scholarly journals Application of modified Manning formula in the determination of vertical profile velocity in natural rivers

2016 ◽  
Vol 48 (1) ◽  
pp. 133-146 ◽  
Author(s):  
S. Song ◽  
B. Schmalz ◽  
J. X. Zhang ◽  
G. Li ◽  
N. Fohrer
Keyword(s):  
Aspect Ratio ◽  
Cross Section ◽  
Cross Sections ◽  
Vertical Profile ◽  
Moderate Level ◽  
Coefficient Of Determination ◽  
Future Research ◽  
Simplified Approach ◽  
Flood Season ◽  
Hydraulic Conditions

Seldom studied before, the vertical profile velocity is indicative of the flood process and nutrient transportation process. In this paper, a substitution of cross section hydraulic radius with vertical depth was made to the Manning formula, which was then applied in the vertical profile velocity determination. Simultaneously, the determination accuracy and its relationship with hydraulic conditions were discussed, based on the 1050 vertical profiles sampled from 140 cross sections in flood and moderate level seasons. The observations show the following. (1) The modified Manning formula provides a simplified approach for vertical profile velocity determination with acceptable accuracy. (2) The fitting quality of the profile velocity from the middle region of the cross section and the flood season were higher than that from near the bank or the moderate level season. The coefficient of determination (R2) of the regression for the moderate level season and the flood season were 0.55 and 0.58, while the Nash–Sutcliffe coefficients were 0.64 and 0.82, respectively. (3) Analysis of the determination error and the coefficient of variation showed a positive correlation with the river aspect ratio. This seems to suggest that the modified Manning formula tends to be more applicable in narrow and deep rivers. More measurements from rivers or channels with a high aspect ratio would be meaningful for future research.

scholarly journals Influence of Cross Section Thickness and Aspect Ratio on Deformation during Diffusion Bonding and Impact of Metal Diffusion and Evaporation on Temperature Measurement Accuracy

2020 ◽  
Author(s):  
Thomas Gietzelt ◽  
Volker Toth ◽  
Manfred Kraut ◽  
Uta Gerhards ◽  
Robin Duerrschnabel
Keyword(s):  
Aspect Ratio ◽  
Temperature Measurement ◽  
Contact Pressure ◽  
Cross Section ◽  
Cross Sections ◽  
Diffusion Bonding ◽  
Bonding Temperature ◽  
Process Engineering ◽  
The Cross ◽  
Micro Process Engineering

Diffusion bonding is often used on pre-machined parts to generate internal cavities, e.g. for cooling injection molding tools close to the mold cavity. Only then, the workpieces are finished to their final dimensions. In the case of micro-process devices, however, it is essential to precisely control the deformation, as otherwise uncontrollable pressure losses will occur with channel cross-sections in the sub-millimeter range. Post-processing is not possible. The most important process parameters for diffusion bonding are temperature, dwell time and contact pressure, with the bonding temperature and contact pressure acting in opposite directions and showing a strong non-linear dependence on deformation. In addition, the deformation is influenced by a number of other factors such as the absolute size of the cross-section and the aspect ratio of the parts, the dimensions and distribution of the internal cross sections and the overall percentage of the cross-section to be bonded. In micro process engineering, small material cross-sections in the range of the materials microstructure can facilitate additional deformation mechanisms such as grain boundary sliding, which are not relevant at all for larger structures. For parts consisting of multiple layers, tolerances in thickness and roughness of multiple surfaces must be levelled, contributing to the percentaged deformation. This makes it difficult, especially in micro process engineering and in single or small series production, to determine suitable joining parameters in advance, which on the one hand do not cause unforeseen large deformations, but on the other hand reliably produce highly vacuum-tight components. Hence, a definition of a fixed percentaged deformation does not work for all kinds of components. This makes it difficult to specify parameters for surely obtain high-vacuum tight parts. For successful diffusion bonding, atoms must diffuse over the bonding planes, forming a monolithic part in which the original layers are no longer visible. Only then, mechanical properties identical to those of the base material, which has been subjected to identical heat treatment, can be achieved. In this paper, the impacts of different material cross section widths as well as of the aspect ratio on deformation were investigated. By accident, it was found that also accuracy of the temperature measurement may have a serious impact in terms of deformation.

Saint-Venant Decay Rates for the Rectangular Cross Section Rod

2004 ◽  
Vol 71 (3) ◽  
pp. 429-433 ◽  
Author(s):  
N. G. Stephen ◽  
P. J. Wang
Keyword(s):  
Finite Element ◽  
Aspect Ratio ◽  
Transfer Matrix ◽  
Cross Section ◽  
Cross Sections ◽  
Rectangular Cross Section ◽  
Decay Rates ◽  
Elastic Rod ◽  
Cross Sectional ◽  
Element Transfer

