A small lake(10^6 sq meters surface area) receives water from a stream flowing a

Question

A small lake(10^6 sq meters surface area) receives water from a stream flowing at 10 cu meters/second. In the lake, P, levels are found to be 0.08 mg/L. There are no other flows into the lake and you can assume that all surface flows into the lake will leave it as surface flow. a. What is the concentration of P in the incoming stream. Assume that V_s = 7.5 meters/year b. Somebody wants to put in a septic tank nearby and the flow of P from that through the drain field to the lake is expected to be 1.0 gram per second. Should this installation be allowed if the lake is to be protected? Your opinion? Calculation?

Explanation / Answer

(a) The concentration of P in an incoming stream will be given as :

using a formula, we have

C = (Q Cin + S) / (Q + vS A)

where, Q = stream flowing rate = 10 m3/s

Cin = concentration of P in an incoming stream flow = 0.08 mg/L = 0.08 g/m3

vS = the P settling rate = 7.5 m/year = 2.3782 x 10-7 m/s

A = surface area of small lake = 1 x 106 m2

then, we get

C = [(10 m3/s) (0.08 g/m3) + (1 g/s)] / [(10 m3/s) + (2.3782 x 10-7 m/s) (1 x 106 m2)]

C = (1.8 g/s) / [(10 m3/s) + (0.23782 m3/s)]

C = (1.8 g/s) / (10.23782 m3/s)

C = 0.175 g/m3

converting g/m3 into mg/L -

C = 0.175 mg/L

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