Ma Mach number

Ft, Thermal accommodation coefficient K, Thermal conductivity Kn, Knudsen number M, Mass of the fluid Ma Mach number m, Mass flow rate... 

Mc mean molecular weight of coolant kg/kmol, lbm/lbm-rnol Ma Mach number... 

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.)... 

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. 

For single-phase gas flow in micro-channels of hydraulic diameter from 101 to 4,010 pm, in the range of Reynolds numbers Re < Recr, the Knudsen number 0.001 < Kn < 0.38, and the Mach number 0.07 < Ma < 0.84, the experimental friction factor agrees quite well with the theoretical one predicted for fully developed laminar flow. 

Mach number Ma. . v NfJIa = c = speed of sound (Gas velocity)/(speed of sound) High speed compressible flow... 

Mach Number Ma = Uq/us Compare impact velocity to speed of sound in liquid Hofmeistei et al. I4101... 

Drag coefficient Q/l. .Re) is the drag coefficient calculated using the correlation for subsonic flow with Ma=l. f V/1.75, Re ) is the drag coefficient calculated using the correlation for supersonic flow with Ma00=1.75 Mach number based on relative velocity between gas and sphere ... 

Figure 5.3. Atomizer geometry (top),computational grid mesh (left) and calculated Mach number contour (right) near a close-coupled atomizer (Atomization gas Ar, Ma = 1 at nozzle exit). (Reprinted with permission from Ref. 325.)...

As long as the Mach number is small—meaning the velocities are small compared to the sound speed—it is reasonable to assume that the incompressible continuity equation is a good approximation for isothermal, single-species flow. That is, velocity variations have little effect on density variations. As a result the simplifications associated with V-V 0 can be enjoyed. In practical terms, most consider that flows with Ma < 0.3 can be assumed to be gas-dynamically incompressible. 

A critical condition can be defined where v has achieved the local velocity of sound (Ma = 1, where Ma is the Mach number = flow velocity/ velocity of sound). At Ma - 1, the quantities jm, p and v have reached critical values, indicated by, ... 

Liquid flows are incompressible to a high level of accuracy, but the level of variation in density in gas flows and the consequent level of approximation made when modeling gas flows as incompressible depends on die Mach number defined as Ma - V/c, where c is the speed of sound whose value is 346 m/s in air at room lemperatute at sea level. Gas flows can often be approximated as incompressible if the density changes are under about 5 percent, which is usually the case when Ma < 0.3. Therefore, the comprc-ssibility effects of air can be neglected at speeds under about 100 m/s. Nole that the flow of a gas is not necessarily a compressible flow. 

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