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Fluids-HW4

Course: WSE ME 530.328, Spring 2009
School: Johns Hopkins
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- 530.328 Fluid Mechanics II Spring 2009 Homework #4 Potential Flow - Due date: Thursday April 2 1. Determine whether the Bernoulli equation can be applied between different radii for the vortex flow fields (a) (b) r. 2. A plane source, of strength q, is located near a 90 corner. The source is equidistant h from each of the two infinite corner planes. Find the velocity potential and stream function of this flow. And then find the pressure distribution along one of the corner planes by assuming at infinity. 3. A flow field can be represented by stream function velocity field. Is this flow field irrotational? If it is, find the potential Find function. . the 4. The velocity field for a 2-D flow is . (in which A=3 , B=1 , t is in seconds and the coordinates are in meters. Is the flow steady or unsteady? Is it incompressible flow? Find the velocity potential if the flow irrotational. 5. A tornado can be modeled by combing a sink, of strength q=3000 , and a free vortex, of strength K=6000 . Obtain the stream function and velocity potential for this flow field. Estimate the radius beyond which the flow can be treated as incompressible. (Criterion: the distance beyond which the velocity is less than 30% of sound speed). Then find the gage pressure at that radius.

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