibration of Stress-Free Hollow Cylinders of Arbitrary Cross Section

1995 ◽  
Vol 62 (3) ◽  
pp. 718-724 ◽  
Author(s):  
K. M. Liew ◽  
K. C. Hung ◽  
M. K. Lim
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Three Dimensional ◽  
Arbitrary Cross Section ◽  
Mode Shapes ◽  
Width Ratio ◽  
Cross Sectional ◽  
Hollow Cylinders ◽  
Displacement Based ◽  
Bending Modes

A three-dimensional elasticity solution to the vibrations of stress-free hollow cylinders of arbitrary cross section is presented. The natural frequencies and deformed mode shapes of these cylinders are obtained via a three-dimensional displacement-based energy formulation. The technique is applied specifically to the parametric investigation of hollow cylinders of different cross sections and sizes. It is found that the cross-sectional property of the cylinder has significant effects on the normal mode responses, particularly, on the transverse bending modes. By varying the length-to-width ratio of these elastic cylinders, interesting results demonstrating the dependence of frequencies on the length of the cylinder have been concluded.

scholarly journals Theory of “dissolution” and “condensation” of the physical geometric characteristics of an arbitrary cross-section under the action of torsion with bending

2019 ◽  
Vol 15 (4) ◽  
pp. 261-270
Author(s):  
Vladimir I. Kolchunov ◽  
Aleksej I. Demyanov ◽  
Nikolay V. Naumov
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Strain State ◽  
Rectangular Cross Section ◽  
Arbitrary Cross Section ◽  
Large Circle ◽  
Stress Strain ◽  
Cross Sectional ◽  
Tangential Stresses ◽  
Stress Strain State

Aim of research - to continue the development of methods for determining the stress-strain state of rods during torsion using materials resistance methods. Methods. A new approach for determining tangential torsional stresses for arbitrary cross sectional rods, based on simplified assumptions of material resistance, is proposed. The main feature of this approach is the approximation of rectangular or any complex cross section of reinforced concrete structures by describing a large circle around the cross section and splitting it into small squares with circles inscribed into them. Results. Three theorems have been formulated, the first of which relates the accumulation of tangential stresses (increments) from the edges of a rectangle to the middle of a rectangular section with the formula for determining tangent stresses for round sections. The second theorem allows to establish a connection between the tangential stresses calculated for each of the small squares-circles and the tangent stresses of the large circle through their increments. The third theorem makes it possible to find tangential stresses for each of the small square circles. The proposed approach allows to remove the need to use special tables for the calculation and not only in the elastic stage. It also makes it possible to separate the stress-strain state in the whole set of round cross-sections from the additional field caused by the deplanation of the rectangular cross-section. In addition, the proposed approach makes it possible to take into account the concentration of angular deformations in the incoming angles and other places with changing geometric parameters.

Anisotropic Elastic Tubes of Arbitrary Cross Section Under Arbitrary End Loads: Separation of Beamlike and Decaying Solutions

2004 ◽  
Vol 72 (4) ◽  
pp. 500-510
Author(s):  
P. Ladevèze ◽  
J. G. Simmonds
Keyword(s):  
Cross Section ◽  
Arbitrary Cross Section ◽  
Constant Thickness ◽  
Cross Sectional ◽  
Edge Zone ◽  
One Dimensional ◽  
Elastic Tubes ◽  
Anisotropic Elastic ◽  
Relative Errors ◽  
Complex Valued

First approximation analytical solutions are constructed for finite and semi-infinite, fully anisotropic elastic tubes of constant thickness h and arbitrary cross section, subject to purely kinetic or purely kinematic boundary conditions. Final results contain relative errors of O(h∕R), where R is some equivalent cross sectional radius. Solutions are decomposed into the sum of an exact beamlike or Saint-Venant solution, treated in Ladevèze et al. (Int. J. Solids Struct., 41, pp. 1925–1944, 2004) and extended in an appendix; a rapidly decaying edge-zone solution; and a slowly decaying semi-membrane-inextensional-bending (MB) solution. Explicit conditions on the boundary data are given that guarantee decaying solutions. The MB solutions are expressed as an infinite series of complex-valued exponential functions times real-valued one-dimensional eigenfunctions which satisfy a fourth-order differential equation in the circumferential coordinate and depend on the pointwise cross sectional curvature only.

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