scholarly journals Assessment of Dimensionless Form of Kostiakov Model

Author(s):  
Mohammad Zakwan
2012 ◽  
Vol 8 (1) ◽  
pp. 1-15
Author(s):  
Gy. Sitkei

Motion of particles with air resistance (e.g. horizontal and inclined throwing) plays an important role in many technological processes in agriculture, wood industry and several other fields. Although, the basic equation of motion of this problem is well known, however, the solutions for practical applications are not sufficient. In this article working diagrams were developed for quick estimation of the throwing distance and the terminal velocity. Approximate solution procedures are presented in closed form with acceptable error. The working diagrams provide with arbitrary initial conditions in dimensionless form of general validity.


Author(s):  
E. de Langre ◽  
J. L. Riverin ◽  
M. J. Pettigrew

The time dependent forces resulting from a two-phase air-water mixture flowing in an elbow and a tee are measured. Their magnitudes as well as their spectral contents are analyzed. Comparison is made with previous experimental results on similar systems. For practical applications a dimensionless form is proposed to relate the characteristics of these forces to the parameters defining the flow and the geometry of the piping.


The behaviour of a viscous vortex ring is examined by a matched asymptotic analysis up to three orders. This study aims at investigating how much the location of maximum vorticity deviates from the centroid of the vortex ring, defined by P. G. Saffman (1970). All the results are presented in dimensionless form, as indicated in the following context. Let Γ be the initial circulation of the vortex ring, and R denote the ring radius normalized by its initial radius R i . For the asymptotic analysis, a small parameter ∊ = ( t / Re ) ½ is introduced, where t denotes time normalized by R 2 i / Γ , and Re = Γ/v is the Reynolds number defined with Γ and the kinematic viscosity v . Our analysis shows that the trajectory of maximum vorticity moves with the velocity (normalized by Γ/R i ) U m = – 1/4π R {ln 4 R /∊ + H m } + O (∊ ln ∊), where H m = H m ( Re, t ) depends on the Reynolds number Re and may change slightly with time t for the initial motion. For the centroid of the vortex ring, we obtain the velocity U c by merely replacing H m by H c , which is a constant –0.558 for all values of the Reynolds number. Only in the limit of Re → ∞, the values of H m and H c are found to coincide with each other, while the deviation of H m from the constant H c is getting significant with decreasing the Reynolds number. Also of interest is that the radial motion is shown to exist for the trajectory of maximum vorticity at finite Reynolds numbers. Furthermore, the present analysis clarifies the earlier discrepancy between Saffman’s result and that obtained by C. Tung and L. Ting (1967).


1988 ◽  
Vol 1 (21) ◽  
pp. 141
Author(s):  
Todd L. Walton ◽  
Philip L.F. Liu ◽  
Edward B. Hands

This paper examines the effects of random and deterministic cycling of wave direction on the updrift beach planform adjacent to a jetty. Results provided using a simplified numerical model cast in dimensionless form indicate the importance of the time series of wave direction in determining design jetty length for a given net sediment transport. Continuous cycling of • wave direction leads to the expected analytical solution. Simplications in the numerical model used restrict the applications to small wave angles, no diffraction, no reflection of waves off structure, no refraction, and no sand bypassing at jetty. The concept can be extended to more sophisticated numerical models.


1977 ◽  
Vol 99 (2) ◽  
pp. 345-352 ◽  
Author(s):  
A. T. Chatas

The purpose of this paper is to indicate a method for estimating values of specified aquifer parameters from an investigation of the reservoir performance of an associated oilfield. To achieve this objective an analysis was made of the simultaneous solution of the material-balance and diffusivity equations, followed by an application of the method of least squares. Three analytical functions evolved, which in dimensionless form were numerically evaluated by computer and tabulated herein. Application of the proffered method requires the simultaneous solution of the three normal equations developed in the paper.


2019 ◽  
Vol 9 (2) ◽  
pp. 211 ◽  
Author(s):  
Filiz Ozgen ◽  
Yasin Varol

The heat transfer of mixed convection in a horizontal channel filled with a porous medium has been studied in this article, given that it plays an extensive role in various technical applications, such as flow of fluid in geothermal resources, formations in chemical industries, the storage of radioactive nuclear waste material, and cooling. Those equations written in a dimensionless form have been solved using the finite difference method for different values of the parameters. The results obtained from the study have been presented through streamlines, isotherms, and both local and average Nusselt numbers. It has been observed that parameters such as the Rayleigh and Peclet numbers have an effect on flow and temperature fields.


1994 ◽  
Vol 49 (9) ◽  
pp. 890-894 ◽  
Author(s):  
M.O. Bulanin ◽  
U. Hohm ◽  
Yu. M . Ladvishchenko ◽  
K . Kerl

Second dielectric virial coefficients Bε (T) of the rare gases Ne, Ar, Kr, and Xe are calculated in a broad range of temperature using accurate HFD-type interatomic interaction potentials and available information on the trace of the pair polarizability Δα. It is shown that the experimentally determined temperature-variation of Bε(T) cannot be reproduced by existing theories. However, it is observed that the reduced dimensionless form of Bε(T) follows a remarkably regular pattern, strongly resembling the sign-inverted temperature variation of the second density virial coefficient Bϱ(T) with the same Boyle-temperature.


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