First, the oxygen saturation OS for each segment is estimated as a function of water temperature T,
Eqn. 4
and an analytical solution of the classic Streeter-Phelps model is used to compute oxygen concentrations from point source loads of BOD.
Eqn. 5
where kd=0.4; ka = 0.95; and kr = 0.4 are the decomposition, the reaction, and the re-aeration rates, respectively (1/day). L is the reach length (m), U the velocity of the water in the reach. is the oxygen concentration (mg/l) at the top of the reach and is the concentration of the pollutant loading (mg/l) at the top of the reach.
BOD removal is given as,
Eqn. 6
The removal rate, krBOD, is influenced by several factors, including temperature, settling velocity of the particles, and water depth. Chapra (1997) provides an expression for krBOD as,
Eqn. 7
where T is the water temperature (in degrees Celsius), H is the depth of the water, and is the settling velocity. In addition, is defined (at a reference temperature of 20 degrees Celsius) as,