Question

Lake Erie has a water volume of about 450 km³ and a flow rate (in and out) of about 175 km² year. If at some instant the lake has pollution concentration p = 0.04%, how long, approximately, will it take to decrease it to p/2, assuming that the inflow is much cleaner, say, it has pollution concentration p/4, and the mixture is uniform (an assumption that is only imperfectly true)?

Answer 1

To find the time it takes to decrease the pollution concentration in Lake Erie, we need to use the concept of mass balance and the given inflow and outflow rates.

Step-by-step explanation:

To answer this question, we need to use the concept of mass balance and assume that the inflow and outflow rates are constant.

Let's denote the time it takes to decrease the pollution concentration to p/2 as t. Since the pollution concentration is decreasing, we can write an equation using the mass balance:

Initial pollution mass = Final pollution mass

Initial pollution mass = (Initial pollution concentration) × (Lake volume)

Final pollution mass = (Final pollution concentration) × (Lake volume)

Since the inflow rate is p/4 and the outflow rate is 175 km²/year, the rate at which the pollution concentration decreases is:

(Inflow rate) - (Outflow rate) = (Change in pollution concentration) × (Lake area)

Substituting the given values and solving the equation will give us the time, t.