Determination of eddy diffusivity (Figs. 18C.1 and 21A.1), in Problem 18C.1 we gave the formula for the concentration profiles in diffusion from a point source in a moving stream. In isotropic highly turbulent flow, Eq. 18C.1-2 may be modified by replacing D_AB by the eddy diffusivity D ^(t) _AB) this equation has been found to be useful for determining the eddy diffusivity. 

(a) Show that if one plots SC_A versus s – z the slope is –v₀/2D ^(t)_AB. 

(b) Use the data on the diffusion of CO₂ from a point source in a turbulent air stream shown in Fig. 21A.1 to get D^(t)_AB for these conditions: pipe diameter, 15.24 cm; v₀ = 1512 cm/s. 

(c) Compare the value of D ^(t)_AB with the molecular diffusivity D_AB for the system CO₂-air. 

(d) List all assumptions made in the calculations.