Dimensional Analysis, Pi Terms, and Dimensionless Numbers: Summary

The answer to the ConcepTest is given below and will open in a separate window. 
Key points from this module:
  1. Forming dimensionless groups helps to make experimental data more widely applicable, but you often need years of experience to decide what experimental variables are important.
  2. You will often find experimental results tabulated by common dimensionless groups such as the Reynolds number.
  3. You can form k−r dimensionless groups (Π-terms), where k is the number of variables and r is the number of dimensions. Oftentimes r=3 because dimensions of mass, length, and time are typically found in the variables.
  4. Selection of repeating variables is arbitrary, provided the dimensions of each repeating variable are different. You can manipulate the dimensionless groups that you found to come up with dimensionless groups that you would have found if you had used other repeating variables.
From studying this module, you should now be able to:
  • Form dimensionless groups, which are also called Pi-terms.
  • Interpret the meaning of common dimensionless groups, such as the Reynold’s number.
Prepared by: Jeffrey Knutsen, Department of Mechanical Engineering, University of Colorado Boulder