A finite element-transfer matrix procedure developed for determination of Saint-Venant decay rates of self-equilibrated loading at one end of a semi-infinite prismatic elastic rod of general cross section, which are the eigenvalues of a single repeating cell transfer matrix, is applied to the case of a rectangular cross section. First, a characteristic length of the rod is modelled within a finite element code; a superelement stiffness matrix relating force and displacement components at the master nodes at the ends of the length is then constructed, and its manipulation provides the transfer matrix, from which the eigenvalues and eigenvectors are determined. Over the range from plane stress to plane strain, which are the extremes of aspect ratio, there are always eigenmodes which decay slower than the generalized Papkovitch-Fadle modes, the latter being largely insensitive to aspect ratio. For compact cross sections, close to square, the slowest decay is for a mode having a distribution of axial displacement reminiscent of that associated with warping during torsion; for less compact cross sections, slowest decay is for a mode characterized by cross-sectional bending, caused by self-equilibrated twisting moment.

scholarly journals Computation of Normal Depth in Parabolic Cross Sections Using The Rough Model Method

2014 ◽  
Vol 8 (1) ◽  
pp. 213-218
Author(s):  
Bachir ACHOUR
Keyword(s):  
Friction Coefficient ◽  
Aspect Ratio ◽  
Cross Section ◽  
Cross Sections ◽  
Flow Resistance ◽  
Open Channel ◽  
Roughness Coefficient ◽  
Model Method ◽  
Rough Model ◽  
Resistance Coefficients

A new method is applied to calculate the normal depth in an open channel of parabolic cross section. This is the rough model method whose main particularity is to ignore the flow resistance coefficients, such as Chezy’s coefficient and manning’s roughness coefficient. The method is applied to a referential rough model, whose friction coefficient is constant, which explicitly express the hydraulic and geometric characteristics of the model such as aspect ratio. By means of a non-dimensional correction factor, the normal depth is explicitly deduced. The rough model method is applicable to the entire domain of turbulent flow.

Heat Transfer in Rotating Narrow Rectangular Ducts With Heated Sides Parallel to the r-z Plane

2001 ◽  
Vol 124 (1) ◽  
pp. 1-7 ◽  
Author(s):  
Fred T. Willett ◽  
Arthur E. Bergles
Keyword(s):  
Heat Transfer ◽  
Aspect Ratio ◽  
Cross Section ◽  
Cross Sections ◽  
Ambient Pressure ◽  
Tangential Velocity ◽  
Thin Foil ◽  
Uniform Heat Flux ◽  
Density Ratios ◽  
Rotating Channel

In gas turbine blade design, a variety of channel shapes and orientations are used in the cooling circuit. Most of the rotating channel heat transfer research to date has considered channels of square or round cross-sections. This research characterizes the effect of rotation on fully developed turbulent convective heat transfer in ducts of narrow cross-section (height-to-width aspect ratio of 1:10). Experiments were conducted using ducts of narrow cross-section, oriented such that the long sides of the duct cross-section are perpendicular to the direction of blade tangential velocity (parallel to the r-z plane). In the experiment, a high-molecular-weight gas (Refrigerant-134A) at ambient pressure and temperature conditions was used to simulate coolant-to-wall density ratios that match engine conditions. Thin foil heaters were used to produce a uniform heat flux at the long sides of the duct; the narrow sides were unheated. Duct Reynolds numbers were varied up to 31,000; rotation numbers were varied up to 0.11. The test results show the effect of rotation and aspect ratio on duct leading and trailing side heat transfer. The results provide insight into the effect of rotation (Coriolis) in the absence of buoyancy effects. Comparisons with previously reported results are presented to show the effect of cross-section shape on rotating channel heat transfer.

scholarly journals Non-Linear Buckling Analysis of Axially Loaded Column with Non-Prismatic I-Section

2019 ◽  
Vol 5 (3) ◽  
pp. 263
Author(s):  
Adrian Pramudita Dharma ◽  
Bambang Suryoatmono
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Cross Sections ◽  
Plastic Material ◽  
Slenderness Ratio ◽  
Buckling Load ◽  
Coefficient Of Determination ◽  
Average Cross Section ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

In order to use material efficiently, non-prismatic column sections are frequently employed. Tapered-web column cross-sections are commonly used, and design guides of such sections are available. In this study, various web-and-flange-tapered column sections were analysed numerically using finite element method to obtain each buckling load assuming the material as elastic-perfectly plastic material. For each non-prismatic column, the analysis was also performed assuming the column is prismatic using average cross-section with the same length and boundary conditions. Buckling load of the prismatic columns were obtained using equation provided by AISC 360-16. This study proposes a multiplier that can be applied to the buckling load of a prismatic column with an average cross-section to acquire the buckling load of the corresponding non-prismatic column. The multiplier proposed in this study depends on three variables, namely the depth tapered ratio, width tapered ratio, and slenderness ratio of the prismatic section. The equation that uses those three variables to obtain the multiplier is obtained using regression of the finite element results with a coefficient of determination of 0.96.

