Experimental study of the velocity of the flow of highly viscous Newtonian liquid in a curved rectangular duct

1986 ◽  
Vol 51 (1) ◽  
pp. 66-74
Author(s):  
Pavel Seichter
Keyword(s):  
Experimental Study ◽  
Stokes Equation ◽  
Cross Section ◽  
Circular Cross Section ◽  
Newtonian Liquid ◽  
Creeping Flow ◽  
Navier Stokes ◽  
Rectangular Duct ◽  
Navier Stokes Equation ◽  
Experimental Values

Thermistor anemometer measurements in a curved rectangular duct and a straight circular cross section tube permitted verification of the theoretical values of tangential velocities computed on the basis of the solution of the Navier-Stokes equation for the drag isothermal and creeping flow of a Newtonian liquid. From comparison of the theoretical and experimental values there follows that the achieved agreement is acceptable.

The Permeability of a Uniformly Vuggy Porous Medium

1973 ◽  
Vol 13 (02) ◽  
pp. 69-74 ◽  
Author(s):  
Graham H. Neale ◽  
Walter K. Nader
Keyword(s):  
Porous Medium ◽  
Flow Field ◽  
Stokes Equation ◽  
Spherical Cavity ◽  
Creeping Flow ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Darcy Equation ◽  
Matrix Permeability ◽  
Flow Vector

Abstract Using the creeping Navier Stokes equation within a spherical cavity and the Darcy equation in the surrounding homogeneous and isotropic porous medium, the flow field in the entire system is evaluated. Applying this result to a representative generalizing model of a uniformly vuggy, homogeneous and isotropic porous medium, an engineering estimation of the interdependence of the matrix permeability km, the vug porosity permeability km, the vug porositytotal volume of vug space 0v = ----------------------------total volume of sample and the system permeability ks of the vuggy porous medium is derived. This interdependence can be expressed by the formula: Introduction The objective of this study is the derivation of an engineering formula that shows the interdependence of matrix permeability, km, vug porosity, 0 v, and system permeability, ks, of a uniformly vuggy porous medium. In the first section, with the above porous medium. In the first section, with the above goal in mind and to satisfy more general interests, we shall study and predict the flow field within a single cavity bounded by a sphere, of radius R, and in the surrounding homogeneous and isotropic porous medium. In the second section, we shall porous medium. In the second section, we shall suggest as a generalizing model of a uniformly vuggy, homogeneous and isotropic porous medium a regular cubic array of monosized spherical cavities. Applying the formula for the pressure field near a single spherical cavity, we shall then develop the sought engineering formula. To describe the creeping flow of the incompressible liquid of viscosity, in the spherical cavity, we shall employ the creeping Navier Stokes equation, .............................(1) The Darcy equation, ,...........................(2) will be used to describe the flow of this liquid in the porous medium of permeability k that fills the space outside the cavity. p designates the liquid pressure referred to datum, denotes the flow pressure referred to datum, denotes the flow vector, and * is used to indicate macroscopically averaged quantities pertaining specifically to a porous medium. porous medium. In hydrodynamics, one generally requests continuity of the pressure, of the flow vector, and of the shear tensor throughout the fundamental domain of the problem - in particular, along the boundary surfaces, which separate subdomains. When applying these principles to this problem, one would impose at the spherical boundary that separates the cavity from the porous medium:continuity of the pressure,continuity of the component of u that is orthogonal to the surface,continuity of the other component of u that is tangential to the surface,continuity of the shear component tangential to the surface. Arguments of this nature have lead to the suggestion of a generalization of the Darcy equation, namely, the Brinkman equation, ...............(3) However, both the necessity and the validity of this generalization have been challenged; indeed, it has been shown that a mathematically consistent solution of our problem may be obtained, using Eqs. 1 and 2 within the respective subdomains, provided one abandons the request for continuity of the shear at the wall of the cavity (compare Boundary Condition d above).** SPEJ P. 69

Wavelet-distributed approximating functional method for solving the Navier-Stokes equation

1998 ◽  
Vol 115 (1) ◽  
pp. 18-24 ◽  
Author(s):  
G.W. Wei ◽  
D.S. Zhang ◽  
S.C. Althorpe ◽  
D.J. Kouri ◽  
D.K. Hoffman
Keyword(s):  
Stokes Equation ◽  
Functional Method ◽  
Navier Stokes ◽  
Navier Stokes Equation

scholarly journals Generalized Navier–Stokes Equations and Dynamics of Plane Molecular Media

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 288
Author(s):  
Alexei Kushner ◽  
Valentin Lychagin
Keyword(s):  
Carbon Dioxide ◽  
Internal Structure ◽  
Stokes Equation ◽  
Hydrogen Cyanide ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations

The first analysis of media with internal structure were done by the Cosserat brothers. Birkhoff noted that the classical Navier–Stokes equation does not fully describe the motion of water. In this article, we propose an approach to the dynamics of media formed by chiral, planar and rigid molecules and propose some kind of Navier–Stokes equations for their description. Examples of such media are water, ozone, carbon dioxide and hydrogen cyanide.

A note on the solution of the Navier-Stokes equations for a spherically symmetric expansion into a very low pressure

1973 ◽  
Vol 59 (2) ◽  
pp. 391-396 ◽  
Author(s):  
N. C. Freeman ◽  
S. Kumar
Keyword(s):  
Shock Wave ◽  
Reynolds Number ◽  
Stokes Equation ◽  
Stokes Equations ◽  
Low Pressure ◽  
Navier Stokes ◽  
Spherically Symmetric ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Type Flow

It is shown that, for a spherically symmetric expansion of a gas into a low pressure, the shock wave with area change region discussed earlier (Freeman & Kumar 1972) can be further divided into two parts. For the Navier–Stokes equation, these are a region in which the asymptotic zero-pressure behaviour predicted by Ladyzhenskii is achieved followed further downstream by a transition to subsonic-type flow. The distance of this final region downstream is of order (pressure)−2/3 × (Reynolds number)−1/3.

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