Mach Number in

Detonation, Mach Number in. Mach (pronounced as Makh) Number, designated as M or Mc, is the ratio of the shock velocity to the sonic velocity and for an ideal gas may be expressed as  

Designating Mach Number as M0, Dunkle gave the following equation  

Refs 1) C.G. Dunkle, Introduction to Theory of Detonation of Explosives , 

Detonation, Mach Reflection and Mach Region. See under Detonation, Mach Wave, etc 

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Free-vortex prewhirl. This type is represented by r Ve = constant with respect to the inducer inlet radius. This prewhirl distribution is shown in Figure 6-13. Vg is at a minimum at the inducer inlet shroud radius. Therefore, it is not effective in decreasing the relative Mach number in this manner. 

The influence of compressibility was assessed by varying the Mach number in the range 0 < Ma < 0.38, while Kn and ks/H were kept low. Friction factor data were reported only with Ma < 1 at the exit, to ensure the flow rate was controlled by viscous forces alone. A mild increase in the friction factor (8%) was observed as Ma approached 0.38. This effect was verified independently by numerical analysis for the same conditions as in the experiment. The range of relative surface roughness tested was 0.001 < ka/H < 0.06, yet there was no significant influence on the friction factor for laminar gas flow. 

The pressure peaks observed in the combustion tests shown in Fig. 14.19 are computed as a function of L/D as shown in Fig. 14.20. The peak pressures computed by means of the Lenoir-Robillard empirical equation are confirmed by the measured pressure at the head-end of the motor. It is evident thatp values predicted without erosive burning are significantly lower than the measured maximum pressures. Fig. 14.21 shows the erosive ratio, 8 = r/to, as a function of the mass flow rate per unit cross-sectional area in the port, G. The erosive ratio increases with increasing Mach number in the port at constant L/D. 

The thrustor was considered to consist of two sections 1) where the mixture is formed and 2) where combustion takes place and the pressure is generated. The principal mechanism involved in the combustion process was assumed to be successive ignition, but other mechanisms such as turbulent frontal combustion were also considered. The analysis yielded two instability criteria, expressed in terms of the Mach number in zone 1, the velocity ratio in zones 1 and 2, the isentropic exponent in zone 2, the activation energy, the temperature of the cold gas, the pressure upstream of the combustion zone, and the pressure drop due to the combustion... 

Mach number. Where compressibility is important, it is necessary to consider the ratio of the fluid velocity (or the velocity of a solid through a stationary fluid) to that of a sound wave in the same medium. This ratio, called the Mach number in honor of an Austrian scientist of that name, is... 

The static reading on a Pitot tube is accurate to 0.5% for Mach numbers up to 0.5. For Mach numbers befween the values of 0.5 to 0.7 the accuracy increases to 1.5%. Above a Mach number of 0.7 fhe error can increase as much as 10% due to the formation of shock waves on and around the tip of the probe. Above a Mach number of 1.0 both the total and static readings vary significantly for the actual values [27]. The Mach number in the above example is calculated as follows ... 

Since the Mach number in this example is less than 0.7 we would not expect any error from formation of shock waves around the probe. 

Equations 8.16, 8.31, and 8.32 can be solved to show the changes in temperature, pressure, and Mach number in a shock wave. The algebra involved is shown in App. F. The results of that algebra are... 

After passage of a shock front, the atmosphere (air) is accelerated to a speed Up in the direction in which the shock moved Up is the particle or wind speed, and may be obtained from either the overpressure or the Mach number. In air. 

Fig. 2. Sonic velocity and Mach number in two-phase hydrogen.

In equation 12, k is the Boltzman constant and m is the atomic mass. The stream velocity is not a constant quantity for any given gas, but varies by less than 5% for Mach numbers in the range 6 - < . For He, v is found to equal 1.78 x lO cm s. Stream velocities calculated from these simple relationships are found experimentally to be accurate to better than 1%. ... 

Shapiro (1977) defined the speed index, S = ulc, similar to die Mach number in gas dynamics, and demonstrated different cases of subcritical (5 < 1) and supercritical (S > 1) flows. It has been shown experimentally in simple experiments with compliant tubes that gradual reduction of the downstream pressure progressively increases the flow rate until a maximal value is reached (Holt, 1969 Conrad, 1969). The one-dimensional theory demonstrates that for a given tube (specific geometry and wall properties) and boundary conditions, the maximal steady flow that can be conveyed in a collapsible tube is attained for 5 = I (e.g., when u = c) at some position along the tube (Dawson Elliott, 1977 Shapiro, 1977 Elad et id., 1989). In this case, the flow is said to be choked and further reduction in downstream pressure does not affect the flow upstream of the flow-limiting site. Much of its complexity, however, is still unresolved either experimentally or theoretically (Kamm et al., 1982 Kanun and Pedley, 1989 Elad et al., 1992). 

Combustion and geochemistry characteristic velocities are usually small compared with the speed of sound. As the Mach number approches zero, the contribution of the pressure gradient in the nondimensional momentum equations, Vp/M, becomes singular. So, a numerical method used to integrate the original set of equations tends to fail when applied to very low Mach numbers in combustion [7] and geochemistry. Therefore, one needs a numerical technique that solves the original compressible flow equations, but that can also be efficiently used at low Mach-numbers. 

For this particular case it is necessary to introduce a flctitious convergent whose ttoat area is the same as the whole areas of the various holes. Isentropic relations are used to find the Mach number in the section A... 

From the above analysis of the Mach disk, we can draw several conclusions. First, the normal shock that occurs at the Mach disk is an effective dissipator that takes the fluid from supersonic to subsonic Mach numbers. In fact, Eq. (57) shows that the higher the upstream Mach number, Masx, the lower the downstream Mach number, Masy. In RESS, the entropy of the fluid always increases, and the largest fraction of this entropy increase (particularly... 

Figure 3 Nnephogram of oxygen mach number in the nozzle...

Here is the explosion pressure, y is the explosion products specific heat ratio, D the detonation velocity, and M the detonation wave Mach number in the cavity. Dimensions of the quantities used for the AP equation are q - MJ/m, A -m/M/ , E - MJ. 

The outlet line from the relief valve is designed based on the Mach number. Generally, the Mach number in between 0.5 to 0.75 is maintained. However, the outlet line size shall not be smaller than the outlet flange of the relief valve. 

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