1 = f (2)  CD = f (Re)
For dynamic similarity, Re = 1 
= 1 since Tm = Tp = 15oC and = f (T) 
= 10 V = 1
7.34 The fluid dynamic characteristics of a golf ball are to be tested using a model in a wind tunnel. Dependent parameters are the drag force, FD, and lift force, FL, on the ball. The independent parameters should include angular speed, , and dimple depth, d. Determine suitable dimensionless parameters and express the functional dependence among them. A golf pro can hit a ball at V = 240 ft/sec and = 9000 rpm. To model these conditions in a wind tunnel with a maximum speed of 80 ft/sec, what diameter model should be used? How fast must the model rotate? (The diameter of a U.S. golf ball is 1.68 in.)
Choose MLT as fundamental units
FD d D V
MLT-2 T-1 L L LT-1 ML-3 ML-1T-1
Dimensional matrix
FD , , d produce a 3 x 3 matrix with a non-zero determinant Rank = 3
|
L
|
T
|
M
|
FD
|
1
|
-2
|
1
|
|
0
|
-1
|
0
|
d
|
1
|
0
|
0
|
D
|
1
|
0
|
0
|
V
|
1
|
-1
|
0
|
|
-3
|
0
|
1
|
|
-1
|
-1
|
1
|
3 repeaters are needed
choose , D , V as repeaters
Check on independence of the dimensions of the repeaters
L T M
-3 0 1
D 1 0 0 0 dimensions of , V , D are independent
V 1 -1 0
Dimensionless groups:
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