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summary1 - Galileo’s Problem ρ g Π 2 h 3 ≤ Π σ h 2...

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Lecture 1 - summary Introduction to the engineering science approach Galileo problem: Could we simply ‘upscale’ an animal, human.. several times and could it still exist? Dimensional analysis shows: If same material is used, a monster can not exist Remedy: Change material (density) as the height is increased in order to create physical similarity h 1 h 2 Express physical situation as function of nondimensional parameters (critical: find correct dependence on variables)
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Unformatted text preview: Galileo’s Problem: ρ g Π 2 h 3 ≤ Π σ h 2 F lim Π ( Π 1 , Π 2 ) Robustness: γ = = ≥ 1 mg Π 2 Π 1 Thus, for a monster to exist need material with higher strength OR material with lower density. Definition of Galileo number : Two events are similar if the invariants are the same, here the Galileo Number: 1 ( ) h ( i ) ( i ) h 1 ( 1 ) ( 2 ) ( ) 2 g Π 1 = Π 1 = ( ) λ = h 2 = ( ) 2 ( ) i 1...
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