Explanation Write the formula to calculate the relation of ideal gas speed of sound. c = k R T (I) Here, the specific heat ratio of air is k , the gas constant of the air is R , and the temperature of the air is T . Write the formula to calculate the velocity of the air. Ma = V c V = Ma × c (II) The velocity of the air flow in the device is V and the Mach number is Ma . Write the formula to calculate the density of the air. ρ = P R T (III) Here, the pressure of the air is P . Write the formula to calculate the stagnation temperature of the air after acceleration. T 0 = T ( 1 + ( k − 1 ) Ma 2 2 ) (IV) Here, the static temperature of the air is T . Write the formula to calculate the stagnation pressure of air. P 0 = P ( T 0 T ) k / ( k − 1 ) (V) Here, the static pressure of air is P . Write the formula to calculate the stagnation density of air. ρ 0 = ρ ( T 0 T ) 1 / ( k − 1 ) (VI) Here, the static density of air is ρ . Conclusion: Refer Table A-2, “Ideal-gas specific heats of various common gases” to obtain value of gas constant and specific heat ratio of air at 300 K temperature as 0.287 kJ / kg ⋅ K and 1.4. Substitute 1.4 for k , 0.287 kJ / kg ⋅ K for R , and 100 ° C for T in Equation (I). c = ( 1.4 ) ( 0.287 kJ / kg ⋅ K ) ( 100 ° C ) = ( 1.4 ) ( 0.287 kJ / kg ⋅ K ) ( 100 +273 .2 ) K = 150 kJ / kg × ( 1000 m 2 / s 2 1 kJ / kg ) = 387.2 ft / s Substitute 0

8th Edition

ISBN: 9780073398174

Author: Yunus A. Cengel Dr., Michael A. Boles

Publisher: McGraw-Hill Education

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Chapter 17.7, Problem 44P

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The effect of Mach number in the range of 0.1 to 0.2 on the velocity, stagnation pressure, temperature and density of the air

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Chapter 17.7, Problem 43P

Chapter 17.7, Problem 45P

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Chapter 17 Solutions

Thermodynamics: An Engineering Approach

Ch. 17.7 - A high-speed aircraft is cruising in still air....Ch. 17.7 - What is dynamic temperature?Ch. 17.7 - Prob. 3P Ch. 17.7 - Prob. 4P Ch. 17.7 - Prob. 5P Ch. 17.7 - Calculate the stagnation temperature and pressure...Ch. 17.7 - Prob. 7P Ch. 17.7 - Prob. 8P Ch. 17.7 - Prob. 9P Ch. 17.7 - Prob. 10P

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