Concept: Dimensional Analysis and Dynamic Scaling Context: Universal Scaling of a Pendulum Defining Question: Why do you need not fear gigantic ants or gargantuan mosquitos? Read Chapter 5 pp. 431-436 Dynamics of Walking and Running Lecture 34 will follow the textbook. EngrD 2190 – Lecture 33
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Concept: Dimensional Analysis and Dynamic Scaling
Context: Universal Scaling of a Pendulum
Defining Question: Why do you need not fear gigantic ants or gargantuan mosquitos?
Read Chapter 5 pp. 431-436Dynamics of Walking and RunningLecture 34 will follow the textbook.
EngrD 2190 – Lecture 33
Include yourself
Due Friday in lecture.
Calculation Sessions this week - Tours of Unit Operations LabNo exposed toes, exposed arms or exposed legs.Each team must submit an analysis of the distillation column,
to be graded as homework.
Prelim 3: Tuesday 11/23, 7:30-9:30 p.m., 245 Olin Hall.Graphical Modeling for Mass Balances - Part 2:
translating thermodynamic maps: T-(x,y) to x-y, for example.operating lines for multistage absorbers and strippersoperating lines for multistage distillationphase maps for pure substances - separating condensible vapors
from non-condensible vapors.design using single-stage and countercurrent multi-stage units -
may include use of T-(x,y), P-(x,y), and H-(x,y) diagrams.Open book, open notes, open exercise solutions.Bring a calculator and a ruler. Graphing calculators are allowed.
Laptops allowed as for Prelims 1 and 2.
Dimensional Analysisand Dynamic Scaling
A ‘Water Bear’ (aka a Tardigrade) - Nature’s Toughest Animal
Dynamic Scaling Example 1 - Motion Through a Fluid
Swimmer stops swimming - swimmer glides for 1-3 body lengths
Dynamic Scaling Example 1 - Motion Through a Fluid
Propellers stop - ship glides for ~100 ship lengths
Dynamic Scaling Example 1 - Motion Through a Fluid
Propulsion stops - paramecium glides for ~0 body lengths
Dynamic Scaling Example 1 - Motion Through a Fluid
Key ratio for motion through fluids:forces frictional
forces inertial
Ratio is negligible for microfluidics
Dynamic Scaling Example 1 - Motion Through a Fluid
Key ratio for motion through fluids:forces frictional
forces inertial
Ratio is large for commercial chemical processes
Reactor cascade connected by 20” pipes.
Flow is 40 tons/minute
Partial oxidation of cyclohexane to cyclohexanol.First step in process to synthesize Nylon.
Flixborough England 1974
Explosion killed 28 and caused $450,000,000 in damages.