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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
(known) actual � freestream + source sheet
(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
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
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?
A B ? ...
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- Fall '05