Explanation Write the formula for velocity of sound at the inlet conditions. c 1 = k R T 1 Here, the specific heat ratio is k , the speed of sound at the inlet condition is c 1 , and the gas constant of air is R . Write formula for the velocity of air at inlet. Ma 1 = V 1 c 1 = V 1 k R T 1 (I) Write the formula of ratio of stagnation temperature to the static temperature at inlet of the nozzle. T 01 T 1 = 1 + k − 1 2 Ma 1 2 T 01 = T 1 ( 1 + k − 1 2 Ma 1 2 ) (II) Here, the inlet static temperature is T 1 , the inlet stagnation temperature is T 01 , the specific heat ratio is k , and Mach number of air at the inlet of nozzle is Ma 1 . Write the formula for stagnation temperature ratio of exit to inlet. T 0 2 T 01 = T 02 / T 0 ∗ T 01 / T 0 ∗ (III) Here, the exit stagnation temperature is T 02 , and the critical stagnation temperature is T 0 ∗ . Write the formula for heat transfer per unit mass ( q ) . q = c p ( T 02 − T 01 ) (IV) Here, the specific heat at constant pressure is c p , the exit stagnation temperature is T 02 , and inlet stagnation temperature is T 01 . Refer Table A-2, “Ideal-gas specific heats of various common gases”. The specific heat ratio ( k ) of air is 1.4 and the specific heat at constant pressure is 1.005 kJ/kg ⋅ K . Refer Table A-34, “Rayleigh flow functions for an ideal gas with k = 1.4 ”. The Rayleigh flow function of inlet stagnation temperature to the critical stagnation temperature corresponding to the inlet Mach number of 0.2494 is 0.2559 . T 01 T 0 ∗ = 0.2559 The Rayleigh flow function of exit stagnation temperature to the critical stagnation temperature corresponding to the exit Mach number of 0.8 is 0.9639 . T 02 T 0 ∗ = 0.9639 Conclusion: Substitute 100 m/s for V 1 , 1.4 for k , 0.2870 kJ/kg ⋅ K for R , and 400 K for T 1 in Equation (I). Ma 1 = 100 m/s ( 1.4 ) ( 0.2870 kJ/kg ⋅ K ) ( 400 K ) = 100 m/s 160.72 kJ/kg × 1000 m 2 / s 2 1 kJ / kg = 100 m/s 400.8989 m/s = 0.2494 Refer Table A-34, “Rayleigh flow functions for an ideal gas with k = 1.4 ”. The Rayleigh flow function of inlet stagnation temperature to the critical stagnation temperature corresponding to the inlet Mach number of 0.2494 is 0.2559 . T 01 T 0 ∗ = 0.2559 Substitute 400 K for T 1 , 1.4 for k , and 0.2494 for Ma 1 in Equation (II). T 01 = 400 K [ 1 + ( 1

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Chapter 17.7, Problem 134RP

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The heat transfer to the air in kJ/kg and the maximum amount of heat transfer without reducing the mass flow rate of air.

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Chapter 17.7, Problem 133RP

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The heat transfer to the air in kJ/kg and the maximum amount of heat transfer without reducing the mass flow rate of air.

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