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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