Paper 28: Laminar Radial Flow between Parallel Plates and its Application to Viscosity Measurements

1965 ◽  
Vol 180 (10) ◽  
pp. 118-126
Author(s):  
John Ll. Moses
Keyword(s):  
Radial Flow ◽  
Stokes Equations ◽  
Rotating Cylinder ◽  
Creeping Flow ◽  
Navier Stokes ◽  
Parallel Plates ◽  
Navier Stokes Equations ◽  
Inertia Term ◽  
Viscosity Measurements ◽  
Final Equation

To supplement viscosity measurements of water made by the more conventional methods, for example by capillary or rotating cylinder viscometers, it was decided to make a ‘radial flow viscometer’ as outlined by H. Gümbel in Barr's ‘Monograph of viscosity’ (1)†. The radial flow viscometer consists principally of two flat discs separated by a known distance, the fluid being forced to flow radially inward and leaving the discs through a hole in the centre of one of the discs. Before the method could be adopted, it was essential to devise a formula which would account for the inertia term in the equation of motion, since disregard of the inertia term would render the final equation inaccurate. An equation has been developed from the Navier-Stokes equations, which gives a solution involving elliptic integrals. An attempt is made to compare the above solution with the well-known creeping flow solution and with experimental results. Preliminary tests for varying flows and varying widths of separation of the discs have shown discrepancies of under 2 per cent between experimental and theoretical values.

Internal laminar flow

2018 ◽  
Author(s):  
Marcel Escudier
Keyword(s):  
Poiseuille Flow ◽  
Stokes Equations ◽  
Circular Cross Section ◽  
Navier Stokes ◽  
Parallel Plates ◽  
Concentric Cylinder ◽  
Navier Stokes Equations ◽  
Concentric Cylinders ◽  
Constant Viscosity ◽  
Pressure Driven Flow

In this chapter it is shown that solutions to the Navier-Stokes equations can be derived for steady, fully developed flow of a constant-viscosity Newtonian fluid through a cylindrical duct. Such a flow is known as a Poiseuille flow. For a pipe of circular cross section, the term Hagen-Poiseuille flow is used. Solutions are also derived for shear-driven flow within the annular space between two concentric cylinders or in the space between two parallel plates when there is relative tangential movement between the wetted surfaces, termed Couette flows. The concepts of wetted perimeter and hydraulic diameter are introduced. It is shown how the viscometer equations result from the concentric-cylinder solutions. The pressure-driven flow of generalised Newtonian fluids is also discussed.

An unsteady two-cell vortex solution of the Navier—Stokes equations

1970 ◽  
Vol 41 (3) ◽  
pp. 673-687 ◽  
Author(s):  
P. G. Bellamy-Knights
Keyword(s):  
Radial Flow ◽  
Stokes Equations ◽  
Circumferential Velocity ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Radial Flux ◽  
Vortex Solution ◽  
Flow Systems ◽  
Vortex Solutions

The steady two-cell viscous vortex solution of Sullivan (1959) is extended to yield unsteady two-cell viscous vortex solutions which behave asymptotically as certain analogous unsteady one-cell solutions of Rott (1958). The radial flux is a parameter of the solution, and the effect of the radial flow on the circumferential velocity, is analyzed. The work suggests an explanation for the eventual dissipation of meteorological flow systems such as tornadoes.

scholarly journals CENTRIFUGAL DESTABILIZATION AND RESTABILIZATION OF PLANE SHEAR FLOWS

1996 ◽  
Vol 06 (02) ◽  
pp. 409-413
Author(s):  
A. J. CONLEY
Keyword(s):  
Viscous Fluid ◽  
Linear Stability ◽  
Stokes Equations ◽  
Path Following ◽  
Incompressible Viscous Fluid ◽  
Navier Stokes ◽  
Parallel Plates ◽  
Plane Shear ◽  
Navier Stokes Equations ◽  
Spectral Techniques

The flow of an incompressible viscous fluid between parallel plates becomes unstable when the plates are tumbled. As the tumbling rate increases, the flow restabilizes. This phenomenon is elucidated by path-following techniques. The solution of the Navier-Stokes equations is approximated by spectral techniques. The linear stability of these solutions is studied.

scholarly journals An Axisymmetric Squeezing Fluid Flow between the Two Infinite Parallel Plates in a Porous Medium Channel

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
S. Islam ◽  
Hamid Khan ◽  
Inayat Ali Shah ◽  
Gul Zaman
Keyword(s):  
Differential Equation ◽  
Porous Medium ◽  
Fluid Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Parallel Plates ◽  
Transform Method ◽  
Navier Stokes Equations ◽  
Differential Transform ◽  
Fluid Parameters

The flow between two large parallel plates approaching each other symmetrically in a porous medium is studied. The Navier-Stokes equations have been transformed into an ordinary nonlinear differential equation using a transformationψ(r,z)=r2F(z). Solution to the problem is obtained by using differential transform method (DTM) by varying different Newtonian fluid parameters and permeability of the porous medium. Result for the stream function is presented. Validity of the solutions is confirmed by evaluating the residual in each case, and the proposed scheme gives excellent and reliable results. The influence of different parameters on the flow has been discussed and presented through graphs.

scholarly journals CREEPING FLOW PAST A POROUS APPROXIMATELY SPHERICAL SHELL: STRESS JUMP BOUNDARY CONDITION

2011 ◽  
Vol 52 (3) ◽  
pp. 289-300 ◽  
Author(s):  
D. SRINIVASACHARYA ◽  
M. KRISHNA PRASAD
Keyword(s):  
Boundary Condition ◽  
Spherical Shell ◽  
Stokes Equations ◽  
Jump Condition ◽  
Creeping Flow ◽  
Navier Stokes ◽  
Free Fluid ◽  
Stress Jump ◽  
Navier Stokes Equations ◽  
Stress Jump Boundary Condition

AbstractThe creeping flow of an incompressible viscous liquid past a porous approximately spherical shell is considered. The flow in the free fluid region outside the shell and in the cavity region of the shell is governed by the Navier–Stokes equations. The flow within the porous annular region of the shell is governed by Brinkman’s model. The boundary conditions used at the interface are continuity of the velocity, continuity of the pressure and Ochoa-Tapia and Whitaker’s stress jump condition. An exact solution for the problem and an expression for the drag on the porous approximately spherical shell are obtained. The drag is evaluated numerically for several values of the parameters governing the flow.

scholarly journals Asymptotic solution of the low Reynolds-number flow between two co-axial cones of common apex

1984 ◽  
Vol 7 (4) ◽  
pp. 765-784 ◽  
Author(s):  
M. A. Serag-Eldin ◽  
Y. K. Gayed
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Asymptotic Series ◽  
Creeping Flow ◽  
Navier Stokes ◽  
Cross Sectional ◽  
Navier Stokes Equations ◽  
Spherical Coordinate ◽  
Flow Solution ◽  
Reynolds Number Flow

The paper is concerned with the axi-symmetrlc, incompressible, steady, laminar and Newtonian flow between two, stationary, conical-boundaries, which exhibit a common apex but may include arbitrary angles. The flow pattern and pressure field are obtained by solving the pertinent Navier-Stokes' equations in the spherical coordinate system. The solution is presented in the form of an asymptotic series, which converges towards the creeping flow solution as a cross-sectional Reynolds-number tends to zero. The first term in the series, namely the creeping flow solution, is given in closed form; whereas, higher order terms contain functions which generally could only be expressed in infinite series form, or else evaluated numerically. Some of the results obtained for converging and diverging flows are displayed and they are demonstrated to be plausible and informative.

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