Speed of sound, SoS

In high-velocity gas flow, velocities are often reached that are comparable to the speed of sound, so the speed of sound plays an important part in what follows. The speed of sound is the speed at which a small pressure disturbance moves through a continuous medium. Sound, as our ears perceive it, is a series of small air-pressure disturbances oscillating in a sinusoidal fashion in the frequency range jfrom 20 to 20,000 cycles per second, or hertz (Hz). The magnitude of the pressure disturbances is generally less than 10 Ibf/in absolute (7 Pa) [l ]. 

Figure 2. Bone speed of sound (SOS) during the first 12 postnatal weeks for infants fed with control formula, sn2 palmitate formula or breast milk.

Figure 1 Schematic of the Ultrasound set-up for measuring speed of sound (SoS).

The equilibrium cell and its loading lines were vacuumed prior to introducing the natural gas, then the system was pressurised by injecting the gas up to a certain pressure at the test temperature. Water was then injected into the cell in different steps to achieve the desired water/gas ratio (i.e., 1, 2, 3,100 bbl/MMscf). In each step, after achieving equilibrium following hydrate formation, speed of sound (SoS) and gas compositions were measured, depending on the device actually used. 

On the other hand, quantitative ultrasound (QUS) has many advantages such as the portability, low cost, suitable for group screening and free ionizing radiation, which are considered to be especially suitable in the assessment of children and pregnant women. In addition, QUS techniques can evaluate the elastic properties of bone in vivo by the two parameters, the speed of sound (SOS) and the broadband ultrasoimd attenuation (BUA, slope of the linearly frequency dependent attenuation). These parameters can... 

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. 

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 ... 

In practice, small pressure waves (such as sound waves) propagate virtually isentropically. The reasons for this are that, being a very small disturbance, the change is almost reversible and, by virtue of the high speed, there is very little heat transfer. Thus the speed of sound c is equal to the speed at which a small pressure wave propagates isentropically, so from equation 6.69... 

Gases are compressible, so their density decreases and velocity increases with pressure drop through a relief system. The increasing velocity leads to choking when the velocity reaches the speed of sound in the gas. This is discussed in more detail in 9.2. 

Here pg and p f are the mass densities of the gel and the solvent, respectively, K is a bulk modulus, c0 is the speed of sound, and i s is the solvent shear viscosity. The solvent bulk viscosity has been neglected. The terms proportional to / arise from an elastic coupling in the free energy between the density deviation of gel and that of solvent The p in Eq. (6.1) coincides with the shear modulus of gels treated so far. We neglect the frequency-dependence of the elastic moduli. It can be important in dynamic light scattering, however, as will be discussed in the next section. 

The same materials developed for aerospace planes may one day be applied to commercial travel. Hypersonic aircraft traveling at many times the speed of sound would reduce the time of a transpacific flight from America to Australia from 16 hours to a mere 3 hours. Whats more, the altitude of the aircraft would necessarily be so high that travelers would get a clear view of the curvature of Planet Earth. 

When an airplane exceeds the speed of sound, we say that it breaks the sound barrier. In so doing, it generates a sonic wave or pressure wave-front. When steam and gas flow into the converging section of the jet diffuser shown in Fig. 16.1, the same thing happens. The gradually converging sides of the diffuser increase the velocity of the steam and gas, as the vapor enters the diffuser throat up to, and even above, the speed of sound. This creates a pressure wavefront, or sonic boost. This sonic boost, will multiply the pressure of the flowing steam and gas by a factor of perhaps 3 or 4. 

The lower velocity in the throat does not affect the jet s performance, as long as the velocity remains above the speed of sound. If the velocity in the throat falls below the speed of sound, we say that the jet has been forced out of critical flow. The sonic pressure boost is lost. As soon as the sonic boost is lost, the pressure in the vacuum tower suddenly increases. This partly suppresses vapor flow from the vacuum tower. The reduced vapor flow slightly unloads condenser 1 and jet 2 shown in Fig. 16.2. This briefly draws down the discharge pressure from jet 1. The pressure in the diffuser throat declines. The diffuser throat velocity increases back to, or above, sonic velocity. Critical flow is restored, and so is the sonic boost. The compression ratio of the jet is restored, and the vacuum tower pressure is pulled down. This sucks more vapor out of the vacuum tower, and increases the loads on condenser 1 and... 

Einstein showed that when a reversible reaction is present sound dispersion occurs at low frequency the equilibrium is shifted within the time of oscillation, the effective specific heat is at a maximum, and the speed of sound c0 is at a minimum. At high frequency the oscillations occur so rapidly that the equilibrium has no time to shift (it is frozen ). The corresponding Hugoniot adiabate (FHA) is shown in the figure. Here the effective heat capacity is minimal, the speed of sound c is maximal cx > c0. From consideration of the final state and the theory of shock waves it follows that C>c0. 

We recall that c is the velocity of the molecules. The index on v means that we calculate the number of collisions necessary for reaction in the part of the zone where the reaction rate is highest and conditions are most conducive, so that i/min is the minimum value of v. Finally, tp is a dimensionless quantity of order (but less than) unity, algebraically (but not exponentially) dependent on the reaction mechanism, the activation heat, the temperatures T0 and TB, and the reagent concentrations. From the formula it is obvious first of all that u is always many times smaller than c, and less than the speed of sound. This fact will be important for the theory of detonation (Part II). 

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. 

In the case of milk, it is possible to take this further. The temperature coefficient of the velocity of sound is well known in both oil and water, so the water content can be obtained from the measured temperature coefficient of the velocity of sound in milk above 40°C where all the fat is liquid the oil content can be obtained by difference. With knowledge of the levels of water and oil, the protein content can be estimated from the absolute value of the speed of sound. The protein content so determined will be influenced by the location and state of the protein (micelle state or at the oil/water interface) arising from processing of the milk and also by other factors such as lactose and salt. 

This is identical to the equation derived in physics for the speed of so in the fluid. Therefore, the maximum fluid velocity obtainable in a pipe of const cross-sectional area is the speed of sound. This does not imply that higt velocities are impossible they are, in fact, readily obtained in converg diverging nozzles (Sec. 7.3). However, the speed of sound is the maximum val that can be reached in a conduit of constant cross section, provided the entran velocity is subsonic. The sonic velocity must be reached at the exit of the pi-If the pipe length is increased, the mass rate of flow decreases so that the so velocity is still obtained at the outlet of the lengthened pipe. 

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