The half-life is the time it takes for half the difference in levels to be wiped
out.
That is...
Substituting from equation 31 with t=0 and
...
The difference in the initial levels cancels, and we can solve for ...
Time to reach half the initial level difference.
Equation (34) makes explicit the relationship between the settling time of the lake, the area of the lake, the relaxation time and the channel cross-section.