f21_ps15_fall03

f21_ps15_fall03 - Fall 2003 Unified Engineering Fluids...

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Unformatted text preview: Fall 2003 Unified Engineering Fluids Problem F21 F21. As shown in class, the nonlifting irrotational flow past a circular cylinder can be represented by superimposing the uniform freestream flow and a doublet. An alternative representation is proposed using a source sheet placed on the cylinder surface as shown. The proposed sheet strength distribution about the cylinder is �(� ) = −2V� cos � . There is no vortex sheet, so on the surface, � = 0. �(�) freestream+doublet model (known) actual � freestream + source sheet model (proposed) You are to determine whether the new model is correct. a) Determine the velocity at p oint A from the known exterior surface velocities for the cylinder. V� (� ) = −2V� sin � , Vr = 0 Using the sheet jump relations, �Vn = � , �Vs = � determine the interior velocity at p oint B. b) Again using the known exterior V� (� ), Vr result at point C, use the sheet jump condition to determine the velocity at p oint D. c) Compare velocities at B and D. What appears to be the fictitious velocity inside the cylinder? d) Is the source sheet jump �Vn = � consistent with the exterior and interior normal flows everywhere on the cylinder surface? Is the proposed source-sheet model correct? C D A B ? ...
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