Many rivers are burdened with tributary streams of warm water and/or liquid wastes containing dissolved or suspended matter. The warm water and waste matter mix thoroughly with the river water some distance downstream from the point of entry of the tributary, but near the point of entry there may be high local temperatures or concentrations of waste. It is often necessary to know the local temperatures or concentrations of waste. The authors have used a formula for computing the turbulent mixing that takes place in such a situation; this formula fits quite well in the case of one Southern river.