Flow in the Hydrodynamic Entrance Region of Ducts of Arbitrary Cross Section

1969 ◽  
Vol 91 (3) ◽  
pp. 345-354 ◽  
Author(s):  
David P. Fleming ◽  
E. M. Sparrow
Keyword(s):  
Experimental Data ◽  
Velocity Field ◽  
Pressure Drop ◽  
Cross Section ◽  
Cross Sections ◽  
Solution Method ◽  
Arbitrary Cross Section ◽  
Entrance Region ◽  
General Method ◽  
Good Agreement

A general method of analysis is presented for determining the developing velocity field and pressure drop for laminar flow in the entrance region of ducts having arbitrary cross sections. Application of the solution method is made to rectangular ducts and to triangular ducts. Available experimental data are compared with the analytical results and good agreement is found to prevail. Development characteristics for six ducts are brought together and compared, and various trends are identified.

Pressure Drop of Fully-Developed, Laminar Flow in Microchannels of Arbitrary Cross-Section

2006 ◽  
Vol 128 (5) ◽  
pp. 1036-1044 ◽  
Author(s):  
M. Bahrami ◽  
M. M. Yovanovich ◽  
J. R. Culham
Keyword(s):  
Experimental Data ◽  
Pressure Drop ◽  
Cross Section ◽  
Numerical Solutions ◽  
Approximate Model ◽  
Arbitrary Cross Section ◽  
Geometrical Parameters ◽  
Polar Moment ◽  
Proposed Model ◽  
Good Agreement

The pressure drop of fully developed, laminar, incompressible flow in smooth mini- and microchannels of arbitrary cross-section is investigated. A compact approximate model is proposed that predicts the pressure drop for a wide variety of shapes. The model is only a function of geometrical parameters of the cross-section, i.e., area, perimeter, and polar moment of inertia. The proposed model is compared with analytical and numerical solutions for several shapes. Also, the comparison of the model with experimental data, collected by several researchers, shows good agreement.

Pressure Drop Due to the Entrance Region in Ducts of Arbitrary Cross Section

1964 ◽  
Vol 86 (3) ◽  
pp. 620-626 ◽  
Author(s):  
T. S. Lundgren ◽  
E. M. Sparrow ◽  
J. B. Starr
Keyword(s):  
Pressure Drop ◽  
Velocity Profile ◽  
Cross Section ◽  
Cross Sections ◽  
Circular Tube ◽  
Essential Feature ◽  
Arbitrary Cross Section ◽  
Entrance Region ◽  
Flow Development ◽  
Prior Analysis

A general analytical method has been devised for determining the pressure drop due to flow development in the entrance region of ducts of arbitrary cross section. The essential feature of the analysis is that the pressure drop can be determined without actually solving for the entrance-region velocity development. Instead, the calculation only requires a knowledge of the fully developed velocity profile. Application of the method is made to a variety of cross sections including the circular tube, elliptical ducts, rectangular ducts, isosceles triangular ducts, and annular ducts. Numerical results are presented and comparisons are made with available experiments and with prior analysis.

In-Plane Vibrations of Thick Circular Rings With T or I Cross Sections

1979 ◽  
Vol 46 (2) ◽  
pp. 470-472
Author(s):  
H. Lecoanet ◽  
J. Piranda
Keyword(s):  
Experimental Data ◽  
Eigenvalue Problem ◽  
Cross Section ◽  
Cross Sections ◽  
Rectangular Cross Section ◽  
Circular Rings ◽  
Theoretical Results ◽  
Good Agreement

This paper deals with the problem of eigenfrequencies and eigenvectors for rings whose cross section may be decomposed in basic rectangular cross sections. The solution is derived from a solution of the in-plane eigenvalue problem for rectangular cross-section thick rings. A good agreement between theoretical results and experimental data is obtained.

