Specific sound velocity

This maximum velocity of a compressible fluid in a pipe is limited by the velocity of propagation of a pressure wave that travels at the speed of sound in the fluid [3]. This speed of sound is specific for each individual gas or vapor or liquid and is a function of the ratio of specific heats of the fluid. The pressure reduces and the velocity increases as the fluid flows downstream through the pipe, wdth the maximum velocity occurring at the downstream end of the pipe. WTien, or if, the pressure drop is great enough, the discharge or exit or outlet velocity will reach the velocity of sound for that fluid. 

Here Q(t) denotes the heat input per unit volume accumulated up to time t, Cp is the specific heat per unit mass at constant pressure, Cv the specific heat per unit mass at constant volume, c is the sound velocity, oCp the coefficient of isobaric thermal expansion, and pg the equilibrium density. (4) The heat input Q(t) is the laser energy released by the absorbing molecule per unit volume. If the excitation is in the visible spectral range, the evolution of Q(t) follows the rhythm of the different chemically driven relaxation processes through which energy is... 

Here p is the solution density, v the sound velocity, ctp the coefficient of thermal expansion, Cp the specific heat, and F the concentration dependence of the equilibrium, r = [LS] -f- [HS] . The measurement of ultrasonic relaxation thus enables the determination of both the relaxation time x and the... 

In the pressure range from 0.66 to 1.32 mbar, the expected specific flow of water vapor is reduced for the mentioned ratios to 66 % or 55 % of that passing through an ideal jet. At 0.04 mbar pressure in the chamber the specific throughput is reduced to 33 % or 10 %. This becomes even more drastic, if the velocity of the water vapor is plotted as a function ofpch (Fig. 1.90). In an ideal jet, the velocity of the vapor flow under the conditions chosen is approx, sound velocity. However even with Ud = 1 the velocity is strongly reduced as a function of pressure, and reaches at 0.04 mbar at only approx, one-third of this maximal speed. 

Notation, k is the wavenumber, Us the sound velocity, F the damping coefficient (11), r the shear viscosity, po the uniform mass density, k the heat conductivity, and Cp the specific heat capacity at constant pressure [4]. 

Taylor (Ref 5) obtd a transient flow behind a C-J discontinuity using Riemann equations for polytropic gases. A plot of u/u2 vs x/Ut shown in Fig 12 of Ref 6 (See here Fig 1) is for u2 =U/3, c2 = 2U/3 and y=1.3, where u is material velocity in x direction, u2 is material velocity immediately behind the discontinuity at Ut (U = velocity of C-J wave t = time coordinate) C2 = sound velocity and y = Cj/cv (cp=specific heat at constant pressure and cv = sp heat at constant volume), Taylor calculated pressure in the rarefaction wave behind C-J point and plotted it in F ig given as Fig 12 of Ref 6 (Our Fig 2)... 

Theory. If p is pressure, v - specific volume, e - specific internal energy, D detonation velocity, u - particle velocity, C - sound velocity, y - adiabatic exponent and q -specific.detonation energy, the velocity of propagation and particle velocity immediately behind any plane detonation wave in an explosive, defined by initial conditions, pD, v0, eQ, and uQ, are given by the first two Rankine-Hugoniot relations ... 

Effects of Mechanical Energy or Forces Viscosity Sound velocity Density and specific gravity... 

Cv(q) reduces to the specific heat at constant volume and Cj(q) reduces to the adiabatic sound velocity at q = 0. 

Geelen especially examined several specific functions (specific refraction r, specific sound velocity u, specific volume i Id). The use of these functions together with the hydrogen content (%H) enables the structural composition of aromatic hydrocarbons to be determined. From data on homologous series of pure mono- and di-aromatic hydrocarbons36 he deduced the following equations for r, d and %H (20°C) ... 

Figure 5. Normalized sound velocity (Av/v), specific heat (c), as well as temperature derivatives of resistivity (p) and magnetic susceptibility /) showing anomalies at the charge ordering transition (240 K) in La, r Sro.33Ni04 (from Ramirez et al.12).

Consider, for example, a single vibrational relaxation process, as in a gas of diatomic molecules exhibiting harmonic oscillations. Then for acoustic frequencies sound velocity becomes frequency dependent. To find F2(a>), the specific heat may be written in the complex form... 

The ratio CJCy of the heat capacity of a gas at constant pressure to that at constant volume will be determined by either the method of adiabatic expansion or the sound velocity method. Several gases will be studied, and the results will be interpreted in terms of the contribution made to the specific heat by various molecular degrees of freedom. 

Dynamic specific modulus E /y, the ratio of dynamic Young s modulus to specific gravity, and loss tangent tan 8 can be used to study the viscoelastic nature of wood. E /y is related to sound velocity and tan 8 to sound absorption or damping within the wood. A large E /y and small tan 8 characterize the acoustic quality of soundboard wood [3]. 

Specific heat (Jg Hardness (Moh s) Young s modulus (GPa) Sound velocity (m s ) Ohmic resistance (f2 m)... 

As shown by the applications developed so far, the characteristics of acoustic levitation make it especially suitable for use in analytical and bioanalytical chemistry — however, the earliest applications focused on the determination of mechanical and physical properties of materials such as specific density, viscosity and surface tension [93,115,116]. Ohsaka et al. developed a method for determining the viscosity of highly viscous liquids (particularly, undercooled liquids, which exist at temperatures below their freezing points [117]). Weiser and Apfel used acoustic levitation to measure mechanical properties such as density, compressibility and sound velocity in biological materials [71]. 

Specificity is the most important requirement in gas analysis. Techniques dependent on the physical properties of the gas molecules, such as thermal conductivity, density, viscosity, and sound velocity, generally have insufficient specificity to differentiate a single gas in a mixture of gases, and therefore must incorporate in the procedure some type of preliminary separation. Vapor phase fractionation (gas chromatography) is an example of a popular analytical technique based upon a physical property (thermal conductivity) of the gas that requires preliminary separation of the gases by means of special columns (molecular sieve, silica gel, etc.). 

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