Practice HW1 - with a polar coordinate system 4(15 pts...

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AE311 Fall 2008 Problem Set 1 Due: 8 Sept 2008 1. (15 pts) Anderson 4 th edition: Problem 1.7 2. (15 pts) Anderson 4th edition: Problem 1.9 3. (15 pts) The velocity field given in Problem 2.4 is called vortex flow , which will be discussed in Chapter 3. For vortex flow: a. Calculate the time rate of change of the volume of a fluid element per unit volume b. Calculate the vorticity c. Is this flow irrotational? Prove your answer Hint : It is simpler to convert the velocity components to polar coordinates and deal
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Unformatted text preview: with a polar coordinate system. 4. (15 pts) Which of the following velocity fields satisfies conservation of mass for an incompressible fluid? a) u = x 3 sin y + x cos z , v = 3x 2 cos y –y 2 z, w = -sin z+zy b) u r = (1/2)rz 2 sin 2 θ , u θ = rz 2 sin θ cos θ , u z = (r 2 + z 3 )(-(1/3)cos 2 θ) c) u r = r 2 /(2Ф) + rФ cos θ , u θ = (3rФ cos 2 θ)/(2 sin θ), u Ф = -2r 2 ln Ф sinθ...
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