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KUNDU Fluid Mechanics 2E Episode 17

Tham khảo tài liệu 'kundu fluid mechanics 2e episode 17', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 694 Com imisihlt now which M 1 at the exit station. The flow is then said to be choked and no more mass time can flow through that duct. This is analogous to flow in a convergent duct. Imagine pouring liquid through a funnel from one container into another. There is a maximum volumetric flow rate that can be passed by the funnel and beyond that flow rate the funnel overflows. The same thing happens here. If f or q is loo large such that no steady-state solution is possible there is an external adjustment that reduces the mass flow rate to that for which the exit speed is just sonic. Both for M 1 and M 1 the limiting curves for f and q indicating choked flow intersect M2 1 at right angles. Qualitatively the effect is the same as choking by area contraction. 9. Mach Cone So far in this chapter we have considered one-dimcnsional flows in which the flow properties varied only in the direction of flow. In this section we begin our study of wave motions in more than one dimension. Consider a point source emitting infinitesimal pressure disturbances in a still fluid in which the speed of sound is c. If the point disturbance is stationary then the wavefronts are concentric spheres. This is shown in Figure 16.17a where the wavefronts at intervals of Ar are shown. Now suppose that the source propagates to the left at speed u c. Figure 16.17b shows four locations of the source that is 1 through 4 at equal intervals of time Ar with point 4 being the present location of the source. At point 1 the source emitted a wave that has spherically expanded to a radius of 3c Ar in an interval of time 3 Ar. During this time the source has moved to location 4 at a distance of 3Í7 Ar from point 1. The figure also shows the locations of the wavefronts emitted while the source was at points 2 and 3. It is clear that the wavefronts do not intersect because u c. As in the case of the stationary source the wavefronts propagate everywhere in the flow field upstream and downstream. It therefore .