Oakridge Eco-Park has a complex water system that maintains equilibrium between three interconnected reservoirs: A, B, and C. The system works as follows:
The park rangers want to ensure the system remains in equilibrium, where the amount of water entering each reservoir equals the amount leaving.
Initial volumes:
Reservoir A: 2000 liters
Reservoir B: 1500 liters
Reservoir C: 1000 liters
Questions:
1. Water flowing out after one hour:
A to B: 20% of 2000 = 400 liters
B to C: 30% of 1500 = 450 liters
C evaporation: 150 liters
2. The system is not in equilibrium because:
A: Input (500L) > Output (400L)
B: Input (400L) < Output (450L)
C: Input (450L) > Output (150L)
3. Equilibrium volumes:
Let a, b, c be the equilibrium volumes for A, B, C respectively.
A: 500 = 0.2a
a = 2500 liters
B: 0.2a = 0.3b
500 = 0.3b
b = 1666.67 liters
C: 0.3b = 150
500 = 150
c = 1666.67 liters
4. Time for A to reach equilibrium:
Using the exponential approach formula:
t = -ln(0.01) / 0.2 ≈ 23.03 hours
5. Flow rate from C to A for equilibrium:
To maintain equilibrium, the flow from C to A should equal the net inflow to C:
Flow C to A = 500 – 150 = 350 liters per hour
6. New equilibrium with 20% less rainwater:
New input to A: 400 liters/hour
A: 400 = 0.2a
a = 2000 liters
B: 0.2a = 0.3b
400 = 0.3b
b = 1333.33 liters
C: 0.3b = 150
400 = 150
c = 1333.33 liters
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