Fluid Mechanics - Vol 2 | 13. Dimensional Homogeneity by Abraham | Learn Smarter
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13. Dimensional Homogeneity

This chapter on dimensional analysis in fluid mechanics introduces the principles of dimensionless groups, dimensional homogeneity, and Buckingham's Pi theorem. It highlights the significance of these concepts in designing fluid experiments and conducting similarity analysis to reduce the number of required experiments. Key fluid properties and their dimensional relationships are also discussed as a central part of fluid behavior understanding.

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Sections

  • 13.

    Fluid Mechanics

    This section introduces the concepts of fluid mechanics, focusing on dimensional analysis, dimensional homogeneity, and Buckingham's pi theorem.

    Learning Practice

  • 13.1.1

    Dimensional Homogeneity

    This section introduces dimensional homogeneity in fluid mechanics, emphasizing the importance of dimensional analysis, Buckingham’s pi theorem, and dimensionless groups in experimental design.

    Learning Practice

  • 13.1.2

    Dimensionless Groups

    This section introduces dimensionless groups in fluid mechanics, focusing on dimensional homogeneity and the application of Buckingham's pi theorem.

    Learning Practice

  • 13.1.3

    Basic Dimensions

    This section covers the fundamental dimensions in fluid mechanics, focusing on dimensional homogeneity, dimensionless groups, and properties of fluids.

    Learning Practice

  • 13.1.4

    Fluid Properties

    This section discusses the fundamental fluid properties and their dimensional analysis, emphasizing the importance of dimensional homogeneity in fluid mechanics.

    Learning Practice

  • 13.1.5

    Pressure And Viscosity

    This section covers fundamental concepts of fluid mechanics, specifically focusing on the principles of pressure and viscosity as they relate to fluid behavior and experiments.

    Learning Practice

  • 13.1.6

    Principle Of Homogeneity

    The Principle of Homogeneity asserts that for an equation to be dimensionally correct, its dimensions must be the same on both sides.

    Learning Practice

  • 13.1.7

    Buckingham's Pi Theorem

    Buckingham's Pi Theorem is a fundamental principle of dimensional analysis that helps create dimensionless parameters used in fluid mechanics experiments.

    Learning Practice

  • 13.2

    Experimental Design And Dimensional Analysis

    This section covers the principles and application of dimensional analysis in fluid mechanics, emphasizing experimental design and the significance of dimensionless groups.

    Learning Practice

  • 13.2.1

    Designing Experiments

    This section discusses how to design experiments in fluid mechanics by employing principles like dimensional analysis and Buckingham’s Pi theorem.

    Learning Practice

  • 13.2.2

    Number Of Experiments

    This section covers the design principles involved in conducting fluid mechanics experiments, emphasizing the importance of dimensional homogeneity and Buckingham's pi theorem.

    Learning Practice

  • 13.3

    Application Of Fluid Mechanics Principles

    This section discusses the application of fluid mechanics principles, emphasizing dimensional analysis, dimensional homogeneity, and Buckingham's pi theorem, essential for designing fluid mechanics experiments.

    Learning Practice

  • 13.3.1

    Drag Force Analysis

    This section explores drag force analysis in fluid mechanics, focusing on dimensional homogeneity and the principles underlying dimensional analysis.

    Learning Practice

  • 13.3.2

    Non-Dimensional Analysis

    This section discusses the principles of non-dimensional analysis in fluid mechanics, focusing on dimensional homogeneity and Buckingham's Pi Theorem.

    Learning Practice

References

ch19 part a.pdf

Class Notes

Memorization

What we have learnt

  • Basic dimensions in fluid m...
  • Dimensional homogeneity ind...
  • Using dimensional analysis ...

Final Test

Revision Tests