Analytical and Experimental Characterization of Flow in Slowly-Varying Cross-Section Microchannels

2010 ◽  
Author(s):  
M. Akbari ◽  
M. Bahrami ◽  
D. Sinton
Keyword(s):  
Pressure Drop ◽  
Cross Section ◽  
Cross Sections ◽  
Rectangular Cross Section ◽  
Arbitrary Cross Section ◽  
Geometrical Parameters ◽  
Elliptical Cross ◽  
Proposed Model ◽  
Hyperbolic Contraction ◽  
Asymmetric Microchannel

This paper outlines a novel approximate solution for determining the pressure drop of laminar, single-phase flow in slowly-varying microchannels of arbitrary cross-section. The proposed analysis is general and applicable to symmetric and asymmetric microchannel cross-sections, as examples compact relationships are reported for elliptical and rectangular shapes for three common wall profiles of linear, sinusoidal and hyperbolic. An experimental setup is designed and pressure drop measurements are conducted to validate the proposed model for streamwised periodic microchannels with rectangular cross-section and linear wall with a range of channel geometrical parameters such as aspect ratio and channel slope. The model is also compared against the numerical and experimental data of hyperbolic contraction with rectangular cross-section collected by others. It is observed that although the proposed model is based on the solution of the elliptical cross-section, it can accurately predict the pressure drop in microchannels of rectangular cross-section.

THE (n, p) CROSS SECTIONS OF TITANIUM ISOTOPES FOR NEUTRON ENERGIES BETWEEN 13.6 MeV AND 19.5 MeV

1966 ◽  
Vol 44 (10) ◽  
pp. 2337-2352 ◽  
Author(s):  
H. L. Pai
Keyword(s):  
Experimental Data ◽  
Cross Section ◽  
Cross Sections ◽  
Emission Cross Section ◽  
Closed Shell ◽  
Proton Emission ◽  
Neutron Energy Range ◽  
Nuclear Temperature ◽  
Good Agreement ◽  
Titanium Isotopes

Using enriched titanium samples, the activation (n, p) and (n, pn; n, np; n,d) cross sections have been measured for the five isotopes of titanium in the neutron energy range from 13.6 to 19.5 MeV. The results were compared with calculations based primarily upon Bodansky's theory (1962), where the first proton emission cross section was taken to be the sum of (n, p) and (n, pn). The (n, pn) cross section was separated from the experimental (n, pn; n, np; n, d) cross section by a multiple-emission calculation. Using the nuclear temperature derived from the experimental data, good agreement was achieved between experiment and theory. It was found that the parameters of Bodansky's equation for the titanium isotopes could be adopted directly from the mass parabolas (Dewdney 1963). It was also found that the (n, p) cross sections were not influenced appreciably by the neutron closed shell.

Laminar Incompressible Flow in the Entrance Region of Ducts of Arbitrary Cross Section

1971 ◽  
Vol 93 (1) ◽  
pp. 113-117 ◽  
Author(s):  
James A. Miller
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Stokes Equations ◽  
Numerical Technique ◽  
Arbitrary Cross Section ◽  
Entrance Region ◽  
Navier Stokes ◽  
Initial Value ◽  
Navier Stokes Equations ◽  
Friction Factors

A combination of the numerical technique of Chorin for the solution of the Navier-Stokes equations and a transformation of the initial value problem to a boundary value problem is shown to allow calculation of the laminar hydrodynamic entrance region of ducts of arbitrary cross section. Numerical examples consisting of the solution for ducts of square and triangular cross sections are presented along with the associated friction factors.

Analytical Solutions for Laminar Fully-Developed Flow in Microchannels With Non-Circular Cross-Section

2009 ◽  
Author(s):  
A. Tamayol ◽  
M. Bahrami
Keyword(s):  
Experimental Data ◽  
Pressure Drop ◽  
General Solution ◽  
Cross Section ◽  
Cross Sections ◽  
Analytical Solutions ◽  
Circular Cross Section ◽  
Fully Developed Flow ◽  
Wide Range ◽  
Simply Connected

