Given: As a consulting engineer you are tasked with estimating the amount of ele

Question

Given: As a consulting engineer you are tasked with estimating the amount of elemental lead (Pb) that a company emits into a lake. By carefully studying Pb sources to the lake you have found that besides the factory emissions of Pb directly into the lake the other important mass balance factors are a river that flows into the lake, a river that flows out of the lake, and deposition of Pb to the lake sediments. Based on your estimates: The lake has dimensions of 10 km x 5 km x 30 m. The inlet and outlet rivers are 100m wide and 10 m deep with flow velocities of 1 m s-1. The steady-state Pb concentration in the lake is 100 ng L-1 and the Pb concentration in the inlet stream is 10 ng L-1. Also, Pb deposits into the lake sediments with a first order decay rate of k = 10 day-1. Find: (a) Derive the mass balance equation for the lake with all important variables included (note: you can give your answer in terms of dC/dt =

Explanation / Answer

a)VdC/dt = 100*10*1*10^-9 - 100*10*1*C - 10*VC/(24*3600)

where V = 10000*5000*30 = 1.5 * 10^8

at steady state dC/dt = 0 and C = 100*10^-9 kg/m^3

Mass emmision rate = kVC = 10*1.5*10^8*100*10^-9 = 150 kg/day

Related Questions

Navigate

• Browse (All)
• Browse G
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.