As shown in the following figure, vortices are shed from the rear of a bluff cylinder placed across a flow. The vortices alternately leave the top and bottom of the cylinder, causing an alternating force normal to the freestream velocity. The vortex shedding frequency, f, depends on the fluid density p, width of the cylinder d, freestream velocity V, and fluid viscosity u. (a) Use Buckingham Pi Theorem to develop a functional relationship for f. Use M, L, t as the primary dimensional. Use p, V, and d as the repeating parameters. (b) Vortex shedding occurs in standard air on two cylinders with a diameter ratio of 2. Determine the velocity ratio for dynamic similarity, and the ratio of vortex shedding frequencies. V Vortices

As shown in the following figure, vortices are shed from the rear of a bluff cylinder placed across a flow. The vortices alternately leave the top and bottom of the cylinder, causing an alternating force normal to the freestream velocity. The vortex shedding frequency, f, depends on the fluid density p, width of the cylinder d, freestream velocity V, and fluid viscosity u. (a) Use Buckingham Pi Theorem to develop a functional relationship for f. Use M, L, t as the primary dimensional. Use p, V, and d as the repeating parameters. (b) Vortex shedding occurs in standard air on two cylinders with a diameter ratio of 2. Determine the velocity ratio for dynamic similarity, and the ratio of vortex shedding frequencies. V Vortices

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

As shown in the following figure, vortices are shed from the rear of a bluff cylinder placed across
a flow. The vortices alternately leave the top and bottom of the cylinder, causing an alternating
force normal to the freestream velocity. The vortex shedding frequency, f, depends on the fluid
density p, width of the cylinder d, freestream velocity V, and fluid viscosity u.
(a) Use Buckingham Pi Theorem to develop a functional relationship for f. Use M, L, t as the
primary dimensional. Use p, V, and d as the repeating parameters.
(b) Vortex shedding occurs in standard air on two cylinders with a diameter ratio of 2.
Determine the velocity ratio for dynamic similarity, and the ratio of vortex shedding
frequencies.
-Vortices
V

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