CIEG 305 TAKE HOME EXERCISE ON DIMENSIONAL ANALYSIS

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CIEG 305 TAKE HOME EXERCISE ON DIMENSIONAL
ANALYSIS
At certain wind speeds cylindrical objects
(flagpoles, wires etc.) may be subjected to
severe vibration (in addition to drag) from
vortex shedding from sided to side. For a small
scale model, what dimensionless criteria should
be considered? In other words, find the
dimensionless groups that form an unknown
function related to the nondimensional shedding
frequency. For movies on vortex shedding go to
http//illustrations.marin.ntnu.no/hydrodynamics/v
iscous/shedding/ Or check out the Tacoma Narrows
Bridge movie although it is largely believed that
vortex shedding played a minimal role
http//www.enm.bris.ac.uk/research/nonlinear/tacom
a/tacnarr.mpg
Variables Structural Radius, r (L) Height, h
(L) Stiffness, S (MT-2) contains modulus of
elasticity including effect of material
density and atomic lattice composition
Fluid Velocity, V (LT-1) Density, ?
(ML-3) Viscosity, µ (ML-1T-1) Drag, F
(MLT-2) Shedding Frequency, ? (T-1)