As illustrated, models are commonly used to study the dispersion of a gaseous pollutant from an exhaust stack located near a building complex. Similarity requirements for the pollutant source involve the following independent variables: the stack gas speed, \(V\), the wind speed, \(U\), the density of the atmospheric air, \(ho\), the difference in densities between the air and the stack gas, \(ho-ho_{s}\), the acceleration of gravity, \(g\), the kinematic viscosity of the stack gas, \(v_{s}\), and the stack diameter, \(D\).

(a) Based on these variables, determine a suitable set of similarity requirements for modeling the pollutant source.

(b) For this type of model a typical length scale might be 1:200. If the same fluids were used in model and prototype, would the similarity requirements be satisfied? Explain and support your answer with the necessary calculations.