Interactive Self-Study Module: Dimensional Analysis, Pi Terms, and Dimensionless Numbers
Overview:
This module uses screencasts to explain the meaning and utility of dimensional analysis. Performing a dimensional analysis to form dimensionless groups allows you to more easily analyze experimental data, especially when fluid flows are too complicated to mathematically model. Your retention of material in this module will increase if you write down reasons for your answers to the ConcepTest and the questions in the screencasts and you try to solve the example problems before watching the solutions in the screencasts. We suggest using the learning resources in the following order:
- Attempt to answer the multiple choice ConcepTest and solve the example problem before watching the screencasts or working with the simulations.
- Watch the screencasts that describe dimensionless numbers and answer the questions within the screencasts.
- Look over the important equations.
- Try to solve the example problems before watching the solutions in the screencasts.
- Answer the ConcepTest.
- Look at the list of key points, but only after you try to list the key points yourself
Motivation:
- Because very few problems involving real fluids can be solved by analysis alone, most fluid mechanics problems rely on experimentally obtained data. Because experiments are usually time consuming and expensive, it is important to make experimental results as widely applicable as possible. The use of dimensionless groups helps achieve this goal.
- This module is primarily intended for a Fluid Mechanics course.
Before studying this module, you should:
- Be able to write down the units for various common parameters. For example, velocity has units of m/s (or ft/s), density has units of kg/m3 (or lbm/ft3), and dynamic viscosity has units of Pa-s, which is equal to kg/m-s (or lbm/ft-s).
- Be able to solve a simple set of linear algebraic equations.
After studying this module, you should 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.