The Streeter-Phelps model can be used to compute the dissolved oxygen concentration in a r...

The Streeter-Phelps model can be used to compute the dissolved oxygen concentration in a river below a point discharge of sewage (Fig. P7.31),

 (P7.31)

where o = dissolved oxygen concentration (mg/L), o_s = oxygen saturation concentration (mg/L), t = travel time (d), L_o = biochemical oxygen demand (BOD) concentration at the mixing point (mg/L), k_d = rate of decomposition of BOD (d⁻¹), k_s = rate of settling of BOD (d⁻¹), k_a = reaeration rate (d⁻¹), and S_b = sediment oxygen demand (mg/L/d).

As indicated in Fig. P7.31, Eq. (P7.31) produces an oxygen “sag” that reaches a critical minimum level o_c, some travel time t_c below the point discharge. This point is called “critical” because it represents the location where biota that depend on oxygen (like fish) would be the most stressed. Develop a MATLAB script that (a) generates a plots of the function versus travel time and (b) uses fminbnd to determine the critical travel time and concentration, given the following values:

FIGURE P7.31: A dissolved oxygen “sag” below a point discharge ofsewage into a river.