P6.3.4** Determine the process gain and the time constant for the dissolved oxygen process shown in Figure P6.3.4 based on the following process model and initial conditions assuming that the air flow rate (Fair) is the input variable. dC. 02 = =k, a(C, -C.,)-Ko, H max * o - O2 02 dt Cor ka=0.25 +0.001(F. -500) - concentration of O2 in the reaction broth (initially 1.1x104 g-moles/1) C, - saturated concentration of O2 in the broth (2.20x10* g-moles/1) K - cellular uptake of O2 (1.98 g-moles O/g-cells) ka - the overall , liquid phase mass transfer coefficient for transport from the bubble surface to the bulk broth (initially 0.25 s) 02 T - broth temperature (35C) x - constant cell concentration in the bioreactor (0.25 g/1) Hmax - maximum specific growth rate (5.56x10s -5 -1 55') Fair - air feed rate (initially 500 cfm) (F ir over ( Air Variable Speed Air Compressor Figure P6.3.4 Schematic of a DO process