Lecture_14_notes - Chemical Engineering 374 Fluid Mechanics...

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1 1 Chemical Engineering 374 Fluid Mechanics Fall 2011 Dimensional Analysis Outline Introduction and Motivation – Theory • Limitations – Experiments • Cost, practicality, efficiency • Qualitative understanding Dimensionless groups – Eliminate the units – Methods Governing Equations Force Ratios Π Method – Examples Similarity / Scale models 2
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2 Pipe Flow Consider flow in a pipe – (We’ll do lots of this!) So far, mostly frictionless flow – (Friction next week) – But we’ve discussed friction on a plate for Newton’s law of viscosity: τ * du/dr. – Friction force is balanced by pressure forces: Pressure drop Δ p balanced by friction Most flows are turbulent (consider averages) Question/Goal: How to characterize pipe flow? 3 P 1 * A P 2 * A τ * π DL The Challenge Turbulent flow is complex – Random, Chaotic How to measure and relate the important properties. .. – List them: V, Δ P, L, D, μ, ρ Or V, Δ P/L, D, μ, ρ 4 P 1 * A P 2 * A τ * π DL
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3 Solutions Solve Governing Equations? (Yes, but its expensive!) Experiments? Design Parameters? Span the Space. How many experiments to do? Measure Δ P/L, for a range of D, v, μ, ρ ? If 10 points in each of D, v, μ, ρ then have 10,000 experiments to do Lets be smart! (be efficient) Dimensional analysis 5 Dimensional Analysis Dimensional analysis is a powerful tool Insight into equations Relationships among parameters Reduce the number of parameters in a system
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Lecture_14_notes - Chemical Engineering 374 Fluid Mechanics...

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