The figure below shows the expected in$-$stream concentration profile of a pollutant

caused by a distributed load. The load has to be distributed over a certain length, L$,$ so

that $80\%$ of the mass input is destroyed over that length. The pollutant undergoes a first$-$

order decay process, of rate constant $K.$ The flow rate of the river is $Q_{{?}_{?}}$ and its area of cross

section is $A.$

Prove that $,L=\frac{5Q}{AK}$

Hints:

$20\%of{W}_{in}=Q_2{C}_2$

$W_{in}=S_{D}AL$

$C_2=\frac{S_D}{K}$