MECE251 Fluids Lesson 10 part I Dimensional Analysis

MECE-251 Fluids, Lesson 10 (part I): Dimensional Analysis 1 - Read Text Sections 2 - Solve Chapter Problems 3 & 4 – Lectures, Example, and Review Problems 5 - Solve Case Study 6 - Complete On-line Lesson Quiz R·I·T MECE-251 1

Main Topics • Nondimensionalizing the Basic Differential Equations • Nature of Dimensional Analysis • Buckingham Pi Theorem • Significant Dimensionless Groups in Fluid Mechanics • Flow Similarity and Model Studies R·I·T MECE-251 2

Main Topics • Nondimensionalizing the Basic Differential Equations • Nature of Dimensional Analysis • Buckingham Pi Theorem • Significant Dimensionless Groups in Fluid Mechanics • Flow Similarity and Model Studies R·I·T MECE-251 3

Nature of Dimensional Analysis Example: Drag on a Sphere R·I·T MECE-251 4

Nature of Dimensional Analysis Example: Drag on a Sphere ü Drag depends on FOUR parameters: sphere size (D); speed (V); fluid density (r); fluid viscosity (m) ü Difficult to know how to set up experiments to determine dependencies ü Difficult to know how to present results (four graphs? ) R·I·T MECE-251 5

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Nature of Dimensional Analysis Example: Drag on a Sphere Cd= ü Only one dependent and one independent variable ü Easy to set up experiments to determine dependency ü Easy to present results (one graph) R·I·T MECE-251 7

Drag coefficient on a smooth sphere R·I·T MECE-251 8

http: //authors. library. caltech. edu/25017/4/chap 5. htm http: //ars. els-cdn. com/content/image/1 -s 2. 0 -S 0928098709001249 -gr 18. jpg R·I·T MECE-251 9

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= R·I·T MECE-251 11

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http: //en. wikipedia. org/wiki/Dimensionless_quantity Reynolds Number Prandlt Number Nusselt Number Grashof Number Rayleigh Number R·I·T MECE-251 13

Next Steps L 10 Task 3 B: Please review the example problem on line. L 10 Task 3 C: we aren't doing this week. L 10 Task 4 B: Please review the example problems on line. L 10 Task 4 C: we aren't doing this week. L 10 Task 5: Work on your cumulative case study. L 10 Task 6: This will be mid-week 11 and partially based on these lectures and partially based on one another's case studies. Reference: Schaum’s Outline of Thermodynamics for Engineers, Second Edition, M. C. Potter and C. W. Somerton, Mc. Graw Hill Several Images are from Fundamentals of Fluid Mechanics, 5/E by Bruce Munson, Donald Young, and Theodore Okiishi R·I·T MECE-251 14