Your municipality withdraws 10,000 gallons per day from an aquifer that originally held 1,000,000 gallons. The recharge rate to the aquifer is 2,000 gallons per day.
Determine how long it will take before the aquifer is depleted
it loses 8000 gal/day
1000000/8000 = 125 days
To determine how long it will take before the aquifer is depleted, we need to calculate the net change in the aquifer's volume per day.
The net change in the aquifer's volume per day can be calculated by subtracting the withdrawal rate from the recharge rate:
Net change = Recharge rate - Withdrawal rate
In this case, the recharge rate is 2,000 gallons per day, and the withdrawal rate is 10,000 gallons per day. Hence,
Net change = 2,000 - 10,000 = -8,000 gallons per day
The negative sign indicates a decrease in the aquifer's volume.
To find the time it takes to deplete the aquifer, we divide the initial volume of the aquifer by the net change per day:
Time = Initial volume / Net change
The initial volume is given as 1,000,000 gallons. Substituting in the values, we have:
Time = 1,000,000 / -8,000
Simplifying:
Time ≈ -125 days
The negative sign indicates that the aquifer will be depleted in approximately 125 days if the current rate of withdrawal continues, which may not be physically possible. However, it's important to note that this calculation assumes constant rates of withdrawal and recharge, and it does not take into account other factors that may affect the aquifer's depletion, such as seasonal variations or changes in land usage.