Final answer:
The question addresses the concepts of fluid dynamics, requiring an understanding of flow rates, the continuity equation, and Bernoulli's principle to solve practical problems like filling a swimming pool with water from different sources.
Step-by-step explanation:
The question presented relates to the principles of fluid dynamics, especially the continuous flow of water through a hose and how the water level in a pond increases due to this constant addition. To answer the question about the rate at which water is added to the pond, we can use the concepts of the continuity equation, Bernoulli's Equation, and the behavior of fluids flowing through different-sized nozzles.
Example Calculations
a) To estimate the time to fill a private swimming pool with a capacity of 80,000 liters using a garden hose delivering 60 liters per minute, divide the total volume of the pool by the rate of flow. This gives you 80,000 L / 60 L/min = 1333.33 minutes, or approximately 22.22 hours.
b) To determine how long it would take to fill the same pool if you could divert a river flowing at 5000 cubic meters per second, convert the pool volume to cubic meters (80,000 L = 80 cubic meters), then divide by the river flow rate. This gives you 80 m³ / 5000 m³/s, which results in 0.016 seconds.