Explanation Show the process of the turbofan engine on T − s diagram. Write the ideal gas equation for air at state 1. v 1 = R T P (I) Here, specific volume at state 1 is v 1 , temperature is T , pressure is P and the gas constant is R . Write the expression to obtain the mass flow rate ( m ˙ ) . m ˙ = A V 1 v 1 m ˙ = ( π D 2 4 ) V 1 v 1 (II) Here, velocity of the turbofan engine is V 1 , and inlet diameter of the engine is D . Write the expression to obtain the mass flow rate at the exit of fan ( m ˙ e ) . m ˙ e = m ˙ 8 (III) Write the expression to obtain the mass flow rate through the fan ( m ˙ f ) . m ˙ f = m ˙ − m ˙ e (IV) Write the expression of specified thrust force ( F ) . F = m ˙ f ( V e x i t − V i n l e t ) (V) Here, exit velocity is engine is V e x i t and inlet velocity is engine is V i n l e t . Write the expression of energy balance on the stream passing through the fan. c p ( T 4 − T 5 ) = V e x i t 2 − V i n l e t 2 2 (VI) Here, specific heat at constant pressure is c p , temperature at state 4 is T 4 and temperature at state 5 is T 5 . Conclusion: Substitute 0.287 kPa ⋅ m 3 / kg ⋅ K for R , 50 kPa for P , and − 20 ° C for T in Equation (I). v 1 = ( 0.287 kPa ⋅ m 3 / kg ⋅ K ) ( − 20 ° C + 273 K ) 50 kPa = 1.452 m 3 / kg Substitute 2.5 m for D , 200 m / s for V 1 and 1.452 m 3 / kg for m ˙ in Equation (II). m ˙ = ( π ( 2.5 m ) 2 4 ) ( 200 m / s 1.452 m 3 / kg ) = 676

8th Edition

ISBN: 9780073398174

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

Publisher: McGraw-Hill Education

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Chapter 9.12, Problem 131P

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The air temperature at the fan outlet.

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Chapter 9.12, Problem 130P

Chapter 9.12, Problem 132P

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