Interactive Self-Study Module: Derivation of a Pressure Field and Fluid at Rest

Overview:

This module uses screencasts to explain how to derive a pressure field using a force balance on a differential element and simplifications for a fluid at rest. Screencasts are used to show how to perform the derivation and simplifications. An example problem allows the users to test themselves. Your retention of material in this module will increase if you write down reasons for your answers to ConcepTests, questions in screencasts, and questions to answer before using interactive simulations, and you try to solve the example problems before watching the screencast solutions. We suggest using the learning resources in the following order:

  1. Attempt to answer the multiple-choice ConcepTest and solve the example problem before watching the screencasts.
  2. Watch the screencasts that describe how to use a force balance on a differential element and answer the question in each screencast.
  3. Review important equations for this topic.
  4. Try to solve the example problem before watching the solution in the screencast.
  5. Answer the ConcepTests.
  6. Look at the list of key points, but only after you try to list the key points yourself. 
Motivation:
  • Understanding a differential derivation of a pressure field and fluid at rest is a key to a strong foundation for fluid statics and dynamics.
  • This module is intended for Fluid dynamics courses.
Before studying this module, you should be able to:
  • use a Taylor series expansion.
  • apply Newton’s Second Law.
After studying this module, you should be able to:
  • Use a differential element to determine the equation of motion for fluid statics and dynamics.
  • Apply Newton’s Second Law to a differential system.
  • Derive the equation of motion for a fluid.