Reflect back to the fundamental equations of fluid motion dicussed in the early sections of this chapter. Sometimes these equations were expressed in terms of differential equations; for the most part, though, we obtained algebraic relations by integrating the differential equations. However, it is useful to think of the differential forms as relations that govern the change in flow field variables in an infinitesimally small region around a point in the flow, (a) Consider a point in an inviscid flow, where the local density is 1.1 kg/m3. As a fluid element sweeps through this point, it is experiencing a spatial change in velocity of 2 percent per millimeter. Calculate the corresponding spatial change in pressure per millimeter at this point if the velocity at the point is 100 m/s. (b) Repeat the calculation for the case in which the velocity at the point is 1000 m/s. What can you conclude by comparing your results for the low-speed flow in part (a) with the results for the high-speed flow in part (b)?
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