7. Dimensional Analysis
The purpose is to reduce the number of
parameters or variables upon which a physical
phenomenon depends.
Variables like
U
,
,
, etc. will be rearranged as
to eliminate the fundamental units.
7.1. Geometrical similarity
In order for two fluid flows to be similar, the
shape of the bodies involved must be
geometrically similar; i.e. can be obtained from
one another by scaling all dimensions by the
same factor.
7.2. Dynamic similarity
Flows which can be obtained from one another
by scaling the dependent and independent
variables, provided certain non-dimensional
parameters are the same, are said to be
dynamically similar. The magnitude of different
forces, like pressure, viscosity, etc. acting at a
given non-dimensional location and time are in
the same ratio.
This is more difficult to achieve
*
What are these non-dimensional parameters?
*
How can they be found?
68

7.3. Buckingham Pi Theorem
Given the quantities that are related by a
physical law, the number of dimensionless

#### You've reached the end of your free preview.

Want to read all 6 pages?

- Fall '08
- ZOHAR
- Fluid Dynamics, Fluid Mechanics