Dimensional Analysis
- Primary dimensions M(mass), L(length), t(time), and T(temperature).
Example: to describe the dimension of density r, we need M and L
[r]=[M/L3], [Dp]=[F/A]=[ma/A]=[ML/t2/L2]=[M/(Lt2)]
Similarly, [m]=[M/(Lt)], [V]=[L/t], [L]=[L], D=[L] See steps 2 & 3 in p. 301
Therefore, there are a total of three (3) primary dimensions involved: M, L, and t. We should be able to reduce the total number of the dimensional parameters to (6-3)=3.
- Now, we need to select a set of dimensional parameters that collectively they includes all the primary dimensions. We will select three since we have three primary dimensions involved in the problem. See step 4 in p. 301
Special notes: do not include m into this set since it is usually less important compared to other parameters such as r (density), V(velocity) and a length scale.
We will select r, V and D for this example