EGN 3353C Fluid Mechanics
Lou Cattafesta
MAE Dept.
University of Florida
Chapter 7:
DIMENSIONAL ANALYSIS AND MODELING
Lecture 23
±
dimension
Æ
measure of a physical quantity without numerical values (e.g., length)
±
unit
Æ
assigns a number to that dimension (e.g., meter)
±
7
fundamental dimensions from which all other secondary dimensions can be expressed in terms of
o
Fluid dynamics usually just concerned with m, L, t, and T.
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View Full DocumentEGN 3353C Fluid Mechanics
Lou Cattafesta
MAE Dept.
University of Florida
Example
:
Write the dimensions of electrical voltage in terms of primary dimensions.
[] []
2
1
2 3 1
force velocity
Power = Voltage×Current
Vo
Power
Current = mLt Lt
I=
ltage
mtI
=
L
⋅
⎡⎤
⎢⎥
⎣⎦
±²³
±
Law of Dimensional Homogeneity
Æ
Every additive term in an equation must have the same dimensions
o
Each term must also have the same units
o
Recommendation
:
Write out all units when performing calculations in order to avoid errors.
Example
:
Various Forms of Bernoulli’s Equation
1.
N
N
N
2
static
hydrostatic
total
pressure
pressure
pressure
q = dynamic
pressure
1
2
t
p
Vg
z
P
ρρ
++
=
Æ
total pressure form
Æ
each term has primary dimensions of
[ ]
[ ]
2
2
1 2
mL
P = Forc
tL
=
m
L
eA
re
t
a=
Æ
each term must have the same units (e.g., Pa)
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 Spring '07
 Lear
 Fluid Dynamics, Fluid Mechanics, 3353C Fluid Mechanics, EGN 3353C Fluid, MAE dept, Lou Cattafesta

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