The shape of free jets of water under gravity

1976 ◽  
Vol 76 (4) ◽  
pp. 625-640 ◽  
Author(s):  
E. O. Tuck
Keyword(s):  
Free Surface ◽  
Aspect Ratio ◽  
Flow Velocity ◽  
Cross Section ◽  
Cross Sections ◽  
Cross Flow ◽  
Free Jets ◽  
Elliptic Cross ◽  
Cross Flow Velocity ◽  
The Cross

A study is made of the form taken by a slender jet of water whose only boundary is a free surface. The only forces acting are inertial and gravitational. Attention is paid to the cross-flow velocity components and to the development of the shape of the cross-section of the jet as it progresses. It is established that a jet with initially elliptic cross-sections can remain elliptical, and the variation in the aspect ratio along the jet is determined.

Electron Irradiation Effects in Polyoxymethylene Crystals Grown Inside Trioxane Crystals

1971 ◽  
Vol 29 ◽  
pp. 78-79
Author(s):  
J. P. Colson ◽  
D. H. Reneker
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Detailed Examination ◽  
The Other ◽  
Electron Micrograph ◽  
Irradiation Effects ◽  
Threefold Axis ◽  
Typical Sample ◽  
Polymer Crystals ◽  
Chain Axis

Polyoxymethylene (POM) crystals grow inside trioxane crystals which have been irradiated and heated to a temperature slightly below their melting point. Figure 1 shows a low magnification electron micrograph of a group of such POM crystals. Detailed examination at higher magnification showed that three distinct types of POM crystals grew in a typical sample. The three types of POM crystals were distinguished by the direction that the polymer chain axis in each crystal made with respect to the threefold axis of the trioxane crystal. These polyoxymethylene crystals were described previously.At low magnifications the three types of polymer crystals appeared as slender rods. One type had a hexagonal cross section and the other two types had rectangular cross sections, that is, they were ribbonlike.

A quantitative approach to inner shell losses

1978 ◽  
Vol 36 (1) ◽  
pp. 526-527 ◽  
Author(s):  
R.D. Leapman ◽  
P. Rez ◽  
D.F. Mayers
Keyword(s):  
Energy Transfer ◽  
Cross Section ◽  
Cross Sections ◽  
Accurate Determination ◽  
Background Intensity ◽  
Core Excitation ◽  
Quantitative Basis ◽  
Cross Section Differential ◽  
Bound Electrons

Microanalysis by EELS has been developing rapidly and though the general form of the spectrum is now understood there is a need to put the technique on a more quantitative basis (1,2). Certain aspects important for microanalysis include: (i) accurate determination of the partial cross sections, σx(α,ΔE) for core excitation when scattering lies inside collection angle a and energy range ΔE above the edge, (ii) behavior of the background intensity due to excitation of less strongly bound electrons, necessary for extrapolation beneath the signal of interest, (iii) departures from the simple hydrogenic K-edge seen in L and M losses, effecting σx and complicating microanalysis. Such problems might be approached empirically but here we describe how computation can elucidate the spectrum shape.The inelastic cross section differential with respect to energy transfer E and momentum transfer q for electrons of energy E0 and velocity v can be written as

Oxygen K near edge structures studied with multiple scattering calculations

1988 ◽  
Vol 46 ◽  
pp. 504-505
Author(s):  
Xudong Weng ◽  
Peter Rez
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Partial Cross Section ◽  
Energy Window ◽  
Edge Structure ◽  
Fine Structures ◽  
Hydrogenic Model ◽  
Electron Energy Loss ◽  
Quantitative Chemical

In electron energy loss spectroscopy, quantitative chemical microanalysis is performed by comparison of the intensity under a specific inner shell edge with the corresponding partial cross section. There are two commonly used models for calculations of atomic partial cross sections, the hydrogenic model and the Hartree-Slater model. Partial cross sections could also be measured from standards of known compositions. These partial cross sections are complicated by variations in the edge shapes, such as the near edge structure (ELNES) and extended fine structures (ELEXFS). The role of these solid state effects in the partial cross sections, and the transferability of the partial cross sections from material to material, has yet to be fully explored. In this work, we consider the oxygen K edge in several oxides as oxygen is present in many materials. Since the energy window of interest is in the range of 20-100 eV, we limit ourselves to the near edge structures.

Absolute inner-shell cross section determination for EELS analysis

1988 ◽  
Vol 46 ◽  
pp. 534-535
Author(s):  
P.A. Crozier
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Absolute Cross Section ◽  
Specimen Thickness ◽  
Mass Thickness ◽  
Scattering Cross ◽  
Before And After ◽  
Estimated Error ◽  
Scattering Cross Sections ◽  
Electron Microscopist

Absolute inelastic scattering cross sections or mean free paths are often used in EELS analysis for determining elemental concentrations and specimen thickness. In most instances, theoretical values must be used because there have been few attempts to determine experimental scattering cross sections from solids under the conditions of interest to electron microscopist. In addition to providing data for spectral quantitation, absolute cross section measurements yields useful information on many of the approximations which are frequently involved in EELS analysis procedures. In this paper, experimental cross sections are presented for some inner-shell edges of Al, Cu, Ag and Au.Uniform thin films of the previously mentioned materials were prepared by vacuum evaporation onto microscope cover slips. The cover slips were weighed before and after evaporation to determine the mass thickness of the films. The estimated error in this method of determining mass thickness was ±7 x 107g/cm2. The films were floated off in water and mounted on Cu grids.

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