Page 37 - Aeronautical Engineer Data Book

24 Aeronautical Engineer’s Data Book
Table 2.12 Dimensional analysis quantities
Quantity Dimensions

Mass (m)
M
Length (l)
L
Time (t)
T
Area (a)
L 2
Volume (V)
L 3
First moment of area
L 3
Second moment of area
L 4
Velocity (v)
LT –1
Acceleration (a)
LT –2
Angular velocity (1)
T –1
Angular acceleration ( )
T –2
Frequency (f)
T –1
Force (F)
MLT –2
–1
Stress {pressure}, (S{P})
ML T –2
2
Torque (T)
ML T –2
–1
Modulus of elasticity (E)
ML T –2
2
Work (W)
ML T –2
2
Power (P)
ML T –3
Density (#)
ML –3
–1
Dynamic viscosity (µ)
ML T –1
2
Kinematic viscosity ( )
L T –1
Hence velocity is called a secondary quantity
because it can be expressed in terms of primary
quantities.
2.7.3 An example of deriving formulae using DA
To find the frequencies (n) of eddies behind a
cylinder situated in a free stream of fluid, we
can assume that n is related in some way to the
diameter (d) of the cylinder, the speed (V) of
the fluid stream, the fluid density (#) and the
kinematic viscosity ( ) of the fluid.
i.e. n = +{d,V,#, }
Introducing a numerical constant Y and some
possible exponentials gives:
d
a
b
c
n = Y{d ,V ,# , }
Y is a dimensionless constant so, in dimensional
analysis terms, this equation becomes, after
substituting primary dimensions: