scholarly journals The rotation of two circular cylinders in a viscous fluid

1922 ◽  
Vol 101 (709) ◽  
pp. 169-174 ◽  
Keyword(s):  
Viscous Fluid ◽  
Boundary Conditions ◽  
Stream Function ◽  
Elastic Stress ◽  
Steady Motion ◽  
Elastic Equilibrium ◽  
Circular Cylinders ◽  
Two Dimensional ◽  
Concentric Circles ◽  
Hydrodynamical Problem

In a previous communication we employed the solution of the equation ∇ 4 ψ = 0 in bipolar co-ordinates defined by α + iβ = log x + i ( y + a )/ x + i ( y - a ) (1) to discuss the problem of the elastic equilibrium of a plate bounded by any two non-concentric circles. There is a well-known analogy between plain elastic stress and two-dimensional steady motion of a viscous fluid, for which the stream-function satisfies ∇ 4 ψ = 0. The boundary conditions are, however, different in the two cases, and the hydrodynamical problem has its own special difficulties.

scholarly journals A Problem on Viscous Fluid Motion Between two Fixed Cylinders

1970 ◽  
Vol 33 (1) ◽  
pp. 107-115
Author(s):  
SK Ken ◽  
MJ Ahammad
Keyword(s):  
Viscous Fluid ◽  
Stokes Equations ◽  
Unit Length ◽  
Outer Cylinder ◽  
Fluid Motion ◽  
Circular Cylinders ◽  
Two Dimensional ◽  
Fluid Bed ◽  
Academy Of Sciences ◽  
Viscous Fluid Motion

A problem on the two dimensional slow viscous fluid motion obeying the Stokes equations is solved in terms of the Earnshaw stream function, when a line source and equal line sink are arbitrarily situated in a viscous fluid bed between two fixed co-axial circular cylinders. Fluid mechanical properties of interest, such as drags and torques acting upon the cylinders are calculated. Also we have shown the variation of the forces per unit length on the inner cylinder with its radius keeping outer cylinder fixed, whose radius is assumed to be one. DOI: 10.3329/jbas.v33i1.2955 Journal of Bangladesh Academy of Sciences, Vol. 33, No. 1, 107-115, 2009

scholarly journals Flow-induced forces arising during the impact of two circular cylinders

2008 ◽  
Vol 616 ◽  
pp. 205-234 ◽  
Author(s):  
N. BAMPALAS ◽  
J. M. R. GRAHAM
Keyword(s):  
Relative Motion ◽  
Conformal Transformation ◽  
Steady Motion ◽  
Inviscid Flow ◽  
Circular Cylinders ◽  
Square Root ◽  
Two Dimensional ◽  
Incident Flow ◽  
Square Root Singularity ◽  
The Impact

This paper presents numerical simulations of two-dimensional incompressible flow around two circular cylinders in relative motion, which may result in impact. Viscous flow computations are carried out using a streamfunction–vorticity method for two equal-diameter cylinders undergoing a two-dimensional impact in otherwise stationary fluid and for cases of similar impact of two cylinders in a steady incident flow. These results are supported by potential flow calculations carried out using a Möbius conformal transformation and infinite arrays of image singularities. The inviscid flow results are compared with other published work and show that the inviscid forces induced on the cylinders have an inverse square root singularity with respect to the time to impact. All impacts considered in this paper result from steady motion of the cylinders along the line joining their centres.

The Stress Field in a Cylindrically Anisotropic Body Under Two-Dimensional Surface Tractions

1972 ◽  
Vol 39 (3) ◽  
pp. 791-796 ◽  
Author(s):  
N. J. Pagano
Keyword(s):  
Stress Field ◽  
Composite Structures ◽  
Elastic Stress ◽  
Anisotropic Body ◽  
Circular Cylinders ◽  
Important Class ◽  
Two Dimensional ◽  
Direct Extension ◽  
Cylindrically Anisotropic ◽  
Dimensional Surface

In this work, a general solution for the elastic stress field in a cylindrically anisotropic body, the hollow circular cylinder, under surface tractions which do not vary along the generator and which can be expressed in the form of a Fourier series, is presented. The form of the solution is sufficiently general to permit direct extension to an important class of composite structures, namely, laminated circular cylinders. Some of the peculiar effects of anisotropy are illustrated by the solution of a specific boundary-value problem—a circular hole in a large plate under tension.

Diffusion and convection of heat from circular cylinders with known boundary conditions

1970 ◽  
Vol 67 (1) ◽  
pp. 201-207
Author(s):  
E. J. Norminton
Keyword(s):  
Circular Cylinder ◽  
Boundary Conditions ◽  
Incompressible Flow ◽  
Circular Cylinders ◽  
Two Dimensional ◽  
Flow Past ◽  
Diffusion And Convection

AbstractThe problem of the diffusion and convection of heat in two-dimensional, incompressible flow past a circular cylinder is considered. Solutions are found for the temperature at any point exterior to the cylinder in terms of the boundary conditions on the surface and two particular boundary conditions are considered.

On the steady motion of viscous liquid in a corner

1949 ◽  
Vol 45 (3) ◽  
pp. 389-394 ◽  
Author(s):  
W. R. Dean ◽  
P. E. Montagnon
Keyword(s):  
Viscous Liquid ◽  
Stream Function ◽  
Steady Motion ◽  
Polar Coordinates ◽  
Two Dimensional ◽  
Sharp Corner

1. In a steady two-dimensional motion of viscous liquid in the sharp corner formed by the rigid straight boundaries θ = 0, α, where r, θ are plane polar coordinates, it is found that, near enough to the corner, the most important term in the stream-function is of the form rmf(θ). The index m is evaluated in §§ 2–4 for values of α between 360 and 90°, and is found to be complex if α is less than about 146°; the limiting form of the stream-function when α is small is considered in § 5.

On wakes in stratified fluids

1968 ◽  
Vol 33 (3) ◽  
pp. 417-432 ◽  
Author(s):  
G. S. Janowitz
Keyword(s):  
Integral Equation ◽  
Viscous Fluid ◽  
Boundary Conditions ◽  
Linear Problem ◽  
The Body ◽  
General Nature ◽  
Two Dimensional ◽  
Governing Equations ◽  
Lee Waves ◽  
Momentum Integral

The general nature of the flow at large distances from a two-dimensional body moving uniformly through an unbounded, linearly stratified, non-diffusive viscous fluid is considered. The governing equations are linearized using the Oseen and Boussinesq approximations, and the boundary conditions at the body are replaced by a linearized momentum-integral equation. The solution of this linear problem shows a system of jets upstream and a pattern of waves downstream of the body. The effects of viscosity on these lee waves are considered in detail.

Slow motion of viscous liquid in a semi-infinite channel

1951 ◽  
Vol 47 (1) ◽  
pp. 127-141 ◽  
Author(s):  
W. R. Dean
Keyword(s):  
Pressure Gradient ◽  
Viscous Liquid ◽  
Stream Function ◽  
Steady Motion ◽  
Slow Motion ◽  
Biharmonic Function ◽  
Two Dimensional ◽  
Calculated Velocity ◽  
Straight Lines ◽  
Stream Lines

1. A slow two-dimensional steady motion of liquid caused by a pressure gradient in a semi-infinite channel is considered. The medium is bounded by two parallel semi-infinite planes represented in Fig. 1 by the straight lines AB, DE. The stream-function ψ is a biharmonic function of x, y which exactly satisfies the condition that AB, DE must be stream-lines, but the condition that there must be no velocity of slip on these boundaries is satisfied only approximately, and the calculated velocity of slip gives a measure of the accuracy of the solution.

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