sln1 - 1 Problem 1(a The dimensions of the various...

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Unformatted text preview: 1 Problem 1 (a) The dimensions of the various quantities concerned are [ v ] = l t ;[ L ] = l ;[ ν ] = l 2 t . The dimensions of Reynolds number R is: [ R ] = vL ν = l t l t l 2 = 1 . So R is dimensionless. (b) The airflow over the wing: v = 500 km/hour ; L (length of the crossection of the wing) ∼ 2 . 5 m ; ν = 1 . 5 × 10- 5 m 2 /s. R = vL ν = 500 km/hour 3 . 6 2 . 5 m 1 . 5 × 10- 5 m 2 /s = 2 . 31 × 10 7 . So it is turbulent. (c) The airflow around foot: v ∼ 1 m/s ; L ∼ . 2 m ; ν = 1 . 5 × 10- 5 m 2 /s. R = vL ν = 1 m/s × . 2 m 1 . 5 × 10- 5 m 2 /s = 1 . 3 × 10 4 > 1000 . So it is turbulent. 1 (d) Flipping a coin: v = v ± ωr = 3 m/s ± 2 πfr f ∼ 10 Hz ; r ∼ . 01 m ; L ∼ . 02 m v = 3 m/s ± 2 π × 10 × . 01 m/s ≥ 2 . 4 m/s R = vL ν ≥ 2 . 4 m/s × . 02 m 1 . 5 × 10- 5 m 2 /s = 3200 > 1000 So there is turbulence. (e) The blood flow in arteries: v = 0 . 2 m/s ; L = 0 . 004 m ; ν = 3 . × 10- 6 m 2 /s....
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This note was uploaded on 08/25/2011 for the course PHYS 7268 taught by Professor Staff during the Spring '11 term at Georgia Tech.

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sln1 - 1 Problem 1(a The dimensions of the various...

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