16m 12 m 20 m D2 D3 2.4 m³/s D₁ 0.8 m³/s B 0.6 m³/s 1.0 m³/s FIGURE 8-16 Air duct in Prob. 8.9. 8.9. Determine the diameters of the circular air duct in the duct system shown schematically in Fig. 8-16 so that the drop in static pressure between points A and B will be a minimum. Further information Quantity of sheet metal available for the system, 60 m² Pressure drop in a section of straight duct, f(L/D)(V/2)p. Use a constant friction factor f 0.02. Air density p, 1.2 kg/m³. Neglect the influence of changes in velocity pressure. Neglect the pressure drop in the straight-through section past an outlet. (a) Set up the objective function and constraint(s) in terms of D1, D2, and D3. (b) Using the method of Lagrange multipliers for constrained optimiza- tion, determine the optimal values of the dimensions and the minimum cost. Ans.: D = 0.468 m. 8.10. Load dienatal