Liquids speed of sound

The uncertainties in the equation of state are 0.1% in density (except near the critical point), 0.25% in vapor-pressure, 1% in heat capacities, 0.2% in the vapor-phase speed of sound, and 3% in the liquid speed of sound. The liquid speed of sound uncertainty is an estimate and cannot be verified without experimental information. The uncertainties above 290 K in vapor pressure may be as high as 0.5%. 

Typical uncertainties are 0.05% for density, 0.02% for vapor pressure, 0.5% to 1% for heat capacity, 0.05% for vapor speed of sound, and 1% for liquid speed of sound, except in the critical region. The uncertainty in viscosity is 1.5% along the saturated-liquid line, 3% in the liquid phase, 0.5% in the dilute gas, 3% to 5% in the vapor phase, and 5% in the supercritical region, rising to 8% at pressures above 40 MPa. Below 200 K, the uncertainty is 8%. The uncertainty in thermal conductivity is 5%. 

When vapor bubbles eollapse inside the pump the liquid strikes the metal parts at the speed of sound. This is the elicking and popping noise we hear from outside the pump when we say that eavitation sounds like pumping marbles and roeks. Sound travels at 4,800 ft per second in water. The velocity head formula gives a elose approximation of the energy contained in an imploding cavitation bubble. Remember that implosion is an explosion in the opposite direction. 

For compressible fluids one must be careful that when sonic or choking velocity is reached, further decreases in downstream pressure do not produce additional flow. This occurs at an upstream to downstream absolute pressure ratio of about 2 1. Critical flow due to sonic velocity has practically no application to liquids. The speed of sound in liquids is very liigh. See Sonic Velocity later in this chapter. 

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. 

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)... 

It should be noted that the derivative is negative, so that at certain conditions the denominator of Eq. (15-51) can be zero, resulting in an infinite pressure gradient. This condition corresponds to the speed of sound, i.e., choked flow. For a nonflashing liquid and an ideal gas mixture, the corresponding maximum (choked) mass flux G follows directly from the definition of the speed of sound ... 

X = (pc2)-1 in place of its isothermal counterpart, where p is the mass density of the liquid and c is the speed of sound. With this modification, the agreement between theory and experiment improves somewhat yet some fundamental difference remains unexplained. 

Time resolution of the enthalpy changes is often possible and depends on a number of experimental parameters, such as the characteristics of the transducer (oscillation frequency and relaxation time) and the acoustic transit time of the system, za, which can be defined by ra = r0/ua where r0 is the radius of the irradiated sample, and va is the speed of sound in the liquid. The observed voltage response of the transducer, V (t) is given by the convolution of the time-dependent heat source, H (t) and the instrument response function,... 

A physical explosion, for example, a boiler explosion, a pressure vessel failure, or a BLEVE (Boiling Liquid Expanding Vapor Explosion), is not necessarily caused by a chemical reaction. Chemical explosions are characterized as detonations, deflagrations, and thermal explosions. In the case of a detonation or deflagration (e.g., explosive burning), a reaction front is present that proceeds through the material. A detonation proceeds by a shock wave with a velocity exceeding the speed of sound in the unreacted material. A... 

The value of C in equation 10.39 depends on the way in which the pipe is restrained but for practical purposes a value of unity is adequate. In this equation, E is Young s modulus of elasticity of the pipe, d, the internal diameter of the pipe and tw its wall thickness. The value of E for steel is about 2 x 10s MPa and K for water is about 2 x 103 MPa thus K/E is about 10-2. It will be seen that the elasticity of the pipe has a negligible effect with thick-wall pipes but with thin-wall ones (say djtw > 40) the propagation speed a will typically be reduced to about 70 per cent of the speed of sound c in the liquid. 

Analytical and empirical correlations for droplet sizes generated by ultrasonic atomization are listed in Table 4.14 for an overview. In these correlations, Dm is the median droplet diameter, X is the wavelength of capillary waves, co0 is the operating frequency, a is the amplitude, UL0 is the liquid velocity at the nozzle exit in USWA, /Jmax is the maximum sound pressure, and Us is the speed of sound in gas. Most of the analytical correlations are derived on the basis of the capillary wave theory. Experimental observations revealed that the mean droplet size generated from thin liquid films on... 

Mach Number Ma = Uq/us Compare impact velocity to speed of sound in liquid Hofmeistei et al. I4101... 

Zafarani-Moattar, M.T. and Shekaari, H. Volumetric and speed of sound of ionic liquid, l-butyl-3-methylimidazolium hexafluorophosphate with acetonitrile and methanol at T = (298.15 to 318.15) K, /. Chem., Eng. Data, 50,1694,2005. Wang, J. et al.. Excess molar volumes and excess logarithm viscosities for binary mixtures of the ionic liquid l-butyl-3-methylimidazolium hexafluorophosphate with some organic solvents, /. Solution Chem., 34, 585, 2005. 

Transport Properties. Viscosity, thermal conductivity, the speed of sound, and various combinations of these with other properties are called steam transport properties, which arc important in engineering calculations. The speed of sound is important to choking phenomena, where the flow of steam is no longer simply related to the difference in pressure. Thermal conductivity is important to the design of heat-transfer apparatus. See Heat-excliange Technology. Shaip declines ill each of these properties occur at the transition from liquid to gas phase, i.e., from water to steam. 

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. 

The linear speed of sound in the liquid is c. A, B, and n are constants that should be set to the appropriate values for water. Any acoustic forcing function is included in the pressure at infinity term, P1oo (t). The pressure at the bubble wall, P(R), is given by... 

Knowing the speed of sound and mass flow rate, we can now determine the PWL in the next table. The position of a phase change line, gas to liquid, may have to be determined where this is critical. 

Takagi, T., Sawada, K., Urakawa, H., Ueda, M., Cibulka, I. (2004) Speeds of sound in dense liquid and vapor pressures for 1,1-difluoroethane. J. Chem. Eng. Data 49, 1652-1656. 

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