3. We consider a polluted lake, estimated by a rectangular shape of length 12 and constant...

 

Transcribed Image Text:

3. We consider a polluted lake, estimated by a rectangular shape of length 12 and constant cross-sectional area A, as illustrated in Figure 12.4 of the textbook. Under the following assumptions (i)-(vi) (i) The volume V is constant. (ii) An unidirectional flow of fresh water is entering the lake and flowing to its exit at a constant rate F m³/s. (iii) The concentration of pollutant depends only on r (horizontal distance from the entry point of the fresh water) and time t, C(x, t). (iv) Pollution travels through the lake only by water flow, that is, by advection. (v) The initial concentration of pollutant in the lake is C(r, 0) = sin² r. (vi) F/A= v= 1. (a) Calculate which is the equation in t whose solution gives the time required to reduce the pollution concentration in the lake to 10% of the initial one. (b) Generate a plot that allow you to estimate the solution of the equation in (a). (c) Using the plot generated in (b) give a numerical estimation for the time required to reduce the pollution concentration in the lake to 10% of the initial one. 3. We consider a polluted lake, estimated by a rectangular shape of length 12 and constant cross-sectional area A, as illustrated in Figure 12.4 of the textbook. Under the following assumptions (i)-(vi) (i) The volume V is constant. (ii) An unidirectional flow of fresh water is entering the lake and flowing to its exit at a constant rate F m³/s. (iii) The concentration of pollutant depends only on r (horizontal distance from the entry point of the fresh water) and time t, C(x, t). (iv) Pollution travels through the lake only by water flow, that is, by advection. (v) The initial concentration of pollutant in the lake is C(r, 0) = sin² r. (vi) F/A= v= 1. (a) Calculate which is the equation in t whose solution gives the time required to reduce the pollution concentration in the lake to 10% of the initial one. (b) Generate a plot that allow you to estimate the solution of the equation in (a). (c) Using the plot generated in (b) give a numerical estimation for the time required to reduce the pollution concentration in the lake to 10% of the initial one.