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written 8.2 years ago by |

The Streeter-Phelps equation is used in the study of water pollution as a water quality modeling tool. The model describes how dissolved oxygen decreases in a river or stream along a certain distance by degradation of biomedical oxygen demand (BOD).

The equation was derived by H.W. Streeter, a sanitary engineer and Earle B. Phelps. The equation is also known as the DO sag equation.

The Streeter-Phelps equation determines the relation between the dissolved oxygen concentration and the biological oxygen demand over time and is a solution to the linear first order differential equation.

$dD/dt = k_1L_t – k_2D$

This differential equation states that the total change in oxygen deficit (D) is equal to the difference between the two rates of deoxygenation and reaeration at any time.

The Streeter-Phelps equation, assuming a plug-flow stream at steady state is then given as

$D = K_1L_a/k_2 – k_1 × (e - k_1t - e - k_2t) + D_ae - k_2t$

Where - D is the saturation deficit, which can be derived from the dissolved oxygen concentration at saturation minus the actual dissolved oxygen concentration.

$K_1$ is the deoxygenation rate usually in d-1

$K_2$ is the reaeration rate usually in d-1

$L_a$ is the initial oxygen demand of organic matter in the water also called the ultimate BOD

$L_t$ is the oxygen demand remaining at time t.

T is the elapsed time usually d.