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Unformatted text preview: ENU 4133 – Data Analysis February 11, 2011 Data Analysis Outline I Review of dimensional homogeneity and introduction to dimensionless modeling (Sections 5.1 and 5.2) I Types of variables and constants (Section 5.2) I Selecting appropriate scaling variables (Section 5.2) I The Buckingham Pi Theroem (Section 5.3) I Nondimensionalization of the basic equations & frequentlyused dimensionless groups (Section 5.4) I Reporting and evaluating results for correlations (not in text) I Demonstration of correlation optimization with spreadsheet (not in text) We will not cover the following textbook topics: the alternate method by Ipsen (starts on page 303), and all of Section 5.5. Example: Pressure Drop in a Pipe Depends on, in general, viscosity ( μ ), diameter ( D ), average flow velocity ( V ), density ( ρ ), pipe roughness ( ), pipe length ( L ), Dimensionless groups: L D (1) D (2) ρ VD μ = Re (3) K (4) f (5) Correlated as: Δ P 1 2 ρ V 2 = L D f Re , D + K (6) Dimensional Homogeneity etc. Dimensions: MLTΘ (mass, length, time, temperature). In some versions of British units, FLTΘ (force, length, time, temperature) is used instead. Both sides of an expression (and all terms on both sides) must have the same dimensions and the same units . It is often useful to have all terms be dimensionless and unitless to ensure generality of the model and applicability with multiple unit systems. White provides techniques to get to: Δ P 1 2 ρ V 2 = L D f Re , D + K (7) Figuring out K and f ( Re , D ) requires some trial and error. Types of Variables and Constants Dimensional variables: varied during test – for example the dependence of Δ P on V (or ˙ m ) – V and Δ P are the dimensional variables. Usually nondimensionalized themselves, but can also be used to nondimensionalize other dimensional variables. Dimensional constants: vary from test to test, but often held constant within a test . In the example, D , μ , and ρ would be dimensional constants for water. Dimensional constants could be made variables by picking different test conditions (fluids, etc.). Types of Variables and Constants (2)...
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 Spring '11
 Schubring
 Buckingham π theorem, dimensionless groups, dimensional variables, appropriate scaling variables

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