CEE
LSA_6_dimensional_analysis.pdf

# R t ρ mass length 15 1 1 f e t r ρ π π constant 5

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R t ρ mass length time 1/5 2/5 1/5 1 1 ( ) 0 f E t R ρ Π = Π = = constant 5 2 (constant) E R t ρ = G.I. Taylor, 1886-1975

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Dimensional Analysis Example 3 (Stochastic Transportation Problem) Area A , δ = # of supply points per unit area (point density). The amount of supply at each point follows normal distribution N (0, σ 2 ) (>0 supply; <0 demand) Question: what’s the expected minimum item-distance, D , to clear the market? Solution: variable item distance Two bases of Ω are (1,1,0,0) and (-1/2,0,-1/2,1) By Buckingham “pi” theorem, or Remark: This is insightful for simulations, to obtain the function form of g (.). 1 0 2 2 1 2 0 0 ~ 2 D A σ δ 2 2 ) ( Rank 4 = = = k p M ) 0 , 0 ( ) , , , ( 4 3 2 1 = M a a a a ) /( , 2 1 A D A σ δ = Π = Π ) /( σ A D A δ 0 )) /( , ( = A D A f σ δ ) ( ) /( A g A D δ σ = ) ( A g A D δ σ = Logistics Systems Analysis
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• Fall '16
• Physical Principles of Engineering Analysis

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