EGM 6812, F11, University of Florida, M. Sheplak
1/16
Section 6, Dimensional Analysis
6 Dimensional Analysis and Similarity
Why?
1.
Reduced number of experiments
2.
Compact data representation
3.
Solve problem fewer times
4.
Lab prototype to full scale
5.
If we non-dimensionalize the governing equations, we can “simplify” the equations by
neglecting certain terms.
Example
Investigate drag on a sphere, with roughness
(i.e. golf ball, high speed)
, , , , ,
DD
F
F
D
u
c
If we investigate 10 iterations of each parameter, we would have to conduct
6
10 experiments.
Instead perform a non-dimensionalization.
6.1 Buckingham
-theorem
Answer-
22
Roughness
Re
,,
1
2
D
D
Ma
C
F
uD u
f
cD
uD
Step 1.
List all variables
, , , , ,
F
F
D
u
c
7
n
Step 2.
Select the primary dimensions
M,L,t
3
r
Step 3.
List dimensions of each parameter
Parameter
F
D
c
u
Dimension ML
t
2
L
L
M
L
3
M
Lt
L
t
L
t
Step 4.
Select “r” repeating parameters (engineering judgment call!)
Don’t choose:
, ,
,
D
Fc
non-repeaters