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

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

See similar textbooks

Concept explainers

Conservation of Energy

In physics, the rule of the conservation of energy states that energy doesn’t disappear from the atmosphere; instead, it changes its form from one type to another. Energy is one of the most important physical quantities in nature, and it cannot be create…

Videos

Question

Chapter 14, Problem 14.113RP

To determine

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

sinθ=4Wπb2ρv2

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14, Problem 14.112RP

Chapter 14, Problem 14.114RP

Students have asked these similar questions

The figure (below) shows a device for clearing debris using a jet of air discharged from a nozzle. As shown, the jet is striking a cube-shaped object (density 1900 kg/m³) sitting on the floor. Assume that in all cases that (i) the entire jet is deflected by the cube; and (ii) the cube slides rather than tumbles. Air jet If the jet diameter is 38 mm and the air velocity is 25 m/s, what is the heaviest cube that could be moved? What are the dimensions of the cube? If needed, assume the coefficient of friction is 0.60.

A spring of force constant K attached to the wall on a horizontal smooth plane. The spring is compressed by a block of mass 6 kg a distance x= 0.2 m. The speed of the block as it released and passes the equilibrium position is 5 m/s. Find the force constant k (in N/m). 100000000000 X=0

An aircraft, of mass 2000 kg, is following a circular path in the vertical plane as shown in Figure 2. When the flight path of the aircraft is at an angle of 30° from the horizontal, the aircraft's velocity is 150 m/sec, the radius of curvature of its trajectory is 1000 metres, and the net thrust (engine thrust minus drag) is T = 30 kN and acts along the flight path. Assume that the lift force L is perpendicular to the flight path. Draw a free-body diagram showing all forces acting on the aircraft. Calculate the resultant acceleration and its angle from the flight path. Also calculate the lift force L. r= 1000 metres 307 Figure 2

Chapter 14 Solutions

Vector Mechanics for Engineers: Statics and Dynamics

Ch. 14.1 - A 30-g bullet is fired with a horizontal velocity...Ch. 14.1 - Two identical 1350-kg automobiles A and B are at...Ch. 14.1 - Prob. 14.3P Ch. 14.1 - Prob. 14.4P Ch. 14.1 - Two swimmers A and B, of weight 190 lb and 125 lb,...Ch. 14.1 - A 180-lb man and a 120-lb woman stand side by side...Ch. 14.1 - A 40-Mg boxcar A is moving in a railroad...Ch. 14.1 - Two identical cars A and B are at rest on a...Ch. 14.1 - A 20-kg base satellite deploys three...Ch. 14.1 - For the satellite system of Prob. 14.9, assuming...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

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: 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