Thermodynamics

834 | ThermodynamicsMa < 1P decreasesV increasesMa increasesT decreasesr decreasesMa < 1P increasesV decreasesMa decreasesT increasesr increasesSubsonic nozzleSubsonic diffuser(a) Subsonic flowFIGURE 17–17Variation of flow properties insubsonic and supersonic nozzles anddiffusers.Ma > 1P decreasesV increasesMa increasesT decreasesr decreasesSupersonic nozzleMa > 1(b) Supersonic flowP increasesV decreasesMa decreasesT increasesr increasesSupersonic diffuserdecelerated in a subsonic diffuser, which has a flow area that increases inthe flow direction, as shown in Fig. 17–17.Property Relations for Isentropic Flowof Ideal GasesNext we develop relations between the static properties and stagnation propertiesof an ideal gas in terms of the specific heat ratio k and the Mach numberMa. We assume the flow is isentropic and the gas has constant specific heats.The temperature T of an ideal gas anywhere in the flow is related to thestagnation temperature T 0 through Eq. 17–4:orNoting that c p kR/(k 1), c 2 kRT, and Ma V/c, we see thatSubstituting yieldsT 0 T V 22c pT 0T 1 V 22c p TV 22c p T V 223kR>1k 124T a k 1 b V 22 c a k 1 b Ma 22 2which is the desired relation between T 0 and T.T 0T 1 a k 12b Ma 2(17–18)