Lecture7_2 - AME 331 Introduction to Fluid Mechanics...

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10/24/2010 1 AME 331 Introduction to Fluid Mechanics Chapter 7: Dimensional Analysis and Similitude Prof. Jesse Little University of Arizona 10/25/10 1 Lecture Preview and Assignments Today 7.3-7.4 Read 7.5-7.6 for next time Homework 7 due today by 2pm Homework 8 due Friday by 2pm 2
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10/24/2010 2 Buckingham Pi (7-3) We found the drag on a smooth sphere can be written as some function, but theory or experiment was needed to tell us what that function is It is more formal although not obviously so to write Where g is some function obviously different from f . In general we can write this function as: 3 Buckingham Pi Theorem (7-3) The Buckingham Pi Theorem Dimensionally homogenous equation ( g from earlier) involving n parameters can be transformed to a relationship among n-m independent dimensionless products m is usually the min number of independent dimensions, r , (i.e. mass, length, time) necessary to define the dimensions of the expression ( g from earlier). Comment on this later These products are commonly called Pi terms and represented by the symbol 4
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