Ae104a_2010_handout_1

Ae104a_2010_handout_1 - in terms of k independent...

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‘We must measure what is measurable and make measurable what cannot be measured.’ (Galileo, 1610) Figure 1: The pipe flow experiment of Osborne Reynolds (1883). He described the similarity of transition of pipe flow from laminar to turbulent (via the Reynolds number) Phil. Trans. Royal Soc., 174 (1883) . Figure 2: The Princeton/ONR Superpipe, used to determine scaling constants for pipe flow to less than 1% accuracy. (Courtesy of A. Smits.) 1
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Figure 3: The evolving role of computers, experiments and theory (A.E. Perry) . 2
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1.3.1 Dimensions and units We distinguish between dimensions (the physical variables) and units (means of quan- tifying dimensions). The classical dimensions are 1. length L 2. mass M 3. time T 4. 5. 6. 7. 8. 1.3.2 Dimensional analysis Buckingham’s Pi Theorem (Edgar Buckingham, 1914) For a problem involving n (non-redundant) physical variables that can be expressed
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Unformatted text preview: in terms of k independent fundamental physical quantities (dimensions), then the original expression is equivalent to an equation involving a set of p = n-k dimensionless variables constructed from the original variables. So if f ( v 1 ,v 2 ,...,v n ) = 0 where the v i are the n physical variables containing k independent physical dimensions then we can write F ( π 1 ,π 2 ,...π p ) = 0 where the π i are dimensionless parameters constructed from the v i by p = n-k equations of the form π i = v m 1 1 v m 2 2 ...v m n n where the m i are rational numbers. 3 1.4 The road map for a successful experimental investigation 1. Justification : 2. Background : 3. Planning : 4. Experimentation : 5. Observation : 6. Hypothesis : 7. Dissemination : 8. Future work : In this course, we will address items 3-4 in particular. 4...
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Ae104a_2010_handout_1 - in terms of k independent...

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