Biomedical Engineering Reference
In-Depth Information
From the time equation,
a52
2
From the length equation,
b5
3
ð2
1
Þ 2
1
1
2
52
2
Therefore, the first
Π
group is
F
v 2 d 2
Π 1 5
ρ
Pick v , d , and
ρ
as the sub-set of dimensional parameters and relate this to
μ
(they represent
M , L , and T ).
The second
Π
group will be set up as
Π 2 5μv a d b
c
ρ
L
t
a
ðÞ
L 3 c
M
Lt
b M
5M 0 L 0 t 0
L a
t a
L b M c
L 3 c
5M 0 L 0 t 0
M
Lt
MðL 2 1
Þðt 2 1
ÞðL a
Þðt 2a
ÞðL b
ÞðM c
ÞðL 2 3 c
Þ 5M 0 L 0 t 0
Separate each variable and relate the exponents:
M :
1
1 c 5
0
L : 2
1
1a1 b2
3 c 5
0
t : 2
1
2 a5
0
From the mass equation,
c52
1
From the time equation,
a52
1
From the length equation,
b5
3
ð2
1
Þ 1
1
1
1
52
1
Therefore, the second
Π
group is
μ
ρvd
Π 2 5
Π
From these two
groups, we can state that
Π 1 5 fðΠ 2 Þ
F
v 2 d 2
μ
ρvd
ρ 5 f
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