Distributed Nonconservative Sources Effects on Water Quality
Streams are often subjected to sources or sinks of a substance which are distributed along the length of the stream. A good example of a distributed source is when a river runs along a farm. The fields act as a distributed source as the runoff brings animal wastes into the stream along the total area. A mass balance equation at steady state with reasonably constant parameters is:

where:

U = velocity, fps
s = Concentration
K = Decay rate
SD = Distributed Source

The distributed source can be external or internal. An example of an external sourse is, again, a farm and can be represented by:

where:
W = Mass per foot of stream bank as a function of time
A = Area

For an internal source, sush as sediment oxygen demands (SB, Benthic uptake) the equation is as follows:

The solution is then:

Where the boundary conditions of s = 0 at x = 0 has been assumed.