Fundamentals of Aerodynamics
6th Edition
ISBN: 9781259129919
Author: John D. Anderson Jr.
Publisher: McGraw-Hill Education
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Chapter 3, Problem 3.13P
Derive Equation
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5.17 The velocity field given by V =Axi-Ayj represents flow in a
rectangular corner. Evaluate the circulation around the unit square
with corners at (x.y)= (1,1), (1,2), (2,2) and (2,1) for the value of
A =0 3s-!.
Example 10.4-2 Stream Function and Velocities from potential Function
The potential function for 2D, irrotational, incompressible flow filed is given as:
Ø = x² – 2y – y²
%3D
Find the stream function y and the velocity components and y?
55. Derive the relation for angular velocity in terms of the velocity components
for fluid rotation in a two-dimensional flow field. [Hint: Use the schematic for ro-
tation in Figure IIa.3.5 and find the angular velocity for line oa as @a = doddt.
Substitute for da= dl,/dx and for dl, from dl, = (JV,/dx)dxdt. Do the same for line
ob to find @p. The z-component of rotation vector is the average of @a and @p.
Do the same for x- and y- components].
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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- Problem 1 Given a steady flow, where the velocity is described by: u = 3 cos(x) + 2ry v = 3 sin(y) + 2?y !! !! a) Find the stream function if it exists. b) Find the potential function if it exists. c) For a square with opposite diagonal corners at (0,0) and (47, 27), evaluate the circu- lation I = - f V.ds where c is a closed path around the square. d) Calculate the substantial derivative of velocity at the center of the same box.arrow_forward4. The velocity distribution of flow over a plate is parabolic with vertex 30 cm from the plate, where the velocity is 180 cm/s. If the viscosity of the fluid is 0.9 N.S/m2 find the velocity gradients and shear stresses at distances of 0, 15 cm and 30 cm from the plate.arrow_forwardPlease solve itsarrow_forward
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- 5.71 A cylinder of radius r; rotates at a speed w coaxially inside a fixed cylinder of radius ro. A viscous fluid fills the space between the two cylinders. Determine the velocity profile in the space between the cylinders and the shear stress on the surface of each cylinder. Explain why the shear stresses are not equal.arrow_forwardA turbine (see the figure of Example IIIa.3.21) is located at an elevation H1 from the surface of a lake with the discharge pipe located at an elevation H2 from the turbine centerline. Find flow velocity, V4 in terms of H1, H2, P1, P4, h,, and p where subscript 4 refers to the discharge piping. [Ans.: V, = (2/p)[(R – P.) + pg (Z, – Z, –h,)]. Lake H, h. D2 4 D4 H4 Turbinearrow_forward4.12. Show that the pattern due to a two-dimensional sink at the origin and sources at (0-5, 0) and (2, 0), all of strength 27, represents flow due to a source near a cylinder. Using angle measurements from a scale drawing, evaluate y for a series of points in the first and second quadrants and, by interpolation, draw the 37 streamlines =, and 4 !3!arrow_forward
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