Work out dissolved oxygen sag instantly with clear inputs, formula shown and shareable results.
The Streeter-Phelps model balances deoxygenation from BOD decay against reaeration from the atmosphere, producing a dissolved oxygen sag curve. The critical point, where oxygen is lowest, occurs where the two rates are equal. The self-purification ratio kr/kd indicates how quickly a river recovers; below 1 the sag is deep and prolonged.
Streeter-Phelps deficit
D(t) = kd L0 / (kr - kd) x (e^(-kd t) - e^(-kr t)) + D0 e^(-kr t)
Critical time
t_c = 1/(kr - kd) x ln(kr/kd x (1 - D0 (kr - kd) / (kd L0)))
Dissolved oxygen is a statutory water quality standard protecting aquatic life. Modelling for consent purposes must use calibrated rate constants and approved methods.
Salmonids need above 6-7 mg/L, coarse fish above 4-5 mg/L, and below about 3 mg/L most fish suffer or die. Consent conditions are set to protect the designated use of the water body.
Turbulence, depth and temperature. A shallow, fast, rocky reach reaerates many times faster than a deep, slow, impounded one, which is why impoundments worsen oxygen sag.