Explanation The p - v diagram of the Diesel cycle is shown below. Figure-(1) Write the expression for compression ratio. r = v 1 v 1 − v s (I) Here, the volume at point 1 is v 1 and the displacement volume is v s . Write the expression between, temperature and compression ratio for process 1-2. T 2 T 1 = ( r ) k − 1 (II) Here, the adiabatic index is k , the temperature at compressor outlet is T 2 , the compressor inlet is T 1 and the compression ratio is r . Write the expression for the cutoff ratio. r c = T 3 T 2 (III) Here, the temperature at point 3 is T 3 and at point 2 is T 2 , the volume of cylinder before expansion is V 3 and after compression is V 2 . Write the expression between, temperature and cutoff ratio for process 4-1. T 4 T 1 = ( r c ) k (IV) Here, the temperature at point 4 is T 4 and at point 1 is T 1 and the cutoff ratio is r c . Write the expression for the inlet volume at point 1. v 1 = m R T 1 p 1 (V) Here, the gas constant is R and mass of the air is m . Write the expression the net developed. w n e t = m [ c p ( T 3 − T 2 ) − c v ( T 4 − T 1 ) ] (VI) Here, the mass of the air is m , engine rpm is N . Write the expression for the net power of the cycle. W ˙ n e t = w n e t × N (VII) Write the expression for the thermal efficiency of diesel cycle. % η t h = w n e t m c p ( T 3 − T 2 ) . N × 100 % (VIII) Conclusion: Substitute 3.17 L for v 1 and 3 L for v s in Equation (I). r = 3.17 L 3.17 L − 3 L = 3.17 L 0.17 L = 19 Substitute 19 for r , 1.4 for k and 295 K for T 1 in Equation (II). T 2 295 K = ( 19 ) 1.4 − 1 T 2 = 295 K × ( 19 ) 0.4 T 2 = 958 K Substitute 958 K for T 2 and 2.5 for r c in Equation (II). 2.5 = T 3 958 K T 3 = 2395 K Substitute 2.5 for r c , 1.4 for k and 295 K for T 1 in Equation (III). T 4 295 K = ( 2.5 ) 1.4 T 4 = 295 K × ( 2.5 ) 1.4 T 4 = 1064 K Substitute 295 K for T 1 , 95 kPa for p 1 , 0.00317 m 3 for v 1 and 0.287 kJ / kg ⋅ K in Equation (IV)

Fundamentals of Engineering Thermodynamics

8th Edition

ISBN: 9781118412930

Author: Michael J. Moran, Howard N. Shapiro, Daisie D. Boettner, Margaret B. Bailey

Publisher: WILEY

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Question

Chapter 9.14, Problem 28P

To determine

The net work developed.

The thermal efficiency.

The net power for the cycle.

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Chapter 9.14, Problem 27P

Chapter 9.14, Problem 29P

Chapter 9 Solutions

Fundamentals of Engineering Thermodynamics

Ch. 9.14 - Prob. 1E Ch. 9.14 - Prob. 2E Ch. 9.14 - Prob. 3E Ch. 9.14 - Prob. 4E Ch. 9.14 - Prob. 5E Ch. 9.14 - 6. What is the purpose of a rear diffuser on a...Ch. 9.14 - 7. What is the meaning of the octane rating that...Ch. 9.14 - Prob. 8E Ch. 9.14 - Prob. 9E Ch. 9.14 - 10. What is the purpose of the gas turbine–powered...

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