In problem 16.3 a spreadsheet approach was demonstrated for solving the problem of calculating the time variation of concentration in a lake with variable inflow and outflow conditions. However, it...

In problem 16.3 a spreadsheet approach was demonstrated for solving the problem of calculating the time variation of concentration in a lake with variable inflow and outflow conditions. However, it may be noticed that in March, the concentration at the end of the month is calculated to be greater than either the concentration at the beginning of the month or the inflow concentration. What is the problem? Develop a modified approach that resolves this problem.

problem 16.3

Consider a small lake with one inflow and one outflow, as sketched in Fig. 16.10. The inflow and outflow rates are not necessarily equal, nor are they constant. The average inflow and outflow rates on a monthly basis, along with the average monthly inflow concentration of a contaminant of interest, are shown in the first three columns of the spreadsheet below. Values for Q are in m3/s and C is in mg/L. If the contaminant decays with rate 0.05 day1 and the concentration in the lake is 35 mg/L on January 1, calculate the concentration at the end of the year. The lake volume on January 1 is 10⁸
m³. Assume fully mixed conditions and no other sources or sinks.