# Dissolved Oxygen Concentration Calculator

To find out the saturation deficit (D) by using Streeter-Phelps equations.

## Streeter-Phelps Equation Calculator works

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.This is due to the shape of the graph of the DO over time.

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.

*∂*D*t*_{1}L_{t} - k_{2}D

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 = _{1} L_{a}_{2} - k_{1}^{-k1t} - e^{-k2t}) + D_{a}e^{-k2t}

**where,**

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

D = DO_{sat} - DO.

D has the dimensions ^{3}

k_{1} is the deoxygenation rate, usually in days^{-1}.

k_{2} is the reaeration rate, usually in days^{-1}.

L_{a} is the initial oxygen demand of organic matter in the water, also called the ultimate BOD (BOD at time t=infinity). The unit of L_{a} is ^{3}

L_{t} is the oxygen demand remaining at time t, L_{t} = L_{a}e^{-k1t}.

D_{a} is the initial oxygen deficit ^{3}

t is the elapsed time, usually [d].

k_{1} lies typically within the range 0.05 to 0.5 days^{-1} and k_{2} lies typically within the range 0.4 to 1.5 days^{-1}.