Download - The Nature of Engineering Knowledge
Consider an architect’s model of a building; the building and the model are geometrically similar, but different sizes
100 m 1 m
Measurements on the model can be translated to measurements on the building via scale factors:
100 m 1 m
Quantity Scale Factor
Length of water pipe
Floor Area
Enclosed Volume
Weight
Ratio of Study space toTravel space
The Froude Number
Fr = V2/Lg
If the Froude number is the same for a ship and its model, both will behave the same way (e.g., capsize and sink)
Reynolds Number
At a critical value of Reynolds number,flow changes from laminar to turbulent
Re = Inertial ForcesViscous Forces
= ρvlμ
The Mach Number
M = v/c
If the Mach number is the same foran aeroplane and its model, bothwill be in the same sonic regime(e.g., both supersonic)
Weber Number
Indicates the ratio between inertialforces and surface-tension forces(this is why you can’t design bugs with a towing tank)
We = ρV2lσ
Usefulness of the Non-Dimensional Numbers
Fluid friction in a pipe is affected byits diameter, and by the fluid’s speed and viscosity.
Using Reynolds number, we caninvestigate all these in one seriesof experiments.
Laplace’s Equation
…applies to heat conduction and electrostatics.
So an electrostatic problem can model a thermal problem.
Δ2 Φ = 0
d2φdx2
d2φdy2
d2φdz2
+ + = 0
Fuzzy Control
Fuzzy logic employs models of systems that
are deliberately imprecise: for example, a
car may be modelled as having three possible speeds, `too slow’, `OK’, `too fast’.
This can yield simple, robust control
algorithms.
Qualitative Physics
In making predictions about the world, we
employ mental models. These are neither
exact nor numerical, but they work.
Qualitative physics attempts to get computers
to do the same thing.