Solution

The parameter values downstream from the site of the contamination are

> DOvals2 := [kd = 0.4, kr = 2.0, DOo = 6.9, T = 26, BODu = 15.2, Do = 1.2, DOsat = 8.1];

with and computed from Table 5-1 and conservation of DO. The specific formula for the dissolved oxygen is

> DOeqn2 := eval( DOeqn, DOvals2 );

A clear picture of the minimum is obtained by plotting the DO sag curve on a short interval:

> plot( rhs(DOeqn2), t=0..10, title=`DO sag curve (downstream)` );

>

The DO level is lowest after approximately =0.77 days (about 18 hours); the lowest DO level is approximately mg/L. More accurate approximations can be obtained by ``zooming in'' on the minimum or by symbolic computation of the minimum:

> tcrit := solve( diff( rhs(DOeqn2), t ) = 0, {t} );

> eval( DOeqn2, tcrit );

>

Since the stream is moving at km/day, the most severe impact of the pollutant is felt approximately km (a little more than 9 miles) downstream from the spill. At that time the DO level of 5.8 mg/L is still about 50% above the lower limit of 4 mg/L for supporting fishlife -- this spill should not seriously affect the stream's ecosystem.