Fundamentals of Aerodynamics
6th Edition
ISBN: 9781259129919
Author: John D. Anderson Jr.
Publisher: McGraw-Hill Education
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Chapter 2, Problem 2.5P
Consider a velocity field where the radial and tangential components of velocity arc
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Chapter 2 Solutions
Fundamentals of Aerodynamics
Ch. 2 - Consider a body of arbitrary shape. If the...Ch. 2 - Consider an airfoil in a wind tunnel (i.e., a wing...Ch. 2 - Consider a velocity field where the x and y...Ch. 2 - Consider a velocity field where the x and y...Ch. 2 - Consider a velocity field where the radial and...Ch. 2 - Consider a velocity field where the x and y...Ch. 2 - The velocity field given in Problem 2.3 is called...Ch. 2 - The velocity field given in Problem 2.4 is called...Ch. 2 - Is the flow field given in Problem 2.5...Ch. 2 - Consider a flow field in polar coordinates, where...
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- The velocity components of an incompressible, two-dimensional field are given bythe following equations: u(x,y) =y^2 -x (1+x) v(x,y) = y(2x+1) Show that the flow field is (a) irrotational and (b) satisfies conservation of mass.arrow_forwardIf the velocity of an incompressible fluid at a point (x,y,z) is given by (image below) prove that the motion is possible and that the velocity potential is −cosθ/r2. Find the equations of the streamlines where r^2 = x^2 +y^2 +z^2 and θ is the angle between r and the z-axis. Kindly, explain all the steps. :)arrow_forwardConsider a velocity field where the x and y components of velocity are given by u = cx and v = -cy, where c is a constant. Obtain the equations of the streamlines.arrow_forward
- Consider the velocity field given by u = y/(x2 + y2) and v = −x/(x2 + y2). For the velocity field given , calculate the circulation around a circular path of radius 5 m. Assume that u and v given are in units of meters per second.arrow_forwardA 2D incompressible velocity field is defined by . If both u and v are 0 at point (x = 0, y = 0), determine a) v component of the velocity and b) an expression for pressure field. Assume gravity is in the – y-direction and pressure is 0 at point (x=0, y=0). The flow is defined by: u=2(x2-y2)arrow_forwardA velocity profile for water is given as a function of x, y and z. How can we determine if the profile is a physically possible flow field? A) If the sum of the derivatives of each component with respect to their flow direction = 0. B) If the flow is irrotational. C) If the vorticity equals 0. D) If we can determine a velocity potential.arrow_forward
- The expression for stream function is described by y = x ^ 3 - 3x * y ^ 2 . Indicate whether the flow is rotational or irrotational. Determine the value or velocity potential o, if it exists.arrow_forwardThe velocity field is given as u=y-1 and v=y-2. The units of u and v are m/s and the units of x and y are meters. a) Draw the stream line passing through the point (x,y)=(4.3). b) Determine the streakline passing through the point (x, y) = (4,3) and compare it with the streamline. c) Determine whether the current is revolving or not.arrow_forwardThe velocity vector in a flow is given by :V=-3xi-4yj-7zk Determine the stream equation passing through a point L(4,2,3)arrow_forward
- The stream function in a two dimensional flow field is given by sie= x2 - y2 .find the magnitude of the velocity at point (1. 1) .arrow_forward1. The components of velocity in a flow field are given byu=x2+y2+z2v=xy+yz+z2w=-3xz- 0.5z2+4a) Determine the volumetric dilatation rate and interpret the result.b) Determine an expression for the rotation vector. Is this an irrotational flow field?arrow_forwardA velocity field is specified as shown, the coordinates are measured in meters. Is the flow field one-, two-, or three-dimensional? Why? Calculate the velocity components at the points (2, 1/2). Develop an equation for the streamline passing through this point. Plot several streamlines in the first quadrant including the one that passes through the point (2, 1/2)arrow_forward
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