Analytical solutions are presented for laminar fully-developed flow in micro/minichannels of hyperelliptical and regular polygonal cross-sections. The considered geometries cover a wide range of common simply connected shapes including circle, ellipse, rectangle, rhomboid, star-shape, equilateral triangle, square, pentagon, and hexagon. Therefore, the present approach can be considered as a general solution. Predicted results for the velocity distribution and pressure drop are successfully compared with existing analytical solutions and experimental data collected from various sources for a variety of geometries, including: polygonal, rectangular, circular, elliptical, and rhombic cross-sections.

scholarly journals Energy Dependence of Total Cross Sections for Reactions with 4, 6he, 6, 7, 9li Nuclei

KnE Energy ◽  
2018 ◽  
Vol 3 (1) ◽  
pp. 21
Author(s):  
Yu Penionzhkevich ◽  
Yu Sobolev ◽  
V Samarin ◽  
M Naumenko
Keyword(s):  
Experimental Data ◽  
Energy Range ◽  
Numerical Solution ◽  
Energy Dependence ◽  
Cross Sections ◽  
Beam Energy ◽  
Microscopic Analysis ◽  
Time Dependent ◽  
Total Cross Sections ◽  
Good Agreement

The paper presents the results of measurement of the total cross sections for reactions 4,6He + Si and 6,7,9Li + Si in the beam energy range 5−50 A⋅MeV. The enhancements of the total cross sections for reaction 6He + Si compared with reaction 4He + Si, and 9Li + Si compared with reactions 6,7Li + Si have been observed. The performed microscopic analysis of total cross sections for reactions 6He + Si and 9Li + Si based on numerical solution of the time-dependent Schrödinger equation for external neutrons of projectile nuclei 6He and 9Li yielded good agreement with experimental data.

RELATIVISTIC OPTICAL MODEL FOR PROTON-NUCLEUS ELASTIC SCATTERING

2002 ◽  
Vol 11 (05) ◽  
pp. 425-436 ◽  
Author(s):  
M. Y. H. FARAG ◽  
M. Y. M. HASSAN
Keyword(s):  
Experimental Data ◽  
Elastic Scattering ◽  
Cross Sections ◽  
Differential Cross ◽  
Optical Potential ◽  
Optical Model ◽  
Potential Model ◽  
Optical Potential Model ◽  
Relativistic Description ◽  
Good Agreement

The relativistic description of the proton-nucleus elastic scattering can be considered within the framework of a relativistic optical potential model. The elastic scattering of proton with the nuclei 12 C , 16 O , 20 Ne , and 24 Mg at 800 MeV and 1.04 GeV are studied for relativistic and nonrelativistic treatments. The real optical potentials and the differential cross sections of these reactions are calculated. The obtained results are compared with the corresponding results obtained from the calculation depending on the Woods–Saxon optical potential which were adjusted to fit the experimental data. The present results are in good agreement with the experimental data.

Microscopic spin-orbit potential for p +6He elastic scattering

2019 ◽  
Vol 28 (09) ◽  
pp. 1950074
Author(s):  
Zakaria M. M. Mahmoud ◽  
Awad A. Ibraheem ◽  
M. A. Hassanain
Keyword(s):  
Experimental Data ◽  
Elastic Scattering ◽  
Cross Sections ◽  
Optical Model ◽  
Spin Orbit ◽  
Current Form ◽  
Density Distributions ◽  
Orbit Potential ◽  
Scattering Cross Sections ◽  
Good Agreement

In this work, we simultaneously reanalyzed the differential elastic scattering cross-sections ([Formula: see text]) and the vector analyzing power ([Formula: see text]) of [Formula: see text]He elastic scattering. This analysis was performed using the folded optical model for both real central and spin-orbit (SO) potentials, respectively. For the imaginary central, we used the usual Woods-Saxon (WS) form. Three different model density distributions are used to calculate the potential. We aimed to examine the applicability of the microscopically derived SO potential and the structure effect of 6He nucleus. The presence of the [Formula: see text] experimental data of [Formula: see text]He makes it interesting for this study. Our calculations showed that the three densities gave similar predictions for the cross-sections data. The three microscopic SO potentials calculations of [Formula: see text] are not in a good agreement with the experimental data. We concluded that the SO formalism in its current form needs more investigations for exotic halo nuclei.

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