Perform a dimensional analysis of the smoke plume rising out of a smokestack. The relevant physical parameters are the smoke mass flow rate, m, the smoke density, ρ_s, the ambient air density, ρ_a, the gravitational acceleration, g, the diameter of the smokestack, D, and the height of the smokestack, h. Choose D, ρ_a and g as the repeating parameters. Determine a set of dimensionless groups that describe this problem and apply the Buckingham Pi Theorem to express the dimensionless mass flow rate as a function of the other groups.

Contributed by Stavros Tavoularis, Department of Mechanical Engineering, University of Ottawa, Ottawa, Canada. Image from Ethical Corporation.