Sound velocity fluids

McQueen et al. (1982) demonstrated that by placing a series of high-impedance transparent fluids (called optical analyzers) over the sample at a series of thicknesses less than d in the target that the overtaking rarefaction (sound) velocity can be accurately obtained. Arrival of rarefaction waves rapidly reduce the shock pressure. These wave arrivals could be very readily detected by the change in light radiance caused by the onset of a decrease in shock amplitude when the rarefaction wave caught up to the shock front. The... 

The maximum possible velocity of a compressible fluid in a pipe is sonic (speed of sound) velocity, as ... 

Condition (2) is also quite common. For instance, in crystals it results in a reduced sound velocity, v q) when q approaches a boundary of the Brillouin zone [93,96], a direct result of the periodicity of a crystal lattice. In addition, interaction between modes can lead to creation of soft mode with qi O and corresponding structural transitions [97,98]. The importance of nonlocality at fluid interfaces and the corresponding softening of surface modes has been demonstrated recently, both theoretically [99] and experimentally [100]. 

In practice, this is equivalent to a reduction in the heat of reaction with consequent, drop in wave velocity. From such considerations it would appear that the highest steady- wave velocity will be realized only if the sum. of sound and fluid velocities at the end of the steady- zone is equal to the wave- speed itself. This condition, postulated by D. -L. Chapman in 1899 and by E. Jouguet in 1904, is known as the Chapman-Jouguet (C-J) condition. In further discussion, Taylor (pp 69ff), following the approach developed by E. Jouguet in 1917 and by R. Becker in 1922, showed that the C-J condition does hold at one point (pi,vj), of all those defined by eq (VI.6) (Ref 26, pp 68-9)... 

Acoustical temperature sensors can theoretically measure temperature from the cryogenic range to plasma levels. Their accuracy can approach that of primary standards. Temperature measurements can be made not only in gases but also in liquids or solids, on the basis of the relationship between the sound velocity and temperature shown in Figure 3.163. The acoustic velocity can be detected by immersing a rod or wire into the fluid or by using the medium itself as an acoustic conductor. The sensor rod can measure the temperature at a point or, by means of a series of constrictions or indents, can profile or average the temperature within the medium. 

Operation. In a diffusion pump, the pump fluid is heated so that a vapour pressure of 1-10 mbar is established in the boiler. The vapour rises in the jet assembly where it is expanded through nozzles and enters the space between the nozzle and the cooled wall of the pump at high supersonic velocity. Pumping action is based on the transfer of momentum in collisions between the high speed (several times the speed of sound) pump fluid vapour molecules and particles that have entered the vapour jet. 

It is far easier to measure sound velocity and attenuation in fluids than solids. The reason for this is that sample presentation is much simpler in the case of fluids because they flow around the transducers, which may be held static or even moved through the sample. This is not generally the case with solids. For an example of the in-line application of ultrasound to the measurement of solid fat content in margarine during manufacture, see Figure 21.2. 

Table 3.4.1 FPW Density Determinations for Low-Viscosity Liquids [62]. Velocity of Sound in Fluid is Denoted by vp. The Measured Frequencies for Air Loading and Methanol Loading Yielded the Device Parameters M = 6.411 x 10 kg/m and Tx + B 539.2 N/m Used in Calculating Predicted Responses for...

Kg/p = Vp — (4/3)V. This new parameter (sometimes thought of as the P-wave velocity of an equivalent fluid, for which G = 0) can be determined directly from static compression data V = Kg/p = (1 + Tay)(bP/bp)p. The bulk sound velocity possesses another desirable feature, in that it can also be constrained indirectly through chemical equilibrium experiments. Chemical equilibria describe free energy minima the pressure dependence of free energy is described by the molar volume, and the pressure dependence of volume (or density) is described by Kp and hence V. Thus, experimental determinations of equilibrium phase boundaries can... 

Note that Eq. 7.5.16 was derived from the energy balance equation (first law of thermodynamics), and it does not impose a limit on the value of 0. However, the second law of thermodynamics imposes a restriction on the conversion of thermal energy to kinetic energy. For compressible fluids in tubes with uniform cross-sectional area, the velocity cannot exceed the sound velocity hence. 

