Aerobic pond is used as a secondary wastewater treatment operation for small communities. the pond is usually shallow enough so that it can be assumed as a well-mixed aerobic reactor. the inflow rate of wastewater entering a 200m^3-aerobic pond is 50 m^3/d and has a substrate (so) concentration of 95 mg bod5/l. the microbe concentration (xo) in the influent is small and can be neglected. the microbial growth and substrate consumption in the pond can be described by the monod equations:
a. assuming the pond is in steady state, write mass balance equation for the microorganism concentration (x) and solve the equation to derive an expression for the substrate (s) concentration as a function of the hydraulic detention time. calculate s using the equation you derived. (ks=60 mgbod5/l, y=0.6 mg vss/mg bod5, k_d=0.06 day-1, mu_m=3 day-1)
b. write the mass balance equation for the substrate in the pond and solve it for the microbe concentration (x) as a function of the substrate concentration and hydraulic detention time. calculate x using the equation you derived.