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Showing papers on "Slip ratio published in 1971"


Journal ArticleDOI
TL;DR: In this article, simple and accurate expressions for the velocity slip coefficient and the diffusion slip velocity are obtained by applying a variational technique to the linearized Boltzmann equation for a multicomponent gas mixture.
Abstract: Simple and accurate expressions for the velocity slip coefficient and the diffusion slip velocity are obtained by applying a variational technique to the linearized Boltzmann equation for a multicomponent gas mixture.

81 citations


Journal ArticleDOI
TL;DR: In this paper, an analysis of internal flows with surface mass transfer is performed in which account is taken of velocity slip at the surface of the porous bounding wall, and solutions for channel and tube flows reveal a variety of interesting effects of the velocity slip, which depend upon whether fluid is injected or withdrawn at the bounding-wall and upon the sign of the streamwise pressure gradient.
Abstract: An analysis of internal flows with surface mass transfer is performed in which account is taken of velocity slip at the surface of the porous bounding wall. The solutions for channel and tube flows reveal a variety of interesting effects of velocity slip, which depend upon whether fluid is injected or withdrawn at the bounding wall and upon the sign of the streamwise pressure gradient. For example, relative to the situation in which there is no slip, the streamwise pressure gradient may either increase or decrease in the presence of slip and may even undergo a change of sign.

29 citations


Patent
11 Mar 1971
TL;DR: In this paper, an improved anti-skid system for a vehicle which effectively utilizes an approximated slip ratio between vehicle or body velocity and wheel velocity to generate a brake release signal for the brake release valve but without actually utilizing a vehicle and body velocity detector is presented.
Abstract: An improved anti-skid system for a vehicle which effectively utilizes an approximated slip ratio between vehicle or body velocity and wheel velocity to generate a brake release signal for a brake release valve but without actually utilizing a vehicle or body velocity detector. Storage apparatus is used to store a reference signal representing vehicle velocity but actually corresponding to a present or just past maximum value of wheel velocity. Control apparatus is then utilized for removing energy from the storage apparatus at a controlled predetermined rate chosen to approximate the expected vehicle deceleration (but without using an actual vehicle or body deceleration detector) such that the reference signal (capacitor voltage) will continue to accurately represent approximate vehicle velocities even during periods of deceleration. Various exemplary embodiments are described for the control apparatus which may be used to hold the discharge rate constant, to change it from a first low rate to a second high rate during brake release (for compensating inherent time lags in the vehicle brake system) and/or to continuously change the rate in an inverse dependency upon wheel deceleration to even more closely approximate actual vehicle deceleration under variable road conditions. Other features of the improved system may be used to result in rapid oscillatory brake releases as a transition both before and after a more prolonged brake release period to provide for smoother operation of the anti-skid system. Spurious influences of any A.C. ripple components on the detected wheel velocity signal may also be substantially eliminated by using some of the features of this system.

23 citations


Book ChapterDOI
01 Jan 1971
TL;DR: In this paper, the vanishing condition of a fourth-order determinant was used to derive the critical flow condition for two-phase annular flows with or without thermal equilibrium in constant cross-section pipes.
Abstract: From international symposium on two-phase systems; Haifa, Israel (29 Aug 1971). See CONF-710836-. For describing two-phase one-component annular flows with thermodynamic equilibrium in constant cross-section pipes, a system of four differential equations must be solved by a stepby-step procedure. It is shown that this system must include one continuity equation, two momentum equations, and one energy equation. The critical flow condition is given by the vanishing condition of a fourth-order determinant. At given pressure and quality, this condition can be presented as a relation between critical mass-velocity and slip- ratio. An entropy balance equation is deduced from the other balance equations by means of the second principle of thermodynamics and it is shown that it can be used to derive the same critical flow condition. This variable slip model exhibits the increase of critical flow-rates with decreasing slip ratios occurring experimentally when decreasing the L/D parameter. The hypothesis of thermal equilibrium may be avoided in order to include jet flows which occur in short pipes. This requires an additional heat-balance equation. The critical flow conditions are also determined for two-component flows with separated phases with or without thermal equilibrium. (auth)

