Mach numbers

Why are fhese beams, or jefs, distinguished from effusive beams by fheir description as supersonic In some ways fhis description is rafher misleading, firsf because particles in an effusive beam may well be fravelling af supersonic velocities and, second, because fhe name implies fhaf somefhing special happens when fhe particle velocities become supersonic whereas fhis is nof fhe case. Whaf supersonic is meanf fo imply is fhaf fhe particles may have very high Mach numbers (of fhe order of f 00). The Mach number M is defined as... 

Compressible Vlow. The flow of easily compressible fluids, ie, gases, exhibits features not evident in the flow of substantially incompressible fluid, ie, Hquids. These differences arise because of the ease with which gas velocities can be brought to or beyond the speed of sound and the substantial reversible exchange possible between kinetic energy and internal energy. The Mach number, the ratio of the gas velocity to the local speed of sound, plays a central role in describing such flows. 

Fig. 20. Scaling of channel enthalpy extraction for the various MHD faciUties discussed in text ( ) achieved, and (e) predicted where O is the average gas conductivity in mho/m B, the average magnetic field in T M, the channel Mach number E, the average channel active length, m and P, the average...

Most often, the Mach number is calculated using the speed of sound evaluated at the local pressure and temperature. When M = 1, the flow is critical or sonic and the velocity equals the local speed of sound. For subsonic flowM < 1 while supersonic flows have M > 1. Compressibility effects are important when the Mach number exceeds 0.1 to 0.2. A common error is to assume that compressibihty effects are always negligible when the Mach number is small. The proper assessment of whether compressibihty is important should be based on relative density changes, not on Mach number. 

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,... 

Solution of Eq. (6-114) for G and differentiation with respect to p reveals a maximum mass flux = P2VMJ RT) and a corresponding exit velocity and exit Mach number Mo = L/. This... 

These equations are consistent with the isentropic relations for a perfect gas p/po = (p/po), T/To = p/poY. Equation (6-116) is valid for adiabatic flows with or without friction it does not require isentropic flow However, Eqs. (6-115) and (6-117) do require isentropic flow The exit Mach number Mi may not exceed unity. At Mi = 1, the flow is said to be choked, sonic, or critical. When the flow is choked, the pressure at the exit is greater than the pressure of the surroundings into which the gas flow discharges. The pressure drops from the exit pressure to the pressure of the surroundings in a series of shocks which are highly nonisentropic. Sonic flow conditions are denoted by sonic exit conditions are found by substituting Mi = Mf = 1 into Eqs. (6-115) to (6-118). 

The exit Mach number Mo may not exceed unity Mo = 1 corresponds to choked flow sonic conditions may exist only at the pipe exit. The mass velocity G in the charts is the choked mass flux for an isentropic nozzle given by Eq. (6-118). For a pipe of finite length. 

With L = length of pipe between points 1 and 2, the change in Mach number may be computed from... 

Equation (6-128) does not require fric tionless (isentropic) flow. The sonic mass flux through the throat is given by Eq. (6-122). With A set equal to the nozzle exit area, the exit Mach number, pressure, and temperature may be calculated. Only if the exit pressure equals the ambient discharge pressure is the ultimate expansion velocity reached in the nozzle. Expansion will be incomplete if the exit pressure exceeds the ambient discharge pressure shocks will occur outside the nozzle. If the calculated exit pressure is less than the ambient discharge pressure, the nozzle is overexpanded and compression shocks within the expanding portion will result. 

There are certain limitations on the range of usefulness of pitot tubes. With gases, the differential is very small at low velocities e.g., at 4.6 m/s (15.1 ft/s) the differential is only about 1.30 mm (0.051 in) of water (20°C) for air at 1 atm (20°C), which represents a lower hmit for 1 percent error even when one uses a micromanometer with a precision of 0.0254 mm (0.001 in) of water. Equation does not apply for Mach numbers greater than 0.7 because of the interference of shock waves. For supersonic flow, local Mac-h numbers can be calculated from a knowledge of the dynamic and true static pressures. The free stream Mach number (MJ) is defined as the ratio of the speed of the stream (V ) to the speed of sound in the free stream ... 

Higher circumferential speed capability due to inherently lower blade tip Mach number... 

Depending on the operating conditions, the first few stages are of 50% reaction to obtain maximum capacity for the selected speed. In the downstream stages, where Mach numbers are lower due to the higher gas temperatures, 80% reaction blading is used to reduce the... 

Increased blade relative velocities, resulting in higher blade relative Mach numbers and lower efficiencies. 

The effect of compressibility is important in high mach number machines. Mach number is the ratio of velocity to the acoustic speed of a gas at a given temperature M = Vja. Acoustic speed is defined as the ratio change in pressure of the gas with respect to its density if the entropy is held constant ... 

By measuring the total and static pressure and using Equation (3-14), the Mach number can be calculated. Using Equation (3-12), the static temperature can be computed, since the total temperature can be measured. Finally, using the definition of Mach number, the velocity of the gas stream can be calculated. 

A double-entry inducer system halves the inlet flow so that a smaller inducer-tip diameter can be used, reducing the inducer-tip Mach number however, the design is difficult to integrate into many configurations. 

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. 

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. 

The incidence angle now must be corrected for the Mach number effect The effect of the Mach number on incidence angle is shown in Figure 7-26. The incidence angle is not affected until a Mach number of. 7 is reached. 

The incidence angle is now fully defined. Thus, when the inlet and outlet air angles and the inlet Mach number are known, the inlet blade angle can be computed in this manner. 

Carter s rule, which shows that the deviation angle is directly a function of the camber angle and is inversely proportional to the solidity 8 = mQ Xja) has been modified to take into account the effect of stagger, solidity, Mach number, and blade shape as shown in the following relationship ... 

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