Ch07_2_MS - MAE130B Ch 07(2 Dimensional Analysis...

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MAE130B – Ch 07 (2) Dimensional Analysis Applications Changzheng Huang
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Ch 07 (2) Changzheng Huang 2 Dimensional Analysis Applications ( ) () 12 3 3 ,, , , k kr uf u u u φ = Π= Π Π Π " " Original equation, What it can do: reduce original k variables into k-r dimensionless parameters. What it can not do: the specific functional format φ . Applications: (1) experimental data correlation. (2) modeling and similitude. Dimensional analysis,
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Ch 07 (2) Changzheng Huang 3 1. Data Correlation ( ) () 12 3 3 ,, , , k kr uf u u u φ = Π= Π Π Π " " Original equation, Dimensional analysis, 1.1 There is only one pi term. 1.2 There are two pi terms. 1 C Π == D Π When there are only one or two pi terms, it is easy to figure out the functional relationship by correlation of experimental data.
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Ch 07 (2) Changzheng Huang 4 1.2 There are two pi terms. () 12 3 ,, , k uf u u u φ = Π= Π " 1 Π 2 Π valid l p p p l ∆= D l V , ρµ ( ) ,,, l pf DV An example Find a general relationship, V (ft/s) p 1 -p 2 (lb/ft 2 ) 1.17 6.26 1.95 15.6 2.91 30.9 5.84 106 11.13 329 16.92 681 23.34 1200 28.73 1730 D=0.496 in L=5 ft ρ =1.94 slugs/ft 3 µ =2.34e-5 lb*s/ft 2
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Ch 07 (2) Changzheng Huang 5 1.2 There are two pi terms.
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This note was uploaded on 03/10/2009 for the course MAE 130B taught by Professor Huang during the Spring '09 term at UC Irvine.

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Ch07_2_MS - MAE130B Ch 07(2 Dimensional Analysis...

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