Consider the University lake system in Baton Rouge, Louisiana, which has a poten

Question

Consider the University lake system in Baton Rouge, Louisiana, which has a potential water quality problem resulting from waste discharged into the nearby Crest Lake. From the following data determine what nutrient level (phosphorus) is to be expected at steady state in the Crest Lake, which is a completely mixed unstratified system. Surface area: 3.4 times 10_4 m2 Mean settling velocity: 10 my Mean detention time: 561 d Phosphorus concentration in the waste: 10 mg/L. Assume no losses due to volatilisation or other reactions of P in the lake. What reduction in discharge level should be accomplished so that the P concentration a reduced to

Explanation / Answer

Phosphorus concentration in the waste = 10mg/L

Mean depth of lake(Dm)=1.5m

Surface area of lake=34000 m2

Mean detention time=561 days=1.537 year

Mean settling velocity= 10m/y

Now

Total settling time=1.5/10=0.15year

Annual phosphorous loading Pa (mg/m2/year) =

(Phosphorous concentration in waste*1000/total settling time)/area of lake

= (10000/0.15)/34000

= 1.96078mg/m2/year

Remaining phosphorous concentration in the lake =

= (Pa*Dt/Dm)*(1/(1+0.824*Dt^0.454))

= (1.96078*1.537/1.5)*(1/(1+0.824*1.537^0.454))

= 1.00379

Phosphorous concentration to be reduced in inlet =1.00379-0.2=0.80379mg/l

Now again

C1/C0= e^-t(Q/V)

V=34000*1.5=51000

T=561 =1.537years

= 0.2/10=0.2150*(Q/51000)

= Q=4744.18

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