Explanation If the inlet velocity is negligible, the inlet properties will be equal to the stagnation properties. T 1 = T 01 = 560 K P 1 = P 01 = 0.6 MPa It is given that the temperature and pressure of helium to be found at the location where the velocity of helium equals to the velocity of the sound. This statement indicates that the exit Mach number is 1. Since the flow is isentropic, the inlet and exit stagnation properties are equal. T 01 = T 02 P 01 = P 02 Write the formula for the ratio of critical (throat) temperature to the stagnation temperature. T ∗ T 0 = 2 k + 1 T ∗ = T 0 ( 2 k + 1 ) (I) Here, actual (static) temperature of helium at the inlet is T 1 , the stagnation temperature of helium at inlet is T 01 , and the specific heat ratio is k . Write the formula for the ratio of critical (throat) pressure to the stagnation pressure. P ∗ P 0 = ( 2 k + 1 ) k / ( k − 1 ) P ∗ = P 0 ( 2 k + 1 ) k / ( k − 1 ) (II) Here, the static pressure of helium at inlet is P 1 , the stagnation pressure of helium at inlet is P 01 . Here, the superscript * indicates the critical state (throat) and the subscript 0 indicates stagnation state. Write the formula for ratio of the inlet area to the critical (throat) area. A 1 A ∗ = 1 Ma 1 [ ( 2 k + 1 ) ( 1 + k − 1 2 Ma 1 2 ) ] ( k + 1 ) / [ 2 ( k − 1 ) ] (III) Refer Table A-1, “Molar mass, gas constant, and critical-point properties”. The gas constant ( R ) of helium is 2.0769 kJ/kg ⋅ K or 2.0769 kPa ⋅ m 3 /kg ⋅ K . Refer Table A-2, “Ideal-gas specific heats of various common gases”. The specific heat at constant pressure ( c p ) of helium is 5

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ISBN: 9780100257054

Author: CENGEL

Publisher: YUZU

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Chapter 17.7, Problem 130RP

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The pressure and temperature of the helium at a location where the velocity equals the speed of sound and what is ratio of the area at this location to the entrance area by assuming inlet velocity is negligible.

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Chapter 17.7, Problem 129RP

Chapter 17.7, Problem 132RP

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Chapter 17 Solutions

EBK THERMODYNAMICS: AN ENGINEERING APPR

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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