Fluid Of Constant Viscosity Research Articles

Rayleigh Taylor instability of a viscous Hall plasma with magnetic field

The influence of finite Larmor frequency on the stability of a viscous, finitely conducting liquid in a downward gravitational field under the influence of a uniform magnetic field directed along or normal to gravity, is investigated. The solution in each case is shown to be characterized by a variational principle Based on the variational principle, an approximate solution is obtained for the stability of a layer of fluid of constant kinematic viscosity and an exponentia density distribution. It has been found that finite resistivity and finite Larmor frequency do not introduce any instabifity in a potentially stable configuration. However, for a potentially unstable configuration we find that, for an ideal Hal plasma, the results depend on the orientation of the magnetic field, though the instability persists for all wave-numbers in the presence of non-ideal (finite resistivity and viscosity) effects. For the field aligned with gravity, it is found that a potentially unstable field-free configuration is stabilized if the buoyancy number B ( = gβ/12 V2) is less than unity. For B > 1, the instability arises for wave-numbers exceeding a critical value, which decreases on allowing for Hall terms in the generalized Ohm's law, suggesting a destabilizing influence of finite Larmor frequency. For an ambient horizontal magnetic field, it is found that an ideal plasma is stable, even for B > 0, for perturbations confined to a cone about the magnetic field vector. The angle of the cone of stable propagation, however, decreases on account of finite Larmor frequency.

Strength of thick-walled permeable cylinders

The problem of a thick-walled porous cylinder subjected to internal, external and axial pressures is investigated. A general solution, within the elastic range, is derived, with due consideration to the effect of injection pressure on the viscosity of the permeating fluid. It is established that, under the same dimensional and boundary conditions, the tangential stress induced in the cylinder would assume its highest values for a porous cylinder with a permeating fluid of constant viscosity, and its lowest values for an impermeable cylinder; the difference in stresses developed in permeable and impermeable cylinders could be quite considerable.

Viscous damping of small amplitude waves in a non-homogeneous fluid of infinite depth

A general formula is derived for the viscous damping of small amplitude waves in a non-homogeneous fluid of infinite depth. In the case when the associated inviscid wave motion is irrotational the formula reduces to a simple form and shows, in particular, that the damping for a non-homogeneous fluid of constant kinematic viscosity is identical to that for a homogeneous fluid.

Separation in the Flow Between Eccentric Rotating Cylinders

This study is concerned with the steady flow of a fluid of constant density and viscosity between two eccentric cylinders of fixed parallel axes. The inner cylinder has a constant angular velocity and the outer one is stationary. Approximate solutions of the Navier-Stokes equations were obtained for the two-dimensional flow. These solutions together with an experiment were utilized to study the appearance of an eddy with separation and reattachment points occurring at the outer cylinder.

Lubricant film thickness and wear in rolling point contact : T. E. Tallian, E. F. Brady, J. I. McCool and L. B. Sibley, ASLE Trans., 8 (1965) 411–424

A numerical solution to the elastohydrodynamic lubrication problem of a rigid cylinder and an elastic layer firmly bonded to a rigid substrate in normal approach and separated by a fluid of constant viscosity is presented. The rate of change of the deformation with time was neglected in the present investigation. The governing equations were solved via an iterative method in order to compute the pressure distribution and the corresponding film profile.Influences of the layer thickness, the layer compressibility and the central squeeze-film velocity on the results were investigated. In the case of the Hertzian contact, the present method was validated against the results reported in Herrebrugh [Elastohydrodynamic squeeze films between two cylinders in normal approach, Trans ASME, J Lubric Technol Ser F 1970; 92:292–302] where the results showed a very good agreement.

