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333HW5 - What is the angular velocity If a small cross is...

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AAE333 Fall 2011 Homework 5 Due: Monday Oct 3 Keywords: Material Derivatives, Substantial Derivatives, Vorticity,Irrotational Flow,Streamfunction, Velocity Potential 1) Consider a 2D velocity field with u=2y, v=-2x with a constant density of 1. Determine the x and y components of force per unit volume required to make the fluid move in this pattern. It turns out this force can be produced by pressure alone. Find the pressure field. Draw isobars and streamlines. Sketch the force vectors around a streamline. Describe the flow in words. 2) In problem 1), what is the acceleration of a fluid particle? How is that related to the material derivative of the velocity? How is it related to the force per unit volume? 3) In problem 1), what is the vorticity of the fluid?
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Unformatted text preview: What is the angular velocity? If a small cross is placed at x=0,y=1 (with the two arms of the cross aligned with the x & y axes at first), draw how that cross would move. 4) Find the circulation about a circle of radius r centered on x=y=0 for the flow in 1) 5) Find the streamfunction for the flow in 1) 6) Is there a velocity potential for the flow in 1)? Explain your answer. 7) A generalization of the flow in prob 1 is u= a x + b y ; v=c x + d y Where a,b,c,d are constants. What values of a,b,c,d would allow there to be a velocity potential? What values of a,b,c,d would allow there to be a stream function? What values of a,b,c,d would allow both a streamfunction and a velocity potential?...
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