Studies on water movements and sediments in Southern Lake Michigan : part 1[-3] ... / by John C. Ayers.

conditions is about 1.7 x 106 cfs which, divided into the 460 x
lo10 llcubic foot volume of the southern basin, gives 271 x 105
seconds or 314 days to bring in a volume of water equal to the
volume of the southern basin.
Continuity would require under these conditions that 1/314th
of the basin volume be discharged from the basin per day, an exchange ratio of 0.0032 per day. This maximum exchange ratio is
used in the "die-away" equation.-0032x
Vt = Ve0032
where the subscripts o and t mean "original" and "at time"
and x is number of days.
Considering flushing-out to be complete when 99% of the
original basin water-content has been removed gives
Vt = 0.01 = e*0032x
in 0.01 = -.0032x
-4.60517 = -.0032x
x = 1439 days or 3.9 years
Minimum net transport over the sill, found in this study,
was 3,800 m3/sec or 0.13 x 10 cfs. Combined with river inputs
this gives 0.14 x 106 cfs total input. Dividing the basin volume
by total input gives 3286 x 105 seconds or 3803 days to supply a
volume of water equal to the basin content.
Volume-content balance requires under these conditions, the
discharge of l/3803th of basin volume per day or an exchange
ratio of 0.00026 per day. With this minimum exchange ratio the
die-away equation gives

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