## Tuesday, November 15, 2011

### MrsDrPoe: Dimensional Analysis, Part I

Happy Thesis Tuesday on the blog!  Today we'll look at a brief introduction to the interesting topic of dimensional analysis.

As with any type of experimentation, fluid flow experiments should be performed in a meaningful and systematic manner.  If we consider, for instance, the pressure change across a section of pipe in Poiselle flow, we can see that this change in pressure is affected by fluid properties (density, rho; and viscosity, mu), pipe diameter, and fluid velocity.  By running countless numbers of measurement experiments, each time varying a single parameter, we could determine how the pressure change is affected by each of these items; however, these relationships would only be valid for this pipe with this fluid and this experimental setup.

WHEW!

In order to improve the quality, applicability, and repeatability of our experimental results, we use dimensionless products or dimensionless groups.  These terms are combinations of variables necessary for a problem and often employ basic dimensions (mass, M; length, L; and time, T) or units (pounds, feet, and seconds, etc.).

The method we use to find these dimensionless terms is called the Buckingham Pi Theorem - "If an equation involving k variables is dimensionally homogeneous, it can be reduced to a relationship among k-r independent dimensionless products, where r is the minimum number of reference dimensions required to describe the variables."

Next week, we'll look at an application of this theorem, which is much simpler than it may sound!