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 2.7P

The velocity field given in Problem 2.3 is called source flow, which will be discussed in Chapter 3. For source flow, calculate:

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

b. The vorticity.

Hint: It is simpler to convert the velocity components to polar coordinates and deal with a polar coordinate system.

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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?  
a. Derive an equation for the material acceleration vector.b. Obtain the vorticity vector for the velocity field.c. Is the flow rotational or irrotational? Show through your derivation.d. Is the flow incompressible or compressible? Show through your derivation.
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