When two streams or rivers merge or water is discharged to a stream it is possible to determine the BOD and DO after mixing assuming steady state conditions and instantaneous mixing.  The two streams are considered as dilutions of each other thus the initial BOD and DO will be 
and
where
* is the initial concentration of BOD in the river downstream of the mixing, also called BOD(0). The unit of  is .
* is the background BOD of the concentration in the river .
* is the BOD of the content of the merging river .
* is the initial concentration of the dissolved oxygen in the river downstream of the conjoining point .
* is the background concentration of the dissolved oxygen content in the river .
* is the background concentration of the dissolved oxygen content in the merging river .
* is the flow in the river upstream from the mixing point .
* is the flow in the merging river upstream from the mixing point .