Speed measurements, sound

Many special-purpose electrical thermometers have been developed, either for use in practical temperature measurement, or as research devices for the study of temperature and temperature scales. Among the latter are thermometers which respond to thermal noise (Johnson noise) and thermometers based on the temperature dependence of the speed of sound. 

When an isotropic material is subjected to planar shock compression, it experiences a relatively large compressive strain in the direction of the shock propagation, but zero strain in the two lateral directions. Any real planar shock has a limited lateral extent, of course. Nevertheless, the finite lateral dimensions can affect the uniaxial strain nature of a planar shock only after the edge effects have had time to propagate from a lateral boundary to the point in question. Edge effects travel at the speed of sound in the compressed material. Measurements taken before the arrival of edge effects are the same as if the lateral dimensions were infinite, and such early measurements are crucial to shock-compression science. It is the independence of lateral dimensions which so greatly simplifies the translation of planar shock-wave experimental data into fundamental material property information. 

Overdriven Detonation The unstahle condition that exists during a defla-gration-to-detonation transition (DDT) before a state of stable detonation is reached. Transition occurs over the length of a few pipe diameters and propagation velocities of up to 2000 m/s have been measured for hydrocarbons in air. This is greater than the speed of sound as measured at the flame front. Overdriven detonations are typically accompanied by side-on pressure ratios (at the pipe wall) in the range 50-100. A severe test for detonation flame arresters is to adjust the run-up distance so the DDT occurs at the flame arrester, subjecting the device to the overdriven detonation impulse. 

McWilliams, D., and R. K. Duggins, 1969, Speed of Sound in Bubbly Liquids, Symp. on Fluid Mechanics Measurements in Two-Phase Flow Systems, Proc. Inst. Meek Eng. 184(Part 3C) 102-107. (3)... 

The exp-6 potential has also proved successful in modeling chemical equilibrium at the high pressures and temperatures characteristic of detonation. However, to calibrate the parameters for such models, it is necessary to have experimental data for product molecules and mixtures of molecular species at high temperature and pressure. Static compression and sound-speed measurements provide important data for these models. 

Sound Speed Measurements. The most precise values of compressibility at 1 atm can be determined from speed of sound measurements. The adiabatic compressibility (63) is related to the speed of sound (u) by... 

C. High-Pressure PVT Properties. Three methods are presently being used to measure the high-pressure PVT properties of electrolyte solutions volumetric methods, (26,32,106) high pressure magnetic float systems, (36,107,108) and high pressure speed of sound systems (109,110,111,112). I will not attempt to review all the modifications made to these systems. 

Figure 8. Comparisons of the specific volumes of water determined from sound speed measurements (31) and direct measurements (106J...

The system was calibrated with water and the sound path (A) was found to increase slightly as the pressure is increased (assuming t is independent of pressure) (112). Since we are interested in measuring the relative speed of sound (Au) in aqueous solutions, we use the velocimeter in a differential mode. The value of t is not a function of pressure (or temperature), as the electronics are kept under ambient pressures. The values of Au were determined from... 

Unfortunately, at present, reliable PVT data for electrolytes at high pressures, temperatures and concentrations are not available to further test the applicability of these simple methods to natural waters. Reliable measurements of the speed of sound in aqueous electrolytes as a function of temperature, pressure and concentration should provide the data needed to test the postulation presented above. Since 1 atm measurements of vu and... 

Fig. 13.17 shows the structure and principle of a T-bumer, as used to measure the response function of propellants. Two propellant samples are placed at the respective ends of the T-burner. The burner is pressurized with nitrogen gas to the test pressure level. The acoustic mode of the burning established in the burner is uniquely determined by the speed of sound therein and the distance between the burning surfaces of the two samples. When the propellant samples are ignited, pressure waves travel from one end to the other between the burning surfaces of the samples. When a resonance pressure exists for a certain length of the T-bumer, the propellant is sensitive to the frequency. The response function is determined by the degree of amplification of the pressure level. 

For our purpose, it is convenient to classify the measurements according to the format of the data produced. Sensors provide scalar valued quantities of the bulk fluid i. e. density p(t), refractive index n(t), viscosity dielectric constant e(t) and speed of sound Vj(t). Spectrometers provide vector valued quantities of the bulk fluid. Good examples include absorption spectra A t) associated with (1) far-, mid- and near-infrared FIR, MIR, NIR, (2) ultraviolet and visible UV-VIS, (3) nuclear magnetic resonance NMR, (4) electron paramagnetic resonance EPR, (5) vibrational circular dichroism VCD and (6) electronic circular dichroism ECD. Vector valued quantities are also obtained from fluorescence I t) and the Raman effect /(t). Some spectrometers produce matrix valued quantities M(t) of the bulk fluid. Here 2D-NMR spectra, 2D-EPR and 2D-flourescence spectra are noteworthy. A schematic representation of a very general experimental configuration is shown in Figure 4.1 where r is the recycle time for the system. 

Since the compressibility is proportional to the pressure derivative of the volume, any experiment that establishes the P-V-T relation of a gas with sufficient accuracy also yields data for the isothermal compressibility. For obtaining the adiabatic compressibility from the P-V-T relation, some additional information is necessary see section (c). Tor instance specific heat data in the perfect gas slate of the substance considered. A more direct way of determining ihe adiabatic compressibility is by measuring the speed of sound i1. the two quantities being related by... 

This instrument is used to measure the flow of clean liquids and involves the determination of the time required for an acutely angled, high frequency pressure wave to reach the opposite wall of a pipe. The elapsed time depends upon the velocity of the liquid u(, whether the pressure wave is moving with, or against the flow and upon the speed of sound in the liquid us. The most common time-of-flight meter is the counter-propagating type in which two transducers are placed on opposite sides of the liquid stream as shown in Fig. 6.3. 

Sonic and ultrasonic thermometers have a unique role for high-temperature applications that involve detection of the average temperature in harsh and abrasive process environments. These sensors operate on the basis of detecting the speed of sound, which is proportional to temperature (Figure 3.163). When the temperature is detected by the measurement of transit... 

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