Lecture 1 - summary
ƒ Introduction to the engineering
science approach
ƒ Galileo problem: Could we simply
‘upscale’ an animal, human..
several times and could it still exist?
ƒ Dimensional analysis shows: If
same material is used, a monster
can not exist
ƒ Remedy: Change material (density)
as the height is increased in order
to create physical similarity
Express physical situation as function of
nondimensional parameters (critical: find
correct dependence on variables)
Galileo’s Problem:
ρgΠ 2h 3 ≤ Π 0σ 0h 2
Robustness:
γ =
Flim Π 0 (Π1 , Π 2 )
=
≥1
mg
Π 2 Π1
Thus, for a monster to exist need material with
higher strength OR material with lower density.
h1
Definition of Galileo number:
h2
Two events are similar if the invariants
are the same, here the Galileo Number:
h1 σ 0(1) ρ (2 )
h (i ) ρ ( i ) g
(1)
(2 )
λ = = (2 ) (1)
Π1 = Π1 =
σ 0(i)
h2 σ 0 ρ