The Calfhead stream (flow rate 0.05m3s-1) discharges into the Oxhead river (flow

Question

The Calfhead stream (flow rate 0.05m3s-1) discharges into the Oxhead river (flow of 3.00 m3.s-1). It is proposed to discharge waste into the Calfhead stream but the EPA requires a stream mixing study be undertaken. A bromide tracer (conservative and not occurring naturally in either stream ) will be introduced into Calfhead stream. The detection limit for bromide is 1 mg.L-1. Calculate how much tracer must be introduced into Calfhead stream so that a detectable concentration is measured in Oxhead river downstream of their junction assuming complete mixing has occurred.

Explanation / Answer

Let us denote the discharge of Calfhead stream by q and Oxhead river by Q. Let the concentration of tracer to be introduced is c. The detectable limit is 1 mg/L so let us assume that this is the concentration of the tracer downstream.

Now,

c*q=1mg/L*(q+Q) Here we have conserved the quantity of tracer.

c*0.05=1mg/L*3.05

Hence,

c=61mg/L (Answer)

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