Methods for Predicting Gas Well Performance

Abstract The depletion performance of gas wells has been investigated bymathematical simulation techniques. The gas well model which was studiedconsisted of a single well located in the center of a bounded, cylindrical, homogeneous reservoir. Dependency of gas compressibility and viscosity onpressure was considered in studies of well performance at both constant massflow rate and constant flowing pressure conditions. To carry out theinvestigation, the nonlinear, second-order, partial differential equation whichdescribes Darcy flow of a nonideal gas through porous media was solvednumerically. Some of the previous investigations of gas well performance have been oflimited general use, because assumptions were introduced to simplify either thegas properties or the basic differential equation. Other studies have beenrigorous in these respects but have presented a very limited set of calculatedresults. The present study was attempted to present a rigorous theoreticalmodel and sufficient numerical results to permit meaningful conclusions to bedrawn. It was found that all terms must be retained in the partial differentialequation to make accurate predictions. The neglect of higher-order terms, e.g., terms of the order of the "gradient squared", leads to serious material balanceerrors at large times and to conservative estimates of gas well performance. The higher the gas flow rate and/or the lower the permeability-thicknessproduct of the formation, the more pronounced are these deviations. Forexample, in a well draining 640 acres in a 25-md-ft formation (8,120 MMcf gasin place) at a constant rate of 993 Mcf/D, the rigorous solution predicts abottom-hole pressure decline from 4,000 to 1,000 psia in 8.7 years. Ifhigher-order terms are neglected in the differential equation, this decline inpressure is predicted to occur in 5.3 years. With the results of the numerical solution of the differential equationas a basis, simple, easy-to-use approximations for predicting gas wellperformance for Darcy flow conditions have been developed. These simpleapproximations are based on the familiar equations for flow of a single, slightly compressible fluid. The approximate methods possess a high degree ofaccuracy and enable the prediction of long-term gas well performance to be madequickly and accurately without the use of a digital computer. Both transientand stable flow period approximations were developed. Introduction In recent years income from the sale of natural gas and associated productshas represented an ever-increasing fraction of the industry's total revenuefrom operations. To meet the surge in demand for natural gas, the industry hasdepended heavily upon established reserves and has actively pursued developmentof new reserves. This search has progressively led to reservoirs whichyesterday were too tight and/or deep to yield the desired return on investedcapital. More than ever before, evaluation accuracy is now required to forecastthe criteria upon which engineering recommendations and management decisionsare based. Considerable effort has been expended by both research and operationspersonnel on the development and application of methods for analyzing andpredicting the performance of gas wells. Fundamentally, the problem is thefamiliar one of extracting data during the drilling, testing and earlyproduction life of a well and applying these data within an accurate simulationmodel to predict long-term behavior. During the past 30 or more years avoluminous literature dealing specifically with gas field problems has beengenerated. A recent book1 lists a comprehensive bibliography of publishedmaterial through 1959. Over 1,200 references are cited. Since then 39additional articles on natural gas technology have been published inTransactions volumes of the Society of Petroleum Engineers of AIME. Most existing theory for predicting gas well performance requires that oneor more idealizations (e.g., steady-state flow, ideal gas of constantviscosity, small and constant compressibility and constant-viscosity fluid) beapplied. Although existing theory may apply directly or be adapted by variousartifices to describe specific gas well and reservoir behavior, no widelyapplicable method is available, and existing methods appear to be subject toappreciable error unless better limits of applicability are defined.

On plane linear magnetohydrodynamic waves

This paper investigates the perturbation modes of the steady parallel flow of a compressible fluid of finite constant viscosity and electrical conductivity in a uniform arbitrarily oriented magnetic field. In particular, in addition to the classical fast and slow sound and Alfven modes, one obtains some waves whose amplitude is finite whenever the diffusive coefficients are finite and which resemble the diffusion of vorticity from stream surfaces in classical hydrodynamics. The paper also re-interprets upward-facing MHD waves and upstream wakes in a new way.

A general solution of the equations of hydrodynamics

Consider a fluid of constant viscosity μ. If the fluid is incompressible, we suppose it to move in a conservative field in which the force per unit mass is - ∇Ω. If the fluid is compressible, we suppose the field of force to be absent. Both cases are included if we write V = ερΩ, where ε = 1 for an incompressible fluid, and ε = 0 for a compressible fluid. The equation of continuity

The Character of the Instability of an Incompressible Fluid of Constant Kinematic Viscosity and Exponentially Varying Density.

The equations determining the rate of growth of a horizontal periodic disturbance (of a given wave number k) in an incompressible fluld of constant kinematic viscosity ( ) and exponentially varying density (p = po exp [p13]) are obtained. It is shown that this rate of growth depends on the two dimensionless parameters L = Ip and G = g7 p3, where I is the depth of the uld layer considered and g is the value of gravity. For a number of assigned values of L and G, the dependence of the growth rate on = k/fl) is established, and the mode of maximum instability (K = K ) is determined. For large or small values of G, simple asymptotic formulas for K are derived,