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).