7.31 The drag of an airfoil at zero angle of attack is a function of density, viscosity, and velocity, in addition to a length parameter. A 1/10th scale model of an airfoil was tested in a wind tunnel at a Reynolds number of 5.5 x 106 , based on chord length. Test conditions in the wind tunnel air stream were 15 C and 10 atm absolute pressure. The prototype airfoil has a chord length of 2 m, and it is to be flown in air at standard conditions. Determine the speed at which the wind tunnel model was tested, and the corresponding prototype speed.
Rem = 5.5 x 106
Tm = 15o C = Tp T = 1
pm = 10 atm, pp = 1 atm p = 10
 = 2 m ; L = 1/10
Choose MLT as fundamental units
FD V 
MLT-2 ML-3 ML-1T-1 LT-1 L
Dimensional matrix
FD , , produce a 3 x 3 matrix with a non-zero determinant Rank = 3
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L
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T
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M
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FD
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1
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-2
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1
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-3
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0
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1
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-1
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-1
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1
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V
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1
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-1
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0
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1
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0
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0
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3 repeaters are needed
choose , V , as repeaters
Check on independence of the dimensions of the repeaters
L T M
-3 0 1
V 1 -1 0 0 dimensions of , V , are independent
1 0 0
Dimensionless groups:
 1 + 1 = 0 1 = -1 ;
-1 - 2 = 0 1 = -2; -3(-1) + (-2) + 1 + 1 = 0 1 = -2
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