Question

A plant grows in a lake with a volume of 1.75x10^11 m^3 at a rate of 1x10^-6s^-1. A stream flows into and out of the river at 14 m^3/s. There isnt any growth upstream of the lake. if the concerntration of the plant is around 4 mg/L, how long will it take to reach 50 mg/L?

Answer 1

A plant grows in a lake with Volume V = 1.75*10^-11 m3

Plant growth rate r = 1*10^-6 s-1

A stream flows in and out of the river at 14m3/s.

But here given there is no growth upstream of the lake means inlet stream having no growth .

Initial Concentration of the plant Cao = 4 mg/L

We want to find the time required for achieving concentration 50 mg/L.

By using growth rate formula for any substance first order, if treated as pfr.

Ca = Cao*exp(r*t)

50= 4*exp(1*10^-6*t)

12.5 = exp(1*10^-6*t)

Taking both side logarithmic,

ln12.5 = 1*10^-6 * t

t = 2525728 sec * (1hr/3600s) = 701.6hr

t = 701.6 hr

time required to increase concentration 50 mg/L .