Explanation Show the given diesel cycle on P − V diagram as in Figure (1). Write the expression of compression ratio for the given cycle. r = v 1 v 2 (I) Here, the compression ratio is r , specific volume at state 1 is v 1 , and specific volume at state 2 is v 2 . Write the expression of ideal gas equation for the air-fuel mixture at state 1. v 1 = R T 1 P 1 (II) Here, specific volume at state 1 is v 1 , the pressure at state 1 is P 1 , and the gas constant is R . Write the expression of total air mass taken by all eight cylinders when they are charged. m = N c y l π 4 ( B 2 S ) v 1 (III) Here, total air mass taken by all eight cylinders is m , the number of cylinders is N c y l , bore of the cylinder is B and stroke of the cylinder is S . Write the expression of mass flow rate ( m ˙ net ) . m ˙ = m n ˙ N rev (IV) Here, speed of the engine is n ˙ , and number of revolutions per cycle in a four-stroke engine is N rev . Write the temperature and specific volume relation for the isentropic compression process 1-2. T 2 = T 1 ( v 1 v 2 ) k − 1 T 2 = T 1 ( r ) k − 1 (V) Here, the temperature at state 1 is T 1 , the temperature at state 2 is T 2 , specific volume at state 1 is v 1 , specific volume at state 2 is v 2 , compression ratio is r and the specific heat ratio is k . Write the expression of heat input to the cycle ( q in ) . q in = c p ( T 3 − T 2 ) (VI) Here, the specific heat at constant pressure is c p . Write the expression of thermal efficiency of the diesel cycle ( η t h ) . η t h = 1 − 1 r k − 1 r c k − 1 k ( r − 1 ) (VII) Here, the compression ratio is r , and cutoff ratio is r c . Write the expression to obtain the power produced by the engine ( W ˙ net ) . W ˙ net = m ˙ η th q in (VIII) Conclusion: Substitute 0.045 v 1 for v 2 in Equation (I). r = v 1 0.045 v 1 = 22.22 Substitute 0.3704 psia ⋅ ft 3 / lbm ⋅ R for R , 510 R for T 1 , 14.4 psia for P 1 in Equation (II). v 1 = ( 0.3704 psia ⋅ ft 3 / lbm ⋅ R ) ( 510 R ) 14.4 psia = 13

8th Edition

ISBN: 9780100257054

Author: CENGEL

Publisher: YUZU

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Chapter 9.12, Problem 49P

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The power produced by the diesel engine.

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Chapter 9 Solutions

EBK THERMODYNAMICS: AN ENGINEERING APPR

Ch. 9.12 - What are the air-standard assumptions?Ch. 9.12 - What is the difference between air-standard...Ch. 9.12 - How does the thermal efficiency of an ideal cycle,...Ch. 9.12 - What does the area enclosed by the cycle represent...Ch. 9.12 - Prob. 5P Ch. 9.12 - Prob. 6P Ch. 9.12 - Can the mean effective pressure of an automobile...Ch. 9.12 - Prob. 8P Ch. 9.12 - What is the difference between spark-ignition and...Ch. 9.12 - Prob. 10P

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