p0848 - 1180 CHAPTER 8 ONE-DIMENSIONAL COMPRESSIBLE FLOW...

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1180 CHAPTER 8. ONE-DIMENSIONAL COMPRESSIBLE FLOW 8.48 Chapter 8, Problem 48 Problem: A compressed gas reservoir has a nozzle attached. There is a normal shock downstream of the nozzle throat. The Mach number of the stream emanating from the nozzle is M = 0 . 48 and the pressure is p = 101 kPa. Also, the gas temperature is T t = 300 K in the reservoir. Determine the density in the reservoir, ρ t , for air and for helium ( γ = 5 3 ). HINT: To simplify your calculations, express Mach numbers in this problem to two significant figures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T = 300 K ρ =? M = 0 . 48 p = 101 kPa . . . . . . . . Solution: To solve, we note that the temperature in the reservoir is the total temperature, T t , which is constant throughout the flow. Also, the pressure in the reservoir is the total pressure, p t , so that once we find its value we can use the perfect-gas law to find the density of the gas in the reservoir. Our solution procedure will be as follows: 1. Use the normal-shock relations to compute M 1 and p 2 /p 1 for the given M 2 ; 2. Use the isentropic-flow relations to find p 1 /p t
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