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Example
Consider pressure drop in a tube of length  , hydraulic diameter d, surface roughness Î, with fluid of density ρ and
viscosity μ moving with average velocity ν
This can be expressed as
f (DP, U, d, , Î, ρ, μ) = 0
Now m=7 since the phenomenon involves 7 independent parameters.
We select ρ, U, d as repeating variables (so that all 3 dimensions are represented)
Now 4 π (7 - 3) parameters are determined as
Now basic units
All Π parameters ® M0 L0 T0
The above four equations yield
a1= -1; b1 = - 2; c1= 0
a2= -1; b2 = - 1; c2= -1
a3= 0; b3 = 0; c3= -1
a4= 0; b4 = 0; c4= -1
Thus writing 
implies 
Therefore, 
 is called relative roughness
Similarly, other sets of Π parameters can be chosen to describe the phenomena. Thus though it does not give the actual relationship, but it puts the data in a compact form
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