Explanation Given information: The relative speed of the expelled fuel is u . The speed of the rocket is v . Calculation: Consider the thrust force is denoted by F and mass flow rate is denoted by d m d t . Calculate the absolute velocity of the exhaust ( v e ) using the relation: v e = u − v Show the expression for the thrust force as follows: F = ( Mass flow rate × relative speed of expelled fuel ) = d m d t × u Calculate the power ( P 1 ) of the thrust force as using the relation: P 1 = F v Substitute d m d t × u for F . P 1 = d m d t × u v The power P 1 is called the useful power. Calculate the power ( P 2 ) associated with the exhaust as follows: P 2 = ( Kinetic Energy of Exhaust Time Taken ) = ( 1 2 ( Δ m ) v e 2 Δ t ) ≈ 1 2 d m d t v e 2 Substitute ( u − v ) for v e . P 2 = ( Kinetic Energy of Exhaust Time Taken ) = ( 1 2 ( Δ m ) v e 2 Δ t ) ≈ 1 2 d m d t ( u − v ) 2 Calculate the total amount ( P ) of power supplied by the engine using the relation: P = P 1 + P 2 (1) Substitute d m d t × u v for P 1 and 1 2 d m d t ( u − v ) 2 for P 2 in Equation (1)

Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9780073398242

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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Chapter 14.3, Problem 14.104P

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Show the expression for mechanical efficiency of the rocket as η=2uv(u2+v2)

Explain the reason for the value of η=1 when u=v.

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Chapter 14.3, Problem 14.103P

Chapter 14, Problem 14.105RP

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Show the expression for mechanical efficiency of the rocket as η = 2 u v ( u 2 + v 2 ) Explain the reason for the value of η = 1 when u = v .

Solution Summary: The author explains the reason for the value of eta =1 when u=v as no power associated with the exhaust.

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Show the expression for mechanical efficiency of the rocket as η=2uv(u2+v2)

Explain the reason for the value of η=1 when u=v.

Want to see the full answer?

Chapter 14 Solutions

Show the expression for mechanical efficiency of the rocket as η = 2 u v ( u 2 + v 2 ) Explain the reason for the value of η = 1 when u = v .

Solution Summary: The author explains the reason for the value of eta =1 when u=v as no power associated with the exhaust.

Concept explainers

Videos

Show the expression for mechanical efficiency of the rocket as η=2uv(u2+v2) Explain the reason for the value of η=1 when u=v.

Want to see the full answer?

Chapter 14 Solutions

Show the expression for mechanical efficiency of the rocket as η=2uv(u2+v2)

Explain the reason for the value of η=1 when u=v.