Explanation Given information: The weight of the airplane is W . The wing span of the airplane is b . The constant velocity of the plane is v . Consider the diameter of the air cylinder is b . Consider the angle of deflection of the cylindrical stream is θ . Calculation: Consider the mass flow the stream is denoted by d m d t . The mass flow is steady as the velocity of the airplane is constant. Calculate the mass flow of the stream using the relation: d m d t = ρ v A (1) Here ρ is the mass density of the air, A is the cross-sectional area of the air cylinder. Show the cross-sectional area of the cylinder ( A ) as follows: A = π b 2 4 (2) Modify Equation (1) using Equation (2). d m d t = ρ v ( π b 2 4 ) Consider the velocity of the air stream in the vertical direction is denoted by v 2 , y . Calculate the velocity v 2 , y using the relation: v 2 , y = − v sin θ Consider the Equilibrium of the plane in the vertical direction. Equate the lift provided by the wings with the self-weight of the plane

12th Edition

ISBN: 9781265566296

Author: BEER

Publisher: MCG

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Chapter 14, Problem 14.113RP

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Show the expression for the angle through which the cylindrical stream is deflected is as follows:

sinθ=4Wπb2ρv2

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Chapter 14, Problem 14.112RP

Chapter 14, Problem 14.114RP

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Show the expression for the angle through which the cylindrical stream is deflected is as follows: sin θ = 4 W π b 2 ρ v 2

Solution Summary: The author explains the expression for the angle through which the cylindrical stream is deflected. The mass flow is steady as the velocity of the airplane is constant.

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Show the expression for the angle through which the cylindrical stream is deflected is as follows:

sinθ=4Wπb2ρv2

Want to see the full answer?

Chapter 14 Solutions

Show the expression for the angle through which the cylindrical stream is deflected is as follows: sin θ = 4 W π b 2 ρ v 2

Solution Summary: The author explains the expression for the angle through which the cylindrical stream is deflected. The mass flow is steady as the velocity of the airplane is constant.

Concept explainers

Videos

Show the expression for the angle through which the cylindrical stream is deflected is as follows: sinθ=4Wπb2ρv2

Want to see the full answer?

Chapter 14 Solutions

Show the expression for the angle through which the cylindrical stream is deflected is as follows:

sinθ=4Wπb2ρv2