1. Critical thinking
(for engineering)

2. 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.

3. Evaluating a result
What are some tests for a result or formula?

4. Example: falling barometer
Dimensions?
Boundary and initial conditions?
Behavior? Dependence on parameters?
Special cases?
Assumptions? h

5. Exercise: drag on a body
FD = drag force [F]
CD = drag coefficient [-]
r = fluid density [M/L3]
U = fluid velocity [L/T]
A = cross-sectional area

6. Exercise: beam deflection
y = deflection
x = position on beam
L = beam length
P = load (force)
E = Young’s modulus
I = moment of inertia
Material
E (109 N/m2)
Wood 13
Aluminum 70
Steel
200

7. Exercise: contaminant plume
L = plume length
V = groundwater velocity
T1/2 = half-life of contaminant
C0 = source concentration
Cs = max. allowable concentration

8. Exercise: rating curve
Which curve best represents river discharge vs. river stage?

9. Exercise: fruit flies in a jar
Which is a better model?
N = number of fruit flies at time t
N0 = initial number
r = reproduction rate
K = constant

10. Dimensional analysis
Often one can predict the form of an answer simply by
considering the dimensions of the parameters.
Approach:
List all parameters (including unknown) and their dimensions.
Determine the number N of parameters and number M of
dimensions.
Determine the number of dimensionless groups (N-M).
Pick any M variables that do not form a dimensionless group
and use them to make the other parameters dimensionless.