As illustrated in Video V7.9, 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, rho, the difference in densities between the air and the stack gas, rho - rho_s, the acceleration of gravity, g, the kinematic viscosity of the stack gas, V_s, and the stack diameter, D. (A) Find 4 pi groups for modeling the pollutant source and choose the correct answer below. a) pi_1 = V/v_s, pi_2 = VD/U, pi_3 = V/gD, pi_4 = rho - rho_s/rho b) pi_1 = D/U, pi_2 = Vg/v_s, pi_3 = v_s/rhoD, pi_4 = v_s/rho - rho_s c) pi_1 = V/U, pi_2 = VD/v_s, pi_3 = V^2/gD, pi_4 = rho - rho_s/rho d) pi_1 = U/V, pi_2 = V/v_sD, pi_3 = V^2/g, pi_4 = rho - rho_s/v_s (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?