Explanation Given: The speed of the jet plane when four engines are in operation is v p = 800 km/h . The consumption rate of fuel is 0.4 kg/s . The speed of the combustion gases relative to the plane is v D / e = 775 m/s . The drag resistance is F D = c v 2 . Draw the free body diagram of the jet airplane as shown in Figure 1. Write the steady flow equation of forces along x − a x i s . ∑ F x = d m d t [ ( v 2 ) x − ( v 1 ) x ] (I) Here, ∑ F x is the resultant of all forces acting along x − a x i s , d m d t is rate of mass flow in to the system, ( v 1 ) x is the initial velocity of the system along the x − a x i s and ( v 2 ) x is the final velocity of the system along the x − a x i s . Write the formula for relative velocity when the plane moving with the ejected mass. v D / e = v e + v p (II) Here, v D / e is the relative velocity of the ejected mass to the rocket, v e velocity of the ejected mass and v p is the velocity of the plane. Conclusion: Write the speed of the jet airplane with the ejected mass in the unit of m/s . v D / e = 800 km h × 1000 m 1 km × 1 h 3600 s = 222.2222 m/s Calculate the velocity of the ejected mass. Substitute 775 m/s for v D / e and 222.2222 m/s for v p in Equation (II). 775 m/s = v e + 222.2222 m/s v e = 775 − 222.2222 v e = 552.7778 m/s Consider the air entering into the system and air exit from the system. Since, the air is collected from the large source that is atmosphere. Hence the inlet velocity of the system is negligible and equal to zero. ( v 1 ) x = 0 Here, the velocity of the exhaust gas is the final velocity of the air leaving the system(exit velocity). v e = ( v 2 ) x = 552.778 m/s Refer Figure (1). Calculate the resultant force of the control volume ∑ F x along the x − a x i s . ∑ F x = F D Substitute c v 2 for F D . ∑ F x = c v 2 Here, v = v p = 222.2222 m/s . Substitute 222.2222 m/s for v . ∑ F x = c ( 222.2222 m/s ) 2 = c ( 49382.7062 ) = 49382.7062 c When, the four engines of the jet are in operation. The mass flow rate of the air entering into the system is multiplied by 4 . d m d t = 4 d m d t Substitute 49382.7062 c for ∑ F x , 4 d m d t for d m d t , 552.7778 m/s for ( v 2 ) x and 0 for ( v 1 ) x in Equation (I). 49382.7062 c = 4 d m d t ( 552

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 15.9, Problem 144P

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The cruising speed of the jet when two of the engines, one on each side are shut off:

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Chapter 15.9, Problem 143P

Chapter 15.9, Problem 145P

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The cruising speed of the jet when two of the engines, one on each side are shut off:

Solution Summary: The author explains the cruising speed of the jet plane when two engines, one on each side, are shut off, the consumption rate of fuel, and the drag resistance.

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The cruising speed of the jet when two of the engines, one on each side are shut off:

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