Fundamentals of Aerodynamics
6th Edition
ISBN: 9781259129919
Author: John D. Anderson Jr.
Publisher: McGraw-Hill Education
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Chapter 3, Problem 3.11P
Prove that the velocity potential and the stream function for a source flow, Equations
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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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- 1. Consider a three-dimensional steady incompressible flow with components: u =-x(y+z), v= y, w=÷(z²-2yz), (a) Is the flow locally rotating? Justify your answer. (b) Determine the equation of vortex lines. (c) Are the vortex lines perpendicular to the streamlines?arrow_forwardOuter pipe wall Consider the steady, incompressible, laminar flow of a Newtonian fluid in an infinitely long round pipe annulus of inner radius R, and outer radius Ro. Assume that the pressure is constant everywhere there is no forced pressure gradient driving the flow, Pi = P2. However, let the inner cylinder be moving at steady velocity V to the right, essentially a piston. The outer cylinder is stationary. This makes an axisymmetric Couette flow. Use cylindrical coordinates and the equations of motion to generate an expression for the x-component of velocity u as a function of r. Ignore the effects of gravity. Fluid: p, H iP R; R, ƏP_ P2- P1 ax x2-X1arrow_forwardFor an Eulerian flow field described by u = 2xyt, v = y3x/3, w = 0: (a) Is this flow one-, two-, or three-dimensional? (b) Is this flow steady? (c) Is this flow incompressible? (d) Find the x-component of the acceleration vector.arrow_forward
- A CFD model of steady two-dimensional incompressiblefl ow has printed out the values of stream function ψ ( x , y ), inm 2 /s, at each of the four corners of a small 10-cm-by-10-cmcell, as shown in Fig. P4.70. Use these numbers to estimate the resultant velocity in the center of the cell and its angleα with respect to the x axis.arrow_forwardConsider a uniform stream of magnitude V inclined at angle ?. Assuming incompressible planar irrotational flow, find the velocity potential function and the stream function. Show all your work.arrow_forward3. The two-dimensional velocity field in a fluid is given by V 2ri+ 3ytj. (i) Obtain a parametric = equation for the pathline of the particle that passed through (1.1) at t = 0. (ii) Without calculating any equation: if I were to draw the streak-line at t = 0 of all points that passed through (1, 1) would it be the same or different? Justify yourself.arrow_forward
- Pls provide proper steps with explanation of concept.arrow_forwardOne of the corner flow patterns of Fig. 8.18 is given by thecartesian stream function ψ = A(3yx2 - y3). Which one?Can the correspondence be proved ?arrow_forwardP4.28 For the velocity distribution of Prob. see below, i.e. u = 4y and v = 2x (incompressible flow) (a) check continuity. (b) Are the Navier-Stokes equations valid? (c) If so, determine p(x,y) if the pressure at the origin is po.arrow_forward
- (b) Two velocity components of a steady, incompressible flow field are given as follows; u = 2ax + bxy + cy? v = axz – byz? where a, b and c are constants. Determine an expression for w as a function of x, y, and z.arrow_forwardK1arrow_forwardExample 6.5. For a three-dimensional flow field described by V = (y? + 22) i + (x² +z?) j + (x²+y²) k find at (1, 2, 3) (i) the components of acceleration, (ii) the components of rotation.arrow_forward
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