Critical thinking

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?
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Example falling barometer
t
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
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Exercise beam deflection
y deflection x position on beam L beam
length P load (force) E Youngs modulus I
moment of inertia
Material E (109 N/m2)
Wood 13
Aluminum 70
Steel 200
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Exercise contaminant plume
L plume length V groundwater
velocity T1/2 half-life of contaminant C0
source concentration Cs max. allowable
concentration
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Exercise rating curve
Which curve best represents river discharge vs.
river stage?
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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.