To determine The thrust force that the engine exerts on the airplane. Explanation Show the control volume for the airliner. Express the mass flow rate through section 1. m ˙ 1 = ρ 1 [ π 4 D 1 2 ] V 1 (I) Here, density of section 1 is ρ 1 , diameter of section 1 is D 1 and volumetric flow rate through section 1 is V 1 . Express the mass flow rate through section 2. m ˙ 2 = m ˙ 1 + m ˙ f u e l (II) Here, mass flow rate of fuel is m ˙ f u e l . Express the cross-sectional area of section 2. A 2 = π 4 D 2 2 (III) Here, diameter of section 2 is D 2 . Express the volumetric flow rate through section 2. V 2 = m ˙ 2 ρ 2 A 2 (IV) Here, density through section 2 is ρ 2 . Express the thrust force that the engine exerts on the airplane. F ' = ( p 2 − p a m b ) A 2 + m ˙ 2 V 2 − m ˙ 1 V 1 (V) Here, pressure at section 2 is p 2 and ambient pressure is p a m b . Conclusion: Substitute 0 .4 kg / m 3 for ρ 1 , 1 m for D 1 and 250 m / s for V 1 in Equation (I). m ˙ 1 = ( 0 .4 kg / m 3 ) [ π 4 ( 1 m ) 2 ] ( 250 m / s ) = 78.54 kg / s Substitute 78.54 kg / s for m ˙ 1 and 3 kg / s for m ˙ f u e l in Equation (II). m ˙ 2 = 78.54 kg / s + 3 kg / s = 81

8th Edition

ISBN: 9781119571490

Author: GERHART

Publisher: WILEY

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Chapter 5.2, Problem 55P

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The thrust force that the engine exerts on the airplane.

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Chapter 5.2, Problem 54P

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