Fundamentals of Aerodynamics
Fundamentals of Aerodynamics
6th Edition
ISBN: 9781259129919
Author: John D. Anderson Jr.
Publisher: McGraw-Hill Education
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Chapter 2, Problem 2.8P

The velocity field given in Problem 2.4 is called vortex flow, which will be discussed in Chapter 3. For vortex flow, calculate:

a. The time rate of change of the volume of a fluid element per unit volume.

b. The vorticity.

Hint: Again, for conveniences use polar coordinates.

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Please indicate the given, assumption and illustration. A source with strength 0.25 m2/s and a vortex with strength 1 m2/s (counter-clockwise) are located at the origin. After working out the equations for the stream function and velocity potential components, determine the following velocity components at a point P(1, 0.5): A) The Radial Velocity component in meters/second.  B) The Tangential Velocity Component in meters/second.
In Cartesian coordinates, a particular velocity field is defined by V = −2x2i + 4xyj + 3k. (a) Is this flow field compressible or incompressible? (b) Find the acceleration of the fluid at the point (1,3,0) (c) Find the volume flux passing through area A shown in Figure P5.16. (d) What are the dimensions of volume flux?  
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