- #1

582153236

- 14

- 0

## Homework Statement

In buckingham pi theorem, you have p=n-k dimensionless groups (π

_{1}, π

_{2},...)

where n=number of total variables and k=number of total units among the variables

For example, let's say we want to relate:

ρ~m/L

^{3}(density)

μ~m/L*t (viscosity)

v~L/t (velocity)

d~L (distance)

D

_{a}~L

^{2}/t (diffusivity)

k~L/t (mass transfer coefficient)

In this case, n=6, k=3 (m, L, t) so we have 3 non dimensional groups.

In the solution to this problem, 3 common variables are chosen, D

_{a}, ρ, d, such that:

π

_{1}=D

_{a}

^{a}ρ

^{b}d

^{c}k

π

_{2}=D

_{a}

^{d}ρ

^{e}d

^{f}v

π

_{3}=D

_{a}

^{g}ρ

^{h}d

^{i}μ

So in this case, D

_{a}, ρ and d are chosen as the common variables among all groups. I am wondering why these three variables were chosen specifically. Can a different combination of variables be chosen to achieve the correct answer? Also, were three variables chosen because there are three units?