Streeter-Phelps equation for DO sag:

Oxygen Deficit = Ss - O

in which:

Ss = dissolved oxygen concentration at saturation, a function of temperature, salinity, and atmospheric pressure (mg/L);

O = dissolved oxygen concentration (mg/L).

Streeter-Phelps equation:

Ss - O = [kd/(ko - kd)] Du [e-(kd/v)x - e-(ko/v)x] + (Ss - O0) e-(ko/v)x

O = dissolved oxygen concentration (mg/L) at distance x (m);

O0 = dissolved oxygen concentration immediately downstream of effluent discharge (mg/L);

Thus:

O = Ss - [kd/(ko - kd)] Du [e-(kd/v)x - e-(ko/v)x] - (Ss - O0) e-(ko/v)x

Other variables as the same as in DO sag equation.

(Note that the Streeter-Phelps equation is undefined for ko = kd).