Fundamentals of Aerodynamics
6th Edition
ISBN: 9781259129919
Author: John D. Anderson Jr.
Publisher: McGraw-Hill Education
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Chapter 3, Problem 3.17P
Consider the lifting flow over a circular cylinder of a given radius and with a given circulation. If
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Consider a large dirigible (like the Goodyear blimp) with length L = 240 m, and average
diameter D = 40 m moving at a speed U = 135 km/hr at high altitude where the air
density is p = 0.9 kg/m³ and the dynamic viscosity is u = 1.8 x 10-5 N – s/m².
Because of the large size of the blimp and its large radius of curvature the primary forces
acting on it are due to shear stresses at the surface, and the entire surface area can be
approximated by its layout as a flat plate. Determine the drag force acting on the dirigible
due to shear stresses, and the power required for the engine.
In deriving the vorticity equation, we have used the identity V × (VP) = 0.
Show that this identity is valid for any scalar λ by checking it in Cartesian and cylindrical coordinates.
(a)
Use the y-momentum equation to show that the pressure
gradient across the boundary layer is approximately zero i.e.
= 0 . Assume the boundary layer to be a two-dimensional
ду
steady and incompressible flow. Neglect gravitational
forces. State clearly all assumptions made.
Use the Bernoulli's equation to prove that the pressure
difference is given by
(b)
P2-P1 = -4pU?
for a fluid with constant density p flowing from point 1 to
point 2 where pi, U1, A1 are the pressure, velocity and flow
cross-section area at point 1 and p2, U2, A2 are the pressure,
velocity and flow cross-section area at point 2 respectively.
The ratio of the cross-section area
A1
= 3.
Chapter 3 Solutions
Fundamentals of Aerodynamics
Ch. 3 - For an irrotational flow. show that Bernoullis...Ch. 3 - Consider a venturi with a throat-to-inlet area...Ch. 3 - Consider a venturi with a small hole drilled in...Ch. 3 - Consider a low-speed open-circuit subsonic wind...Ch. 3 - Assume that a Pitot tube is inserted into the...Ch. 3 - A Pilot tube on an airplane flying at standard sea...Ch. 3 - At a given point on the surface of the wing of the...Ch. 3 - Consider a uniform flow with velocity V. Show that...Ch. 3 - Show that a source flow is a physically possible...Ch. 3 - Prove that the velocity potential and the stream...
Ch. 3 - Prove that the velocity potential and the stream...Ch. 3 - Consider the flow over a semi-infinite body as...Ch. 3 - Derive Equation (3.81). Hint: Make use of the...Ch. 3 - Derive the velocity potential for a doublet; that...Ch. 3 - Consider the nonlifting flow over a circular...Ch. 3 - Consider the nonlifting flow over a circular...Ch. 3 - Consider the lifting flow over a circular cylinder...Ch. 3 - The lift on a spinning circular cylinder in a...Ch. 3 - A typical World War I biplane fighter (such as the...Ch. 3 - The Kutta-Joukowski theorem, Equation (3.140), was...Ch. 3 - Consider the streamlines over a circular cylinder...Ch. 3 - Consider the flow field over a circular cylinder...Ch. 3 - Prove that the flow field specified in Example 2.1...
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