Question

Mixing in a big tank As a result of the discharge of untreated sewage from upstream sewage works and of rural and urban runoff, particularly during summer rainstorms, the mean bacterial faecal coliform count in Lake Burley Griffin in 1974 was approximately 107 m−3 , well above the safe level of 4 × 106 m−3 . The volume of the lake is approximately 26 × 106 m3 . With only fresh (i.e. bacteria-free) water entering the lake at a rate of 4 × 106 m3 per month, how long would it take for the coliform count to drop to a safe level?

Answer 1

So the mean bacterial faecal coliform count in Lake Burley Griffin in 1974 was approximately .

The volume of the lake is approximately   =  

The volume of fresh water entering the lake per month =   =  

Safe level of bacterial faecal coliform count =

So the safe level for a volume of   of the lake is    of bacterial faecal coliform count.

but now it is  .

So total bacteria count now= =  .

Now keeping the bacteria count at , we increase the amount of fresh water in the lake at the rate of

per month to find out how long

it takes to get to the safe level that is .

  

so assuming the the lake reaches safe level after x months, then :