Example 2-11 Sonic Velocity

Water vapor (4930 lbs/hr) is flowing in a 3-inch line at 730°F. The outlet pressure is less than one half the inlet absolute pressure. What is maximum flow that can be expected  

Applied Process Design for Chemical and Petrochemical Plants 

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This is a low value, therefore, the possibility exists of an up-rate relative to any nozzle flow limits. At this point, a comment or two is in order. There is a rule of thumb that sets inlet nozzle velocity limit at approximately 100 fps. But because the gases used in the examples have relatively high acoustic velocities, they will help illustrate how this limit may be extended. Regardless of the method being used to extend the velocity, a value of 150 fps should be considered maximum. When the sonic velocity of a gas is relatively low, the method used in this example may dictate a velocity for the inlet nozzle of less than 100 fps. The pressure drop due to velocity head loss of the original design is calculated as follows ... 

Step 2, Reuse the rotor tip speed and sonic velocity from Example 4-1 as the conditions used in their development that have not changed. 

This sonic velocity occurs in a pipe system in a restricted area (for example, valve, orifice, venturi) or at the outlet end of pipe (open-ended), as long as the upstream pressure is high enough. The physical properties in the above equations are at the point of maximum velocity. 

For example, for a line discharging a compressible fluid to atmosphere, the AP is the inlet gauge pressure or the difference between the absolute inlet pressure and atmospheric pressure absolute. When AP/Pi falls outside the limits of the K curves on the charts, sonic velocity occurs at the point of discharge or at some restriction within the pipe, and the limiting value for Y and AP must be determined from the tables on Figure 2-38A, and used in the velocity equation, Vj, above [3]. 

A relief device should be installed vertically and preferably on a nozzle at the top of the equipment (for example, vessel) or on a tee connected to a pipeline. When discharging a gas or vapor, the fluid reaches sonic velocity when passing through a relief device. Thus, the gas flow rate or AP can be determined by a method as described in Chapter Three. 

Because the pulse frequency is very high ( 10 kHz), one can utilise the method as an on-line system to monitor orientation induced during fibre processing operations such as fibre drawing, spinning, etc. " Generally the technique is applied in conjunction with other methods. For example, in Fig. 49 data of Charch and Moseley " are given on a drawn Nylon 66 fibre. Note that X-ray diffraction as well as sonic velocity data have been combined with the stress strain behaviour of the filaments. 

The first example of an industrial application for bacterial cellulose is its use as an acoustic transducer diaphragm (Nishi et al. 1990). An acoustic transducer diaphragm requires a high sonic velocity and a high internal loss. The sonic velocity is calculated from the specific Young s modulus, which in a dried sheet of bacterial cellulose is approximately 5000 m/s. Regarding its internal loss, a bacterial cellulose sheet has a high internal loss of 0.03, equal to that of conventional paper. 

Rock drillability is also controlled by strength properties. Therefore, correlations between elastic wave velocities and parameters of rock drillability have also been investigated. For example, Somerton et al. (1969) reported that sonic velocity is a good indicator of rock drillability for hme- and sandstones, and the type of drilling tool. 

It is cavitation in a heterogeneous medium which is the most studied by sonoche-mists. When produced next to a phase interface, cavitation bubbles are strongly deformed. A liquid jet propagates across the bubble towards the interface at a velocity estimated to hundreds of metres per second. At a liquid-liquid interface, the intense movement produces a mutual injection of droplets of one liquid into the other one, i. e. an emulsion (Fig. 3.3). Such emulsions, generated through sonication, are smaller in size and more stable than those obtained conventionally and often require little or no surfactant to maintain stability. It can be anticipated therefore that Phase Transfer Catalysed (PTC) reactions will be improved by sonication. Examples are provided later in this chapter. 

Fig. 13.21 shows another example of oscillatory burning of an RDX-AP composite propellant containing 0.40% A1 particles. The combustion pressure chosen for the burning was 4.5 MPa. The DC component trace indicates that the onset of the instability is 0.31 s after ignition, and that the instability lasts for 0.67 s. The pressure instability then suddenly ceases and the pressure returns to the designed pressure of 4.5 MPa. Close examination of the anomalous bandpass-filtered pressure traces reveals that the excited frequencies in the circular port are between 10 kHz and 30 kHz. The AC components below 10 kHz and above 30 kHz are not excited, as shown in Fig. 13.21. The frequency spectrum of the observed combustion instability is shown in Fig. 13.22. Here, the calculated frequency of the standing waves in the rocket motor is shown as a function of the inner diameter of the port and frequency. The sonic speed is assumed to be 1000 m s and I = 0.25 m. The most excited frequency is 25 kHz, followed by 18 kHz and 32 kHz. When the observed frequencies are compared with the calculated acoustic frequencies shown in Fig. 13.23, the dominant frequency is seen to be that of the first radial mode, with possible inclusion of the second and third tangential modes. The increased DC pressure between 0.31 s and 0.67 s is considered to be caused by a velocity-coupled oscillatory combustion. Such a velocity-coupled oscillation tends to induce erosive burning along the port surface. The maximum amplitude of the AC component pressure is 3.67 MPa between 20 kHz and 30 kHz. - ...

The speed of sound is attained at the throat of a converging/diverging nozzle only when the pressure at the throat is low enough that the critical value of P-JP is reached. If insufficient pressure drop is available in the nozzle for the velocity to become sonic, the diverging section of the nozzle acts as a diffuser. That is, after the throat is reached the pressure rises and the velocity decreases this is the conventional behavior for subsonic flow in diverging sections. The relationships between velocity, area, and pressure in a nozzle are illustrated numerically in Example 7.3. 

Sonic energy can be also used to initiate and/or accelerate dry agglomeration of ultrafine particles that are suspended, for example, in flue gases [B.43, B.48]. An acoustic field imposes sound pressure and energy. For a typical pressure of 160dB the acoustic velocity is about 5 m/s and a typical frequency of 2000 FIz causes a fully en-... 

The elastic properties of hydrates are important to understanding the sonic and seismic velocity field data obtained from the natural hydrates-bearing sediments. Data on the mechanical properties of CO2 hydrates are hmited. Table 10.3 shows the elastic properties of ice, CH4 hydrates, and CO2 hydrates. It should be noted that these properties may vary for different guests and occupancies. For example, Kiefte et al. [21] measured the compressional velocity of methane, propane, and hydrogen sulfide hydrates as 3.3, 3.7, and 3.35 km/s, respectively. 

The speed at which inertial effects propagate through a system can be characterized in terms of another wave velocity, that of the dynamic wave - of which a common example is a pressure wave, which travels through air at the sonic (i.e. dynamic-wave) velocity. A general theory then provides a remarkably simple means of quantifying, at least notion-ally, the condition for stable behaviour the velocity of the dynamic wave must be greater than that of the kinematic wave. The basis for this... 

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