摘要:

The div‐invariance of the Lagrangian density is used to determine the canonical form of the energy‐momentum tensor for the Herivel‐Lin spatial variational principle and to show the formal equivalence of the principles due to Herival and Bateman.

ISSN:0031-9171    

DOI:10.1063/1.1761997

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

The pressure field, the Bernoulli‐sum variation, and the different terms of the impulse‐momentum and work‐energy relations have been determined computationally for a conduit expansion of 2:1 and a Reynolds number of 48 in the narrow part of the conduit. The procedure used was the integration of an explicit discretized form of the Navier‐Stokes equations. The calculations were carried out with an IBM 7044 electronic computer. It was found that some terms of the differential and integrated forms of the basic equations were relatively small. The integrated form of the work‐energy relation can be simplified to only three of its terms. The role of the eddy was found to be essentially that of shaping the main flow, the exchange of momentum and energy with the main flow being rather small.

ISSN:0031-9171    

DOI:10.1063/1.1761998

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

The drag on a two‐dimensional cylinder located unsymmetrically between parallel planes is calculated for low Reynolds numbers. The presence of the walls has the mathematical effect of rendering Stokes' approximation uniformly valid. In physical terms, the drag is shown to be independent of the Reynolds number and dependent on cylinder diameter, channel width, and relative fluid velocity at the cylinder axis. The drag is calculated by perturbation methods and is shown to be independent of the fluid shear to the order of approximation given. Thus the solution is applicable to a wide range of boundary conditions. The analysis is compared with the results of two experimental investigations employing radically different shear flows.

ISSN:0031-9171    

DOI:10.1063/1.1761999

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

A torsion pendulum was used to oscillate two solid cylinders in liquid helium II at subcritical velocities. The cylinders were sections of Plexiglas rod, constrained to move with their axes parallel to and equidistant from the axis of rotation by means of two parallel disks (end plates). Theoretical expressions based on the two‐fluid model are derived for the added moment of inertiaIaand the logarithmic decrement 2&pgr;&dgr;. The experimental results between 2.17 and 1.25°K are in close agreement with theory except for a small (1 to 2%) end effect onIa. Penetration depths ranged between 0.03 and 0.59 of the cylinder radius. No dependence ofIaand &dgr; on amplitude was observed for amplitudes up to 0.5 radius.

ISSN:0031-9171    

DOI:10.1063/1.1762000

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

The solutions obtained by Stokes in 1851 for the linear oscillations of a sphere and a cylinder in a viscous fluid are corrected for damping. The effect of damping is to increase both the added mass coefficientkand the damping coefficientk′above the results of Stokes. The correction factors are essentially the same for both cylinder and sphere as well as for the oscillating plane, which suggests that this correction is independent of geometry.

ISSN:0031-9171    

DOI:10.1063/1.1762002

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

The problem of unsteady energy transfer during the expansion of a spherical mass of compressible, gray radiating gas at near‐atmospheric pressure is analyzed. The gas is assumed to be perfect and in local thermodynamic equilibrium. Scattering of radiation as well as ionization and dissociation phenomena are neglected. Energy transfer by conduction is assumed to be insignificant compared to that by radiation or convection. The formulation of the problem is based on first principles of radiative transfer and gas dynamics and is thus valid for a medium of arbitrary optical radius. A finite difference scheme is employed to obtain a first approximation to the solution of the conservation equations. The numerical results are presented graphically for a wide range of parameters of physical interest.

ISSN:0031-9171    

DOI:10.1063/1.1762003

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

The flow of a compressible, viscous, heat‐conducting, radiating gray gas near a flat plate set impulsively in motion in its own plane is considered. The plate Mach number is assumed to be sufficiently large so that dissipation cannot be neglected but not so large that the orders of magnitude of the thermophysical properties are changed. Asymptotic expansions are made for large ratio of the photon to molecular mean free path,N, and general values of the Boltzmann number Bo. In the limitN→ ∞ with Bo finite and plate temperature equal to the temperature of the gas at rest, the asymptotically optimal scalings split the problem into an optically thin, compressible, viscous boundary layer with radiative emission but no self‐absorption and an optically finite, inviscid, acoustic flow with full radiative interaction. The equations in the boundary layer and in the inviscid region are solved numerically for several representative cases. In the boundary layer the velocity profile is only weakly affected by radiation, whereas the temperature is substantially reduced below the radiationless value. In the inviscid region an acoustic wave propagates normal to the plate and is dispersed by long‐range radiative interaction.

ISSN:0031-9171    

DOI:10.1063/1.1761962

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

The collision‐dominated theory of the spherical electrostatic probe is extended to moderate degrees of ionization by taking into account the effect of electron‐ion collisions. It is shown that, in the limitR/&lgr;D→ ∞, the solution of the moderately ionized case can be obtained from that of the weakly ionized case by a simple transformation.

ISSN:0031-9171    

DOI:10.1063/1.1761963

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

A kinetic equation for a homogeneous electron gas is derived to all orders in the plasma parameter &lgr; (the reciprocal number of electrons per Debye sphere). It has the form∂&phgr;1∂t=n=1∞ (e2)n(R¯(n)+&bgr;¯n−R¯n(n)),whereR¯(n)is a Fokker‐Planck type collision integral which rigorously describes distant collisions between (n+1) electrons and diverges logarithmically at small impact parameter; &bgr;¯nis a Boltzmann‐like collision integral for close collisions between (n+1) electrons and diverges at large impact parameter; andR¯n(n)accounts for intermediate collisions between (n+1) electrons and diverges at both large and small impact parameter. Whether or not the various divergent parts of (R¯(n)+ &bgr;¯n−R¯n(n)) exactly cancel each other out has not yet been proven for alln. The infinite sum, however, is a direct consequence of Liouville's equation and is exact at allt. The first term (R¯(1)+ &bgr;¯1−R¯1(1)) has been proven convergent elsewhere. The second‐order term (R¯(2)+ &bgr;¯2−R¯2(2)), which corresponds to ternary correlations (ternary collisions), is examined in detail and found to have its order of magnitude given byO(&lgr;2log &lgr;) +O(&lgr;2).

ISSN:0031-9171    

DOI:10.1063/1.1761964

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

The question of plasma containment in a torus is much more complicated than in an open‐ended mirror system. Serious questions arise of the nonexistence of flux surfaces, of noncontained particle drifts, and of nonexistence of self‐consistent equilibria at small gyroradius.

ISSN:0031-9171    

DOI:10.1063/1.1761965

出版商:AIP    

年代:1967

数据来源: AIP