Critical thinking
(for engineering)
Exercise
By timing the fall of a barometer, a friend measures the
height of a 20-story building to be 71 feet.
Is this estimate reasonable?
If so, explain why.
If not, give a cogent reason and suggest possible mistakes.
Evaluating a result
What are some tests for a result or formula?
Example: falling barometer
h  gt
1
2
2
t
Dimensions?
Boundary and initial conditions?
Behavior? Dependence on parameters?
Special cases?
Assumptions?
h
Exercise: drag on a body
FD  C D U A
1
2
FD
CD

U
A
2
= drag force [F]
= drag coefficient [-]
= fluid density [M/L3]
= fluid velocity [L/T]
= cross-sectional area
Exercise: beam deflection
y
x
L
P
E
I
= deflection
= position on beam
= beam length
= load (force)
= Young’s modulus
= moment of inertia
Material
E (109 N/m2)
Wood
13
Aluminum
70
Steel
200
Exercise: contaminant plume
VT1/ 2  C0
L
ln 
ln 2  CS
L
V
T1/2
C0
Cs



= plume length
= groundwater velocity
= half-life of contaminant
= source concentration
= max. allowable concentration
Exercise: rating curve
Which curve best represents
river discharge vs. river stage?
Exercise: fruit flies in a jar
Which is a better model?
N  N 0 exp( rt )
N0 K
N
N 0  ( K  N 0 ) exp( rt )
N
N0
r
K
= number of fruit flies at time t
= initial number
= reproduction rate
= constant
Dimensional analysis
Often one can predict the form of an answer simply by
considering the dimensions of the parameters.
Approach:
1. List all parameters (including unknown) and their dimensions.
2. Determine the number N of parameters and number M of
dimensions.
3. Determine the number of dimensionless groups (N-M).
4. Pick any M variables that do not form a dimensionless group
and use them to make the other parameters dimensionless.