We have measured sound velocities of various supercritical fluid systems. An attempt to carry forward such measurements on higher temperature isotherms of formic acid was frustrated by chemical reaction toward products that may include carbon dioxide, carbon monoxide, water, hydrogen and differentiated solid-like products at even higher temperatures and pressures. Nonetheless, the diamond anvil cell provides a unique opportunity to study the chemistry and kinetics of fluids under extreme conditions. We also find that CH2O2 is present during the detonation of some common explosives. 

With this definition all the steady-state drag data on single, smooth spheres moving in infinite , quiescent, newtonian fluids at moderate velocities can be represented by aj single curve on Fig. 6.22. This figure shows also drag coefficients for disks and cylinders, to be discussed later. It is limited to steady velocities of less than about one half the local speed of sound velocities higher than this are discussed elsewhere [18]. 

At sufficiently low frequency and small amplitude the sound velocity W in a fluid can be regarded as a purely thermodynamic property related to the adiabatic compressibility jSs = — 1 [V dVldp)s and the density p = M[V by... 

A practical explanation for the velocity-porosity variations is provided by a simple elastic theory (Wood, 1941) where seawater-saturated, unconsolidated marine sediments are considered to be nonrigid systems, consisting of discrete, noninteracting mineral grains suspended in seawater (Hamilton, 1971,1972). Sound velocity would only depend on the relative proportion of solid and fluid, and their respective compressibilities and densities, expressed through Hookean elastic equations (except for attenuation which must be treated viscoelastically) (Hamilton, 1972,1980). 

When the flow velocity reaches the sound velocity in the fluid, (i.e., the Mach number is one) the flow becomes choked, and the mass flow through the nozzle cannot be raised further by decreasing the back pressure. Flash evaporation in the nozzle can affect choking of the nozzle. 

Macroscopic volume and mass Gas sorption SEM Static or d3mamic fluid permeation Sound velocity measurement Wetting EDX... 

It is well known that electrical conductivity of liquid solutions depends on the concentration of ions and their activity. The aqueous fluids in pipelines usually are electrolyte solutions and the conductivity is proportional to the salt concentration. The activity of the ions is related to temperature, and impurity like nonconductive chemical additives. Measurements of electrical conductivity could directly reflect the concentrations of chemicals such as salts, THIs (alcohol) and KHIs (polymers). (Clay and Medwin, 1977) [6] presented a simple correlation in which the sound velocity in sea water was described as a function of sahnity and temperature. Acoustic velocity has been successfully applied to investigate a variety of solutions and binary gas mixtures (Jerie, et al., 2004 Vibhu, et al., 2004 Goodenough, et al., 2005 Vyas, et al., 2006) [11] [25] [9] [26]. As a result, electrical conductivity and acoustic velocity were chosen as two parameters to simultaneously determine both salt and inhibitor concentrations. Artificial neural network (ANN) provides a numerical tool for such applications in which multi-parameter correlations are needed but the interaction and the relations between the parameters are not well known (Sundgren, et al., 1991 Broten and Wood, 1993) [21] [4]. Therefore, ANN correlations were developed to determine salt and inhibitor concentrations using the measured electrical conductivity, acoustic velocity, and temperature. 

Due to the number of fluids investigated, results are reported in Table Il-a and Table Il-b and some typical cases are plotted in figures 1 and 2. A discontinuity in the sound velocity versus pressure curves can be observed in some lubricants (fig. 2). This discontinuity is interpreted 24 by the apparition of an amorphous phase (a solid like phase) in the sample. Due to the hydrostatic pressure, molecules are compressed and the free volume available is also reduced. Ultra sonic waves are sensitive to this evolution longitudinal waves introduced local pressure fluctuations and the speed of propagation is dependant of the density and the molecular state of the tested sample. 

The velocity in the narrowest cross section in a safety valve may reach the sound velocity at maximum. Simultaneously, the pressure decreases to its minimum value, the fluid dynamic critical pressure, and the mass flow rate is maximized. 

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