Explanation Given: The initial mass of the rocket is m 0 . Velocity of fuel expelled is v e . Acceleration of the rocket to be maintained is a 0 . Calculations: Consider the fixed control volume consists of entire rocket and the contents present in it. Assuming the flow as steady, incompressible and inviscid, consider the ideal fluid flow of air. Draw the free body diagram of the control volume as in Figure (1). Express the mass of fuel as a function of time. m ˙ f = − d m d t Write the equilibrium force equation in vertical direction from the Figure (1). Σ F y = m d V cv d t + m ˙ a V c v − ( m ˙ a + m ˙ f ) V e − m g = m a 0 + 0 − ( 0 − d m d t V e ) d m d t = − m ( a 0 + g ) V e (I) Apply variable separation and integrate, d m m = − a 0

2nd Edition

ISBN: 9780134649290

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 6, Problem 90P

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The mass flowrate of fuel that is required to be consumed.

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Chapter 6, Problem 89P

Chapter 6, Problem 91P

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