Explanation Write the expression to calculate stagnation temperature T 0 . T 0 = T i + V i 2 2 c p (I) Here, temperature at inlet is T i , specific heat at constant pressure is c p and velocity of air at the initial state is V i . Write the thermodynamic relation between stagnation pressure and temperature. P 0 P i = ( T 0 T i ) k / ( k − 1 ) (II) Here, stagnation pressure is P 0 , pressure at the initial state is P i , and ratio of specific heats is k . Write the expression for the velocity of sound in fluid at the initial state. c i = k R T i (III) Here, velocity of sound in the fluid at the initial state is c i , and gas constant of air is R . Write the relation between Mach number and fluid velocity. Ma i = V i c i (IV) Here, Mach number is Ma. At a Mach number of 1 the stagnation pressure and temperature is same at inlet and outlet, they remain constant right through the nozzle since the flow is isentropic. The properties of the fluid are at its critical for a Mach number of 1, Refer Table A-32, “One-dimensional isentropic compressible-flow functions for an ideal gas with k = 1.4 ”, write the following expressions of critical pressure and temperature for a Mach number of 1. T = 0.8333 T 0 (V) P = 0.5283 P 0 (VI) Here, the exit temperature is T , exit pressure is P , temperature at the outlet is T 0 , and pressure at the outlet is P 0 . Conclusion: Substitute 630 R for T i , 450 ft / s for V i , and 0.240 Btu / lbm ⋅ R for c p in Equation (I). T 0 = 630 R + ( 450 ft / s ) 2 2 × 0.240 Btu / lbm ⋅ R T 0 = 630 R + ( 450 ft / s ) 2 2 × 0.240 Btu / lbm ⋅ R ( 1 Btu / lbm 25037 ft 2 / s 2 ) T 0 = 646.9 R Substitute 30 psia for P i , 646.9 R for T 0 , 1.4 for k and 630 R for T i in Equation (II). P 0 30 psia = ( 646

8th Edition

ISBN: 9780073398174

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

Publisher: McGraw-Hill Education

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Chapter 17.7, Problem 59P

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The exit pressure, exit temperature and the ratio of the throat area to the nozzle entrance area.

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Chapter 17.7, Problem 58P

Chapter 17.7, Problem 62P

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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