A factory discharges its waste into a river upstream from a lake. The discharge release rate is 2 kg formaldehyde per day. The decay is a first order process with a decay rate of 0.000005/s. The waste is discharge into the river 30 km upstream from the lake through an effective diffuser. The river flow velocity is 6 km/d. The volumetric flow rate for the river is 106 m3/d. the lake has dimensions of 4,000 m long by 600 m wide by 8 m deep. (Total Volume is 1.92 x 107 m3). There is an outlet stream from the lake with a flow rate of 106 m3/d.
Estimate the formaldehyde concentration in the lake using the plug flow model for the river and the completely mixed model for the lake.