11 citations


Journal ArticleDOI
TL;DR: In this article, the authors studied the nature of flow choking in steam-water mixtures passing through a tube with ever increasing pressure gradient and found that flow regimes varied from purely entrained to annular entrained and slug entrained as quality decreased.
Abstract: The nature of flow choking has been studied as steam-water mixtures are passed through a tube with ever increasing pressure gradient. Choked flow for two-phase, one-component mixtures has been characterized with a separated flow model as resulting from maximization of the ratio of gas to liquid velocities, or slip ratio. Slip ratios at choking were measured and found to increase from 1.2 to 5.0 at 30 lb./sq.in. exit plane pressure with decrease in quality from 0.95 to 0.02. Separated models predict either 9.3 or 28.4 with no quality dependence. The difference is attributed to liquid entrainment. Flow regimes were observed to vary from purely entrained to annular entrained to slug entrained as quality decreased. Normal shock waves were observed in the free jet at qualities above 0.25. Choking flow rates were predicted with an average error of less than 2% with a stagnation energy balance model using an empirically developed slip ratio relation corrected for entrainment.

6 citations



Journal ArticleDOI
TL;DR: In this paper, an analytical continuum solution of the Rayleigh problem in slip flow with applied magnetic field is obtained using a modified initial condition and slip boundary conditions, and the results are uniformly valid for all times and show that the velocity slip and local skin friction coefficient remain almost unaffected by the imposition of the magnetic field for small times.
Abstract: An analytical continuum solution of the Rayleigh problem in slip flow with applied magnetic field is obtained using a modified initial condition and slip boundary conditions. The results are uniformly valid for all times and show that the velocity slip and the local skin friction coefficient remain almost unaffected by the imposition of the magnetic field for small times. They increase however with the magnetic field for large times. The present results reduce to the corresponding results of the hydrodynamic case when there is no magnetic field.

4 citations


Journal ArticleDOI
TL;DR: In this article, it was shown that the discharge at the slip point defines regions with and without deposition, and that it is desirable to operate pipelines with high solids' concentration.
Abstract: Earlier work showed that the limit of deposition is given by the slip point, when the bed begins to slide. It had been found that the pressure gradient at slip point depends on the angle subtended by the bed and other factors. In this paper, suitable parameters representative of the pressure gradient, discharge and concentration of solids at the slip point are expressed in terms of this angle. For specific cases, with given pipe size and particle properties, the angle of deposition can be eliminated by plotting gradient parameter versus discharge parameter. This gives a graph similar to those generally used for plotting experimental results for two-phase pipeline flow, on which the locus of the slip point defines regions with and without deposition. It is found that the discharge at the slip point defines regions with and without deposition. It is found that the discharge at the slip point rises to a maximum and then decreases with increasing gradient. In combination with efficiency considerations, this indicates that it is desirable to operate pipelines with high solids' concentration.

2 citations


Journal ArticleDOI
TL;DR: In this article, the time-dependent motion of small gas bubbles in a decelerating liquid is studied and the distance traveled by the bubble and for the bubble slip are derived as functions of liquid gas bubble densities, initial velocities, and in terms of a parameter denoting the ratio of the pressure and viscous interaction forces.
Abstract: The time-dependent motion of small gas bubbles in a decelerating liquid is studied. Expressions for the distance traveled by the bubble and for the bubble slip are derived as functions of liquid gas bubble densities, initial velocities, and in terms of a parameter denoting the ratio of the pressure and viscous interaction forces. Results indicate that in cases where the initial velocity of the bubble is lower than the liquid velocity less the limiting slip, the bubble accelerates relative to the liquid. In cases where the bubble initial velocity is equal to or greater than that of the liquid, the bubble decelerates much faster than the liquid until a limiting slip between the gas bubble and liquid is reached. At the equilibrium conditions, in all cases the gas bubble velocity is found to be smaller than that of the corresponding liquid velocity.

1 citations