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 Dimensions? Boundary and initial conditions? Behavior? Dependence on parameters? Special cases? Assumptions? h

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

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

Exercise: contaminant plume L = plume length V = groundwater velocity T1/2 = half-life of contaminant C0 = source concentration Cs = 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 = number of fruit flies at time t N0 = initial number r = reproduction rate K = constant

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.