Hydraulic Engineering - Vol 2 | 9. Dimensional Analysis and Hydraulic Similitude (Contd.,) by Abraham | Learn Smarter
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9. Dimensional Analysis and Hydraulic Similitude (Contd.,)

The chapter focuses on dimensional analysis and hydraulic similitude, emphasizing the steps involved in solving pipe flow problems. It covers the listing of variables, expressing them in terms of basic dimensions, determining the number of Pi terms, and selecting repeating variables. The chapter concludes with a discussion on using Buckingham Pi theorem to establish relationships among these variables.

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Sections

  • 1

    Hydraulic Engineering

    This section covers the principles of dimensional analysis and hydraulic similitude pertinent to pipe flow in hydraulic engineering.

    Learning Practice

  • 2

    Lecture-24

    This section discusses the principles of dimensional analysis and hydraulic similitude, emphasizing problem-solving steps related to pipe flow.

    Learning Practice

  • 2.1

    Dimensional Analysis And Hydraulic Similitude (Contd.,)

    This section delves into the process of dimensional analysis in hydraulic engineering, specifically focusing on pipe flow problems and the steps involved in applying Buckingham Pi theorem.

    Learning Practice

  • 3

    Steps In Dimensional Analysis

    This section outlines the systematic steps involved in performing dimensional analysis, particularly through the use of the Buckingham Pi theorem.

    Learning Practice

  • 3.1

    Step 1: List All The Variables

    The section outlines the first crucial step in dimensional analysis by detailing how to identify and list all relevant variables of a hydraulic engineering problem.

    Learning Practice

  • 3.2

    Step 2: Express Each Variable In Terms Of Basic Dimensions

    In this section, we focus on expressing various fluid dynamics variables in terms of their fundamental dimensions, a crucial step in the application of Buckingham's Pi theorem for dimensional analysis.

    Learning Practice

  • 3.3

    Step 3: Determine The Unique Number Of Pi Terms

    This section discusses the determination of unique pi terms through Buckingham's Pi theorem, emphasizing the importance of identifying variables, their dimensions, and the resulting dimensionless groups in dimensional analysis.

    Learning Practice

  • 3.4

    Step 4: Select A Number Of Repeating Variables

    This section highlights the importance of selecting repeating variables in dimensional analysis for hydraulic engineering, emphasizing the number of repeating variables necessary based on the reference dimensions involved in the problem.

    Learning Practice

  • 3.5

    Step 5: Form A Pi Term

    This section discusses the process of forming a Pi term in dimensional analysis, focusing on the selection and treatment of variables.

    Learning Practice

  • 3.6

    Step 6: Repeat Step 5 For Remaining Variables

    This section outlines the process of repeating step 5 in dimensional analysis to form additional dimensionless Pi terms when more non-repeating variables are present.

    Learning Practice

  • 3.7

    Step 7: Check All Resulting Pi Terms

    This section emphasizes the importance of verifying that all formed Pi terms in dimensional analysis are dimensionless.

    Learning Practice

  • 4

    General Procedure Of Dimensional Analysis

    The section outlines the steps involved in performing dimensional analysis using the Buckingham Pi theorem, emphasizing the systematic approach to identifying and analyzing variables.

    Learning Practice

  • 5

    Rules And Guidelines For Choosing Variables

    This section discusses the crucial steps and guidelines necessary for selecting appropriate variables in dimensional analysis, focusing on the Buckingham Pi theorem.

    Learning Practice

  • 5.1

    Categories Of Variables

    This section discusses the categories of variables relevant to dimensional analysis in hydraulic engineering.

    Learning Practice

  • 5.2

    Choosing Independent Variables

    This section discusses the methodologies for selecting independent variables in dimensional analysis, emphasizing the importance of the Buckingham Pi theorem.

    Learning Practice

  • 6

    Question On Buckingham Pi Theorem

    This section delves into the Buckingham Pi Theorem and its application in dimensional analysis, specifically in solving hydraulic engineering problems.

    Learning Practice

  • 6.1

    Variables To Be Considered

    This section introduces the process of dimensional analysis in hydraulic engineering, emphasizing the importance of identifying and using variables effectively.

    Learning Practice

  • 6.2

    Finding Pi Terms

    This section focuses on the steps involved in determining Pi terms through dimensional analysis in pipe flow problems.

    Learning Practice

  • 6.3

    Resulting Pi Terms

    This section discusses the process of dimensional analysis using the Buckingham Pi theorem, specifically focusing on determining the resulting Pi terms for fluid flow problems.

    Learning Practice

References

24.pdf

Class Notes

Memorization

What we have learnt

  • Dimensional analysis is cru...
  • Dimensional variables must ...
  • The relationship between pr...

Final Test

Revision Tests