Module 10: Dimensional Analysis, Similitude and Modeling

This module covers how to minimize the amount of effort and time on experimentation to obtain fluid flow characteristics. To accomplish this, we go over the Buckingham Pi theorem, show how to obtain Pi terms by using established steps. We then discuss similarity requirements and prediction equations to relate fluid flow characteristics between a prototype and scaled-down (or sometimes up) model.

Student Learning Outcomes: After completing this module, you should be able to:

* Apply the Buckingham Pi theorem

* Develop a set of dimensionless groups, called Pi terms, for a given fluid flow phenomenon

* Recognize and take advantage of common dimensionless groups in fluid mechanics

* Apply the concept of modeling and similitude to relate fluid flow between prototype and a model

Lecture Videos:

Link to Module 10 Playlist Link to Module 10 Lecture Videos

Links to Individual Module 10 Videos:

Lecture 1 - Dimensional Analysis and General Dimensions: In this segment, we review the mathematical branch of dimensional analysis, its application to fluid mechanics, and discuss general dimensions, and dimensionally homogenous nature of mathematical equations.

Lecture 2 - Buckingham Pi Theorem and Steps for obtaining Pi terms: In this segment, we go over the Buckingham Pi theorem, which relates the number of physical parameters to non-dimensional Pi terms. We also layout specific steps to be followed for obtaining the non-dimensional Pi terms

Lecture 3 - Common Dimensionless Numbers in Fluid Mechanics: In this segment, we review dimensionless numbers commonly used in fluid mechanics. These numbers are essential in that you can use them as your Pi terms if the parameters are relevant.

Lecture 4 - Obtaining Pi Terms - An Example: In this segment, we show detailed steps of obtaining Pi terms for a relatively simple physical fluid mechanics/aerodynamics case

Lecture 5 - Pi Terms for a Turbulent Flow in a Pipe - An Example: In this segment, we obtain Pi terms for turbulent flow in a pipe and illustrate every step clearly

Lecture 6 - Similitude and Modeling: In this segment, we go over the geometric, kinematic, and dynamic similarity requirements and establish the modeling requirements for a scaled-down (or up) model of the prototype

Lecture 7 - Similitude and Modeling - An Example: In this segment, we go apply the similitude and modeling criteria to a wind and water test of a vehicle

Lecture 8 - Comprehensive Example of Similitude and Modeling: In this segment, we go over a comprehensive example of obtaining prediction equations, similarity requirements, and a scale of interest

Lecture 9 - Module 10 Recap

Congratulations, you just finished module 10! Please proceed to module 11

College Fluid Mechanics

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