CEE
LSA_6_dimensional_analysis.pdf

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

Info icon This preview shows pages 2–3. Sign up to view the full content.

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
Image of page 2

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

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
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.
  • Fall '16
  • Physical Principles of Engineering Analysis

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern