Mach lines

FIGURE 4.5. (a) Variables specified along a noncharacteristic line, (b) Variables specified along streamlines and Mach lines, (c) Variables specified along intersecting Mach lines. 

Similarly, along the Mach lines, which are defined by Ax = (i %)At, equation (91) assumes the total-differential form... 

Isothermal Gas Flow in Pipes and Channels Isothermal compressible flow is often encountered in long transport lines, where there is sufficient heat transfer to maintain constant temperature. Velocities and Mach numbers are usually small, yet compressibihty effects are important when the total pressure drop is a large fraction of the absolute pressure. For an ideal gas with p = pM. JKT, integration of the differential form of the momentum or mechanical energy balance equations, assuming a constant fric tion factor/over a length L of a channel of constant cross section and hydraulic diameter D, yields,... 

There are three forms of inducer camber lines in the axial direction. These are circular arc, parabolic arc, and elliptical arc. Circular arc camber lines are used in compressors with low pressure ratios, while the elliptical arc produces good performance at high pressure ratios where the flow has transonic mach numbers. 

Since the pressure drop is quite high, there is a possibility of approaching sonic velocity in the line. This will result in a potential noise problem. Hence, it is a good practice to limit the velocity to 60 percent of the sonic velocity or a 0.6 Mach number. 

The flow of a compressible fluid through an orifice is limited by critical flow. Critical flow is also referred to as choked flow, sonic flow, or Mach 1. It can occur at a restriction in a line such as a relief valve orifice or a choke, where piping goes from a small branch into a larger header, where pipe size increases, or at the vent tip. The maximum flow occurs at... 

When the relieving scenarios are defined, assume line sizes, and calculate pressure drop from the vent tip back to each relief valve to assure that the back-pressure is less than or equal to allowable for each scenario. The velocities in the relief piping should be limited to 500 ft/sec, on the high pressure system and 200 ft/sec on the low pressure system. Avoid sonic flow in the relief header because small calculation errors can lead to large pressure drop errors. Velocity at the vent or flare outlet should be between 500 ft/sec and MACH 1 to ensure good dispersion. Sonic velocity is acceptable at the vent tip and may be chosen to impose back-pressure on (he vent scrubber. 

Figure 7-44 shows the sequence of events involved in diffraction of a blast vave about a circular cylinder (Bishop and Rowe 1967). In these figures the shock fronts are sho m as thick lines and their direction of movement by arrows normal to the shock front. In Figure 1.13a, the incident shock 1 and reflected shock are joined to the cylinder surface by a Mach stem M. R is now much weaker and is omitted in succeeding figures. 

The temperature or enthalpy of the gas may then be plotted to a base of entropy to give a Fanno line.iA This line shows the condition of the fluid as it flows along the pipe. If the velocity at entrance is subsonic (the normal condition), then the enthalpy will decrease along the pipe and the velocity will increase until sonic velocity is reached. If the flow is supersonic at the entrance, the velocity will decrease along the duct until it becomes sonic. The entropy has a maximum value corresponding to sonic velocity as shown in Figure 4.11. (Mach number Ma < 1 represents sub-sonic conditions Ma > 1 supersonic.)... 

Fig. 9.13 Mach Zehnder interferometer (MZI) sensor interrogation circuit using (a) conventional linear waveguide geometry and (b) folded spiral waveguide geometry. The dashed line in (b) indicates the sensor window boundaries in this infra red camera image...

Mach-Zehnder interferometer, 22 153 Mackenzie-Shuttleworth model, 23 75 Mackie line effect, 19 209, 210 Macor glass-ceramic, 22 635 Macquartite, 6 471t Macrinite, 6 707t Macrobicyclic effect, 24 39 Macrocrystalline wax, 26 214 Macrocycles, 24 35, 45 developments of, 24 36 Macrocyclic complexes, rhodium, 29 645 Macrocyclic compounds, chelating agents, 5 710, 713t... 

In the expansion wave, the flow velocity is increased and the pressure, density, and temperature are decreased along the stream line through the expansion fan. Since Oj > 02, it follows that Mi flow through an expansion wave is continuous and is accompanied by an isentropic change known as a Prandtl-Meyer expansion wave. The relationship between the deflection angle and the Mach number is represented by the Prandtl-Meyer expansion equation.l - l... 

The point of intersection of I, R M is known as the triple point, TP. The resulting existence of the above three waves, causes a density discontinuity. The surface of this discontinuity, known as slipstream, S, represents a stream line for the flow relative to the intersection. Between this and the reflecting surface is the region of high pressure, known as Mach region here the pressure is approx twice that behind the incident wave. The top of this pressure region, the triple point, travels away from the reflected surface. As pressure and impulse appear to have their maximum values just above and below the triple point, respectively, the region of maximum blast effect is approximately that of the triple point... 

The induction time data and density profiles pf detonations in oxy-hydrogen and oxy-methane mixtures were analyzed on the basis of the kinetic data obtained by the reflected-wave technique and similar methods. A plot of the ignition delay vs 1/T in oxy-ammonia mixtures gave a straight line with a slope corresponding to an activation energy of 42.5 kcal/mole. In these mixtures the induction zone is not uniform, but the shock front is flat and end of the reaction zone is clearly discernible. Onedimensional detonation waves of low Mach number but relatively stable were obtained in a gas preheated to 600-1800°K ahead of the shock front... 

In his supplement to Syllabus, Dunkle remarked (Ref 22, p lid) that schlieren photography of deton waves in 40/60 C2H2/O2 initially at 1/4 atm showed a wavy pattern of criss-crossing dark diffuse lines behind the front. Fay Opel (Ref 17) calculated that if these lines are a weak wake of Mach waves in supersonic flow, the flow of the burnt gases with respect to the front is Mach 1.14 rather than Mach 1.00 as in a C-J process. However, at this pressure the reaction is complete within a fraction of a millimeter behind the front, and the flow could very well accelerate to Mach 1.14 with density decrease below the C-J value. Fay Opel traced the effect to the boundary layer. 

Fig. 25 Schematic of a Mach-Zehnder interferometer (upper) for 2-D recording via two-photon photochromism (beam spiitters are 50 50 at 45°, iaser exposure time) 0.5-3 min, output beam angie 2°. Dark lines in image (lower) resuit from high intensity bright fringe-induced photoisomerization of fuigide 1 in a poiymeric fiim (13 xm line width and 155 p.m line spacing)...

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