Explanation Write the expression to calculate the velocity of sound in fluid before the shock. c 1 = k R T 1 (I) Here, ratio of specific heats is k , velocity of sound in the fluid before the shock is c 1 , and gas constant of air is R, temperature of air before the shock is T 1 . Write the relation between Mach number and fluid velocity before the shock. Ma 1 = V 1 c 1 (II) Here, Mach number of the fluid before shock is Ma 1 . Write the expression to calculate the entropy change of air. s 2 − s 1 = c p ln T 2 T 1 − R ln P 2 P 1 (III) Here, specific heat at constant pressure is c p , entropy of air before the normal shock is s 1 , entropy of air after the normal shock is s 2 , and gas constant of air is R . Conclusion: Refer Table A-2, “Ideal-gas specific heats of various common gases”, obtain the following properties for air at room temperature. c p = 1.005 kJ / kg ⋅ K R = 0.287 kJ / kg ⋅ K k = 1.4 Substitute 1.4 for k , 0.287 kJ / kg ⋅ K for R , and 230 K for T 1 in Equation (I). c 1 = 1.4 × 0.287 kJ / kg ⋅ K × 230 K = 1.4 × 0.287 kJ / kg ⋅ K × 230 K ( 1000 m 2 / s 2 1 kJ / kg ) = 304 m / s Therefore, at the specified condition, velocity of sound in the fluid before the shock is 304 m / s . Substitute, 815 m / s for V 1 , and 304 m / s for c 1 in Equation (II). Ma 1 = 815 m / s 304 m / s = 2

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The entropy change of air across the normal shock wave.

Solution Summary: The author explains the entropy change of air across the normal shock wave and the equation to calculate the velocity of sound in fluid